Initial import: KiCad zone resistance plugin

DC/AC resistance, power dissipation, and via/injection-area currents of
copper zone fills. KiCad 10 IPC-API plugin (kicad-python/kipy):
multi-layer via-coupled FDM solver, multi-part terminals via User.1/User.2
marker layers, pads as contacts, uniform-injection and equipotential
contact models, per-foil skin effect, optional solder/copper buildup on
mask openings. 54-case test suite incl. exact analytic references.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

.gitignore

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+.venv/
+__pycache__/
+*.pyc
+.pytest_cache/

README.md

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+# Fill Resistance — KiCad 10 plugin
+
+Computes the **DC resistance of copper zone fills** between two contacts,
+**single- or multi-layer**: the chosen net's fills on the selected copper
+layers are solved as coupled finite-difference sheets linked by the net's
+**via and through-hole-pad barrels** (18 µm plating, configurable). Shows
+per-layer rasterized maps, potential, current density, and **power
+density**, reports **per-via currents** (via ampacity!) and total
+dissipation at a **selectable test current**. PNGs + a text summary are
+saved per run.
+
+Uses the KiCad **IPC API** (`kicad-python` / `kipy`), not the deprecated
+SWIG API. Requires KiCad **10.0.1+**.
+
+## Setup (one-time)
+
+1. **Enable the API server**: KiCad → Preferences → Plugins → check
+   *Enable KiCad API*.
+2. **Check the interpreter path** on the same page: should be
+   `C:\Program Files\KiCad\10.0\bin\pythonw.exe` (after a 9→10 upgrade it
+   can point at KiCad 9).
+3. **Deploy**:
+   ```powershell
+   powershell -ExecutionPolicy Bypass -File deploy.ps1        # junction (dev)
+   powershell -ExecutionPolicy Bypass -File deploy.ps1 -Mode Copy
+   ```
+4. **Restart KiCad**; first load builds the plugin venv (numpy, scipy,
+   matplotlib, PySide6 — takes minutes; the Ω button appears when done).
+   If stuck: Preferences → Plugins → *Recreate Plugin Environment*.
+
+## Usage
+
+1. Mark the current-injection terminals. Each terminal may have
+   **multiple parts** (all merged into one externally-bonded contact):
+   - **V+ rectangles on `User.1`**, **V− rectangles on `User.2`**
+     (marker layers, configurable via `ELECTRODE_POS_LAYER` /
+     `ELECTRODE_NEG_LAYER`), any number per side, axis-aligned;
+   - **pads** (real copper shape; through-hole pad contacts all layers,
+     SMD pad its own layer) — selected pads fill a side that has no
+     rectangles;
+   - legacy: exactly 2 selected contacts with no marker rectangles still
+     works; empty selection scans the whole board's marker layers.
+2. **Select the contacts**, click the **Fill Resistance** Ω button.
+3. In the **dialog**, pick the net (defaults to the selected pad's net),
+   check the **layers** to include, set each contact's layer scope
+   ("All selected layers" = bolted-lug/through contact), the **test
+   current**, and optionally a grid cell size. Multiple layers are coupled
+   through the net's via/pad barrels automatically.
+4. Read R / voltage drop / total power in the figure titles and status
+   bar. Outputs land in `<board dir>\fill_res_results\<timestamp>\`:
+   per-layer `1_raster_map` / `2_potential` / `3_current_density` /
+   `4_power_density` PNGs, `summary.txt` (incl. the busiest vias with
+   per-via current and dissipation, and the **current through each
+   injection area** — computed flux with the equipotential model,
+   prescribed area share with the uniform model), `geometry_dump.json`.
+
+## Model & limits
+
+- Sheet model per layer: R□ = ρ/t, ρ = 1.68e-8 Ωm (20 °C), t from the
+  board's physical stackup. Layer z-positions from the stackup drive the
+  barrel lengths.
+- Via/pad barrels: thin-wall annulus, R = ρ·L/(π·d·t_plating),
+  `VIA_PLATING_UM = 18` in `fill_resistance/config.py`. Vias are always
+  plated; capped vs uncapped does not change the layer-to-layer DC path
+  (the ≥5 µm cap sits over the hole mouth in parallel with the
+  annular-ring contact, not in series). A barrel passing an antipad
+  bridges the layers above/below with the full barrel length.
+- Tracks and pad copper (other than the selected contacts) are **not**
+  part of the conductor model — zone fills + barrels only.
+- **Solder buildup on mask openings** (dialog checkbox, **off by
+  default**; `INCLUDE_MASK_BUILDUP`): zones drawn on `F.Mask`/`B.Mask`
+  are treated as mask openings that collect `SOLDER_THICKNESS_UM`
+  (50 µm) of solder on the exposed pour, plus an optional user-defined
+  added copper thickness (dialog field, e.g. a soldered busbar/wire).
+  The sheet conductance there becomes t_Cu/ρ_Cu + t_solder/ρ_solder +
+  t_extra/ρ_Cu (SAC305 ρ = 1.32e-7 Ωm: 50 µm solder ≈ 6.4 µm copper);
+  interface faces use harmonic-mean conductances. Buildup areas render
+  tin-gray on the raster map; |J| in them is referenced to the
+  conductance-equivalent copper thickness.
+- **Contact models** (dialog / `CONTACT_MODEL`): default **uniform
+  injection** — a conductor pressed on top feeds the current orthogonally
+  with uniform surface density, so |J| ramps across the contact area
+  (R = ΔV̄/I from area-averaged terminal potentials); or
+  **equipotential** — ideal bonded lug (Dirichlet). The two bracket a
+  real contact: R_equipotential ≤ R_real ≤ R_uniform.
+- Fields are reported at the dialog's test current; power scales with I².
+- **Skin effect (f > 0)**: per-layer effective sheet resistance from the
+  exact 1D foil-diffusion solution `Zs = τρ·coth(τt)`, `τ = (1+j)/δ`
+  (`SKIN_SIDES = 1` in config: plane facing a return plane; `2` =
+  isolated foil), and the analogous correction for the 18 µm barrel wall.
+  Enter one frequency per run (e.g. a switching harmonic, with its RMS
+  amplitude as the test current) — suffixes `k`/`M` accepted.
+  **Caveat:** only through-thickness crowding is modeled. Lateral
+  (proximity-effect) redistribution needs a magneto-quasistatic solver
+  and is not captured — since the resistance-driven distribution is the
+  minimum-dissipation one, AC results are a rigorous **lower bound**.
+  Rule of thumb for 70 µm foil: skin is negligible below ~300 kHz
+  (δ = 173 µm at 142 kHz), ~+11 % at 1 MHz.
+- 5-point FDM per layer on an auto-sized shared grid (~500 k cells total
+  across layers by default). Direct sparse solve up to 700 k unknowns,
+  Jacobi-CG above. Discretization error typically ≲ 2 % at defaults —
+  halve the cell size and compare to judge convergence.
+
+## Offline / development
+
+Every run writes `geometry_dump.json`; re-solve without KiCad:
+
+```powershell
+.venv\Scripts\python.exe -m fill_resistance.standalone dump.json `
+    [--current 40] [--cell-um 50] [--layers F.Cu,In1.Cu] [--no-show] `
+    [--out DIR] [--force-iterative]
+```
+
+Dev environment, tests, headless extraction:
+
+```powershell
+uv venv --python 3.11 .venv
+uv pip install --python .venv\Scripts\python.exe kicad-python numpy scipy matplotlib pytest
+.venv\Scripts\python.exe -m pytest tests -q          # incl. exact analytic cases
+.venv\Scripts\python.exe smoke\smoke_probe.py        # IPC API probe vs live KiCad
+.venv\Scripts\python.exe -m fill_resistance.board_io dump.json [NET]  # extract only
+```
+
+## Troubleshooting
+
+- **No toolbar button**: venv still building (wait), or build failed →
+  *Recreate Plugin Environment*; check the interpreter path (setup 2).
+- **"Could not connect to KiCad's IPC API"**: API server not enabled, or
+  KiCad not running (no headless mode in KiCad 10).
+- **"KiCad is busy"**: a modal dialog is open in KiCad — close it, rerun.
+- **Windows don't appear**: they may open behind KiCad (raised
+  best-effort); PNGs are always saved regardless.
+- **Result seems too low/high**: remember the model is fills + barrels
+  only, with ideal contacts; measure electrode-to-electrode.

conftest.py

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+import os
+import sys
+
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))

deploy.ps1

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+# Deploy the plugin into the KiCad user plugins directory.
+#   .\deploy.ps1                 -> NTFS junction (best for development)
+#   .\deploy.ps1 -Mode Copy      -> plain copy (no repo link)
+param(
+    [ValidateSet('Junction', 'Copy')]
+    [string]$Mode = 'Junction',
+    [string]$KiCadVersion = '10.0'
+)
+
+$src = $PSScriptRoot
+$pluginsDir = Join-Path ([Environment]::GetFolderPath('MyDocuments')) "KiCad\$KiCadVersion\plugins"
+$dst = Join-Path $pluginsDir 'fill-resistance'
+
+if (-not (Test-Path $pluginsDir)) {
+    Write-Error "KiCad plugins dir not found: $pluginsDir"
+    exit 1
+}
+
+if (Test-Path $dst) {
+    $item = Get-Item $dst -Force
+    if ($item.LinkType) {
+        # junction: rmdir removes the link only, never the target contents
+        cmd /c rmdir "$dst"
+    } else {
+        Remove-Item $dst -Recurse -Force
+    }
+}
+
+if ($Mode -eq 'Junction') {
+    New-Item -ItemType Junction -Path $dst -Target $src | Out-Null
+    Write-Host "junction created: $dst -> $src"
+} else {
+    $exclude = @('.venv', '.git', 'tests', 'smoke', '__pycache__', '.pytest_cache')
+    New-Item -ItemType Directory -Force $dst | Out-Null
+    Get-ChildItem $src -Force | Where-Object { $exclude -notcontains $_.Name } |
+        ForEach-Object { Copy-Item $_.FullName -Destination $dst -Recurse -Force }
+    Write-Host "copied plugin to: $dst"
+}
+Write-Host "Restart KiCad (or refresh plugins) and wait for the plugin venv build."

fill_res_action.py

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+"""Entrypoint launched by KiCad when the toolbar button is pressed.
+
+Lives at the plugin root (next to plugin.json) and only bootstraps the
+package import path, so fill_resistance/ can use normal absolute imports.
+"""
+import os
+import sys
+
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+
+from fill_resistance.main import main
+
+if __name__ == "__main__":
+    main()

fill_resistance/board_io.py

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+"""All KiCad IPC access. This is the ONLY module that imports kipy;
+everything downstream works on plain geometry dataclasses.
+
+Run `python -m fill_resistance.board_io dump.json [net]` against a live
+KiCad to extract without the dialog (all layers of the net, defaults).
+"""
+from __future__ import annotations
+
+from dataclasses import dataclass, field
+from pathlib import Path
+
+from kipy import KiCad
+from kipy.board import Board
+from kipy.board_types import BoardRectangle, Pad
+from kipy.proto.board.board_pb2 import BoardStackupLayerType
+from kipy.proto.board.board_types_pb2 import ZoneType
+from kipy.util.board_layer import (canonical_name, is_copper_layer,
+                                   layer_from_canonical_name)
+
+from . import config
+from .errors import ApiVersionError, CandidateError, SelectionError
+from .geometry import (Electrode, LayerFill, Polygon, Problem, Rect,
+                       SurfaceBuildup, ViaLink, linearize_ring)
+
+MASK_TO_COPPER = {"F.Mask": "F.Cu", "B.Mask": "B.Cu"}
+
+# zone fills are polygonal in practice; tolerance only guards arc nodes
+ARC_TOL_NM = 10_000
+
+
+def connect() -> tuple[KiCad, Board]:
+    try:
+        kicad = KiCad()
+        kicad.ping()
+    except Exception as e:
+        raise ApiVersionError(
+            f"Could not connect to KiCad's IPC API: {e}\n"
+            f"Is KiCad running with the API server enabled "
+            f"(Preferences > Plugins > Enable KiCad API)?"
+        )
+    try:
+        print(f"connected to KiCad {kicad.get_version()}")
+    except Exception:
+        pass
+    try:
+        board = kicad.get_board()
+    except Exception as e:
+        raise SelectionError(
+            f"Could not get the open board from KiCad: {e}\n"
+            f"Open the PCB in the board editor and run again."
+        )
+    return kicad, board
+
+
+def board_dir(board: Board) -> Path:
+    # document.board_filename is a bare file name (no directory) in
+    # KiCad 10.0.1; the project path is the reliable location
+    try:
+        path = board.get_project().path
+        if path and Path(path).is_dir():
+            return Path(path)
+    except Exception:
+        pass
+    try:
+        filename = getattr(board.document, "board_filename", "") or ""
+        if Path(filename).is_absolute():
+            return Path(filename).parent
+    except Exception:
+        pass
+    return Path.cwd()
+
+
+# --- stackup geometry --------------------------------------------------------
+
+@dataclass
+class StackupInfo:
+    names: list[str]                      # copper layers, top to bottom
+    thickness_nm: dict[str, int]
+    z_nm: dict[str, int]                  # copper center depth
+    z_bot_nm: int                         # total stack thickness
+
+
+def get_stackup_info(board: Board) -> StackupInfo:
+    names: list[str] = []
+    thickness: dict[str, int] = {}
+    z_center: dict[str, int] = {}
+    z = 0
+    for sl in board.get_stackup().layers:
+        t = int(sl.thickness or 0)
+        if sl.type == BoardStackupLayerType.BSLT_COPPER:
+            name = canonical_name(sl.layer)
+            if t <= 0:
+                t = int(config.FALLBACK_THICKNESS_UM * 1000)
+                print(f"warning: stackup gives no thickness for {name}; "
+                      f"assuming {config.FALLBACK_THICKNESS_UM} um")
+            names.append(name)
+            thickness[name] = t
+            z_center[name] = z + t // 2
+        z += t
+    if not names:
+        raise CandidateError(
+            "Could not read any copper layer from the board stackup."
+        )
+    return StackupInfo(names=names, thickness_nm=thickness, z_nm=z_center,
+                       z_bot_nm=z)
+
+
+# --- electrodes from selection ----------------------------------------------
+
+def _box2_to_rect(box, layer_name: str) -> Rect:
+    try:
+        pos, size = box.pos, box.size
+        return Rect.normalized(pos.x, pos.y, pos.x + size.x, pos.y + size.y,
+                               layer_name)
+    except AttributeError:
+        c, s = box.center, box.size
+        return Rect.normalized(c.x - s.x // 2, c.y - s.y // 2,
+                               c.x + s.x // 2, c.y + s.y // 2, layer_name)
+
+
+def _convert_poly(poly_with_holes) -> Polygon:
+    def ring(polyline):
+        nodes = []
+        for node in polyline.nodes:
+            if node.has_point:
+                nodes.append(("pt", (node.point.x, node.point.y)))
+            elif node.has_arc:
+                arc = node.arc
+                nodes.append(("arc", ((arc.start.x, arc.start.y),
+                                      (arc.mid.x, arc.mid.y),
+                                      (arc.end.x, arc.end.y))))
+        return linearize_ring(nodes, ARC_TOL_NM)
+
+    return Polygon(outline=ring(poly_with_holes.outline),
+                   holes=[ring(h) for h in poly_with_holes.holes])
+
+
+def _pad_drill_nm(pad_or_via) -> int:
+    try:
+        return int(pad_or_via.padstack.drill.diameter.x)
+    except Exception:
+        return 0
+
+
+def _pad_default_contact(pad: Pad) -> str:
+    if _pad_drill_nm(pad) > 0:
+        return "all"                       # through-hole: contacts the stack
+    try:
+        copper = [canonical_name(l) for l in pad.padstack.layers
+                  if is_copper_layer(l)]
+        if len(copper) == 1:
+            return copper[0]               # SMD: its own layer
+    except Exception:
+        pass
+    return "all"
+
+
+def _pad_polygons(board: Board, pad: Pad, contact: str) -> list[Polygon] | None:
+    layer_ids = []
+    if contact != "all":
+        try:
+            layer_ids.append(layer_from_canonical_name(contact))
+        except Exception:
+            pass
+    for name in ("F.Cu", "B.Cu"):
+        try:
+            layer_ids.append(layer_from_canonical_name(name))
+        except Exception:
+            pass
+    for lid in layer_ids:
+        try:
+            shape = board.get_pad_shapes_as_polygons(pad, layer=lid)
+            if shape is not None:
+                return [_convert_poly(shape)]
+        except Exception:
+            continue
+    return None
+
+
+def _to_electrode(board: Board, item) -> Electrode:
+    if isinstance(item, BoardRectangle):
+        tl, br = item.top_left, item.bottom_right
+        rect = Rect.normalized(tl.x, tl.y, br.x, br.y,
+                               canonical_name(item.layer))
+        cx = (rect.x0 + rect.x1) / 2e6
+        cy = (rect.y0 + rect.y1) / 2e6
+        return Electrode(rect=rect, contact="all",
+                         label=f"rect({cx:.1f},{cy:.1f})")
+    # Pad
+    pad: Pad = item
+    contact = _pad_default_contact(pad)
+    net = pad.net.name if pad.net is not None else "?"
+    label = f"pad {pad.number}@{net}"
+    box = board.get_item_bounding_box(pad)
+    if box is None:
+        raise SelectionError(f"Could not get the bounding box of {label}.")
+    rect = _box2_to_rect(box, "pad")
+    return Electrode(rect=rect, contact=contact,
+                     polygons=_pad_polygons(board, pad, contact), label=label)
+
+
+def _net_hint_of(pads: list[Pad]) -> str | None:
+    for pad in pads:
+        if pad.net is not None:
+            return pad.net.name
+    return None
+
+
+def get_electrodes(board: Board
+                   ) -> tuple[list[Electrode], list[Electrode], str | None]:
+    """Terminals from the selection. Each terminal may have MULTIPLE parts
+    (all merged into one externally-bonded contact):
+
+    - rectangles on ELECTRODE_POS_LAYER -> V+ parts, on ELECTRODE_NEG_LAYER
+      -> V- parts; selected pads fill a side that has no rectangles;
+    - no marker rectangles selected: legacy mode, exactly 2 items
+      (rects/pads, any layer) -> one part each;
+    - empty selection: board-wide scan of both marker layers.
+    """
+    pos_l = config.ELECTRODE_POS_LAYER
+    neg_l = config.ELECTRODE_NEG_LAYER
+    scheme = (f"Draw V+ rectangle(s) on {pos_l} and V- rectangle(s) on "
+              f"{neg_l} (axis-aligned), and/or select pads for a side "
+              f"without rectangles.")
+
+    selection = list(board.get_selection())
+    rects = [s for s in selection if isinstance(s, BoardRectangle)]
+    pads = [s for s in selection if isinstance(s, Pad)]
+
+    if not selection:
+        allr = [s for s in board.get_shapes() if isinstance(s, BoardRectangle)]
+        pos = [r for r in allr if canonical_name(r.layer) == pos_l]
+        neg = [r for r in allr if canonical_name(r.layer) == neg_l]
+        if pos and neg:
+            print(f"selection empty - using {len(pos)} rectangle(s) on "
+                  f"{pos_l} as V+ and {len(neg)} on {neg_l} as V-")
+            return ([_to_electrode(board, r) for r in pos],
+                    [_to_electrode(board, r) for r in neg], None)
+        raise SelectionError(
+            f"Nothing selected, and the board-wide scan found "
+            f"{len(pos)} rectangle(s) on {pos_l} / {len(neg)} on {neg_l} "
+            f"(need at least one on each).\n{scheme}"
+        )
+
+    pos = [r for r in rects if canonical_name(r.layer) == pos_l]
+    neg = [r for r in rects if canonical_name(r.layer) == neg_l]
+    other = [r for r in rects if canonical_name(r.layer) not in (pos_l, neg_l)]
+
+    if pos or neg:
+        if other:
+            raise SelectionError(
+                f"{len(other)} selected rectangle(s) are on neither marker "
+                f"layer ({pos_l} = V+, {neg_l} = V-). {scheme}"
+            )
+        es1 = [_to_electrode(board, r) for r in pos]
+        es2 = [_to_electrode(board, r) for r in neg]
+        if pads and es1 and es2:
+            raise SelectionError(
+                f"Cannot assign the {len(pads)} selected pad(s): both marker "
+                f"layers already provide rectangles. Use pads only for a "
+                f"side that has none."
+            )
+        if pads:
+            pad_parts = [_to_electrode(board, p) for p in pads]
+            if not es1:
+                es1 = pad_parts
+            else:
+                es2 = pad_parts
+        if es1 and es2:
+            return es1, es2, _net_hint_of(pads)
+        raise SelectionError(
+            f"Only one terminal defined: V+ has {len(es1)} and V- has "
+            f"{len(es2)} contact(s). {scheme}"
+        )
+
+    items = rects + pads
+    if len(items) == 2:
+        return ([_to_electrode(board, items[0])],
+                [_to_electrode(board, items[1])], _net_hint_of(pads))
+    raise SelectionError(
+        f"The selection has {len(rects)} rectangle(s) (none on the marker "
+        f"layers) and {len(pads)} pad(s); without marker layers exactly 2 "
+        f"contacts are needed.\n{scheme}"
+    )
+
+
+# --- fills -------------------------------------------------------------------
+
+def gather_net_fills(board: Board) -> dict[str, dict[str, list[Polygon]]]:
+    """net -> layer_name -> merged fill polygons (non-empty only)."""
+    fills: dict[str, dict[str, list[Polygon]]] = {}
+    for zone in board.get_zones():
+        if zone.type != ZoneType.ZT_COPPER:
+            continue
+        net = zone.net.name if zone.net is not None else "<no net>"
+        for layer, polys in zone.filled_polygons.items():
+            if not is_copper_layer(layer) or not polys:
+                continue
+            fills.setdefault(net, {}).setdefault(
+                canonical_name(layer), []).extend(
+                _convert_poly(p) for p in polys)
+    return fills
+
+
+def _rect_overlaps(rect: Rect, polygons: list[Polygon]) -> bool:
+    for p in polygons:
+        px0, py0 = p.outline.min(axis=0)
+        px1, py1 = p.outline.max(axis=0)
+        if rect.x0 <= px1 and rect.x1 >= px0 and rect.y0 <= py1 and rect.y1 >= py0:
+            return True
+    return False
+
+
+def nets_overlapping(fills: dict, es1: list[Electrode],
+                     es2: list[Electrode]) -> list[str]:
+    """Nets whose fills overlap both terminals (any part, any layer each -
+    the connection may go through vias). Permissive bbox prefilter."""
+    out = []
+    for net, per_layer in fills.items():
+        hit1 = any(_rect_overlaps(e.rect, polys) for e in es1
+                   for polys in per_layer.values())
+        hit2 = any(_rect_overlaps(e.rect, polys) for e in es2
+                   for polys in per_layer.values())
+        if hit1 and hit2:
+            out.append(net)
+    return sorted(out)
+
+
+def gather_mask_buildups(board: Board) -> dict[str, list[Polygon]]:
+    """Zones on F.Mask/B.Mask (mask openings) -> fill polygons keyed by
+    the outer copper layer they expose."""
+    out: dict[str, list[Polygon]] = {}
+    for zone in board.get_zones():
+        try:
+            filled = zone.filled_polygons
+        except Exception:
+            continue
+        for layer, polys in filled.items():
+            copper = MASK_TO_COPPER.get(canonical_name(layer))
+            if copper and polys:
+                out.setdefault(copper, []).extend(
+                    _convert_poly(p) for p in polys)
+    return out
+
+
+def any_zone_unfilled(board: Board) -> bool:
+    return any(z.type == ZoneType.ZT_COPPER and not z.filled
+               for z in board.get_zones())
+
+
+def refill(board: Board) -> None:
+    print("refilling zones - this modifies the open document ...")
+    board.refill_zones(block=True)
+
+
+# --- barrels -----------------------------------------------------------------
+
+def _padstack_span(padstack, stackup: StackupInfo) -> tuple[int, int]:
+    """(z_top, z_bot) of the barrel; falls back to the full stack."""
+    try:
+        copper = [canonical_name(l) for l in padstack.layers
+                  if is_copper_layer(l)]
+        zs = [stackup.z_nm[c] for c in copper if c in stackup.z_nm]
+        if len(zs) >= 2:
+            return min(zs) - 1, max(zs) + 1
+    except Exception:
+        pass
+    return -1, stackup.z_bot_nm + 1
+
+
+def gather_barrels(board: Board, net_name: str,
+                   stackup: StackupInfo) -> list[ViaLink]:
+    barrels = []
+    for via in board.get_vias():
+        if via.net is None or via.net.name != net_name:
+            continue
+        drill = int(via.drill_diameter or 0) or _pad_drill_nm(via)
+        if drill <= 0:
+            continue
+        z_top, z_bot = _padstack_span(via.padstack, stackup)
+        barrels.append(ViaLink(x=via.position.x, y=via.position.y,
+                               drill_nm=drill, z_top_nm=z_top,
+                               z_bot_nm=z_bot, kind="via"))
+    if config.INCLUDE_TH_PADS:
+        for pad in board.get_pads():
+            if pad.net is None or pad.net.name != net_name:
+                continue
+            drill = _pad_drill_nm(pad)
+            if drill <= 0:
+                continue
+            barrels.append(ViaLink(x=pad.position.x, y=pad.position.y,
+                                   drill_nm=drill, z_top_nm=-1,
+                                   z_bot_nm=stackup.z_bot_nm + 1, kind="pad"))
+    return barrels
+
+
+# --- top level ----------------------------------------------------------------
+
+def build_problem(board: Board, net: str, layer_names: list[str],
+                  es1: list[Electrode], es2: list[Electrode],
+                  stackup: StackupInfo, fills: dict,
+                  buildups: dict[str, list[Polygon]] | None = None,
+                  extra_cu_um: float | None = None) -> Problem:
+    per_layer = fills.get(net, {})
+    layers = []
+    for name in stackup.names:                 # keep stackup order
+        if name not in layer_names:
+            continue
+        polys = per_layer.get(name, [])
+        if not polys:
+            print(f"note: net {net} has no fill on {name} - layer skipped")
+            continue
+        if config.COPPER_THICKNESS_UM is not None:
+            t, source = int(config.COPPER_THICKNESS_UM * 1000), "override"
+        else:
+            t, source = stackup.thickness_nm[name], "stackup"
+        layers.append(LayerFill(layer_name=name, thickness_nm=t,
+                                z_nm=stackup.z_nm[name], polygons=polys))
+    if not layers:
+        raise CandidateError(
+            f"Net {net} has no fill on any of the selected layers "
+            f"({', '.join(layer_names)})."
+        )
+    vias = gather_barrels(board, net, stackup) if len(layers) > 1 else []
+    included = {l.layer_name for l in layers}
+    buildup_list = [
+        SurfaceBuildup(layer_name=name, polygons=polys)
+        for name, polys in (buildups or {}).items() if name in included
+    ]
+    print(f"net {net}: {len(layers)} layer(s) "
+          f"({', '.join(l.layer_name for l in layers)}), "
+          f"{len(vias)} via/pad barrel(s)"
+          + (f", solder buildup on "
+             f"{', '.join(b.layer_name for b in buildup_list)}"
+             if buildup_list else ""))
+    return Problem(
+        board_path=board.name or "",
+        net_name=net,
+        rho_ohm_m=config.RHO_CU_OHM_M,
+        plating_nm=int(config.VIA_PLATING_UM * 1000),
+        layers=layers,
+        vias=vias,
+        electrodes1=es1,
+        electrodes2=es2,
+        thickness_source=("override" if config.COPPER_THICKNESS_UM is not None
+                          else "stackup"),
+        buildups=buildup_list,
+        solder_thickness_nm=int(config.SOLDER_THICKNESS_UM * 1000),
+        solder_rho_ohm_m=config.SOLDER_RHO_OHM_M,
+        extra_cu_nm=int((extra_cu_um if extra_cu_um is not None
+                         else config.BUILDUP_EXTRA_CU_UM) * 1000),
+    )
+
+
+if __name__ == "__main__":
+    import sys
+
+    from .geometry import save_problem
+
+    out = Path(sys.argv[1]) if len(sys.argv) > 1 else Path("geometry_dump.json")
+    _, board = connect()
+    stackup = get_stackup_info(board)
+    es1, es2, net_hint = get_electrodes(board)
+    if any_zone_unfilled(board):
+        refill(board)
+    fills = gather_net_fills(board)
+    nets = nets_overlapping(fills, es1, es2)
+    if len(sys.argv) > 2:
+        net = sys.argv[2]
+    elif net_hint in nets:
+        net = net_hint
+    elif len(nets) == 1:
+        net = nets[0]
+    else:
+        print(f"candidate nets: {nets}; pass one as second argument")
+        sys.exit(1)
+    problem = build_problem(board, net, list(fills.get(net, {})), es1, es2,
+                            stackup, fills)
+    save_problem(problem, out)
+    print(f"wrote {out}")

fill_resistance/config.py

@@ -0,0 +1,72 @@
+"""All tunable constants. v1 has no GUI dialog: edit here, re-run.
+
+A future version may read overrides from <project>/fill_res_config.json.
+"""
+
+# --- Grid sizing ---
+# Benchmarked on the VOUT+ plane (147x59 mm): R changes < 0.3% from
+# 150 um cells down to 50 um; 1.7M unknowns direct-solve in ~17 s
+# (raster ~20 s). Accuracy is feature-limited (slots/necks narrower than
+# one cell), not plane-limited - override CELL_UM_OVERRIDE for boards
+# with sub-cell slots.
+TARGET_CELLS = 2_000_000        # auto cell size aims for roughly this many cells
+HARD_MAX_CELLS = 16_000_000     # abort above this (see GridSizeError message)
+MIN_CELL_UM = 25.0              # clamp for auto cell size
+MAX_CELL_UM = 500.0
+CELL_UM_OVERRIDE: float | None = None   # force a cell size, bypasses auto (not HARD_MAX)
+MARGIN_CELLS = 2                # empty guard cells around the copper bbox
+
+# --- Physics ---
+RHO_CU_OHM_M = 1.68e-8          # copper resistivity at 20 degC
+COPPER_THICKNESS_UM: float | None = None  # None -> stackup, fallback 35.0 with warning
+FALLBACK_THICKNESS_UM = 35.0
+TEST_CURRENT_A = 1.0            # default injected current (dialog/CLI-selectable)
+VIA_PLATING_UM = 18.0           # barrel plating thickness (always plated).
+                                # Capped vs uncapped vias do not change the
+                                # layer-to-layer DC path: the >=5um cap sits
+                                # over the hole mouth in parallel with the
+                                # annular-ring contact, not in series.
+INCLUDE_TH_PADS = True          # plated through-hole pads stitch layers too
+SKIN_SIDES = 1                  # skin-effect field config: 1 = plane facing a
+                                # return plane (conservative), 2 = isolated foil
+
+# --- Solder / mask-opening buildup ---
+INCLUDE_MASK_BUILDUP = False    # OFF by default; dialog-toggleable. Zones on
+                                # F.Mask/B.Mask = mask openings that collect
+                                # solder on the pour underneath
+SOLDER_THICKNESS_UM = 50.0      # solder height over opened copper
+SOLDER_RHO_OHM_M = 1.32e-7      # SAC305, ~7.9x copper
+BUILDUP_EXTRA_CU_UM = 0.0       # optional user-added copper (busbar/wire
+                                # soldered into the opening); dialog-settable
+
+# --- Zone / layer selection ---
+LAYER_HINT: str | None = None   # e.g. "F.Cu" to disambiguate candidate fills
+ELECTRODE_POS_LAYER = "User.1"  # rectangles on this layer mark V+ contact parts
+ELECTRODE_NEG_LAYER = "User.2"  # rectangles on this layer mark V- contact parts
+ALWAYS_REFILL = False           # refill zones even if KiCad says they are filled
+
+# --- Solver ---
+CONTACT_MODEL = "uniform"       # "uniform": conductor pressed on top injects
+                                # orthogonally with uniform surface density
+                                # (J ramps across the contact); "equipotential":
+                                # ideal bonded lug (Dirichlet). The two bracket
+                                # a real contact: R_equi <= R_real <= R_uniform.
+SPSOLVE_MAX_UNKNOWNS = 2_500_000  # above this, use CG (Jacobi) instead of
+                                  # direct solve (measured: direct is ~14x
+                                  # faster at 1.7M unknowns, ~3 GB peak)
+CG_TOL = 1e-8
+CG_MAXITER = 50_000             # CG iterations are cheap; large grids need many
+
+# --- Geometry ---
+ARC_TOL_FRACTION = 0.5          # arc sagitta tolerance as a fraction of cell size
+
+# --- Plots / output ---
+CMAP_POTENTIAL = "viridis"
+CMAP_CURRENT = "inferno"
+CMAP_POWER = "magma"
+POWER_DYNAMIC_RANGE = 1e4       # LogNorm span for the power map (power ~ J^2)
+LOG_CURRENT_SCALE = True
+CURRENT_DYNAMIC_RANGE = 1e3     # LogNorm vmin = vmax / this
+DPI = 150
+INTERACTIVE = True              # False -> save PNGs only, never open windows
+OUTPUT_DIRNAME = "fill_res_results"

fill_resistance/dialog.py

@@ -0,0 +1,193 @@
+"""Qt selection dialog shown on plugin launch: net, layers, per-electrode
+contact, test current, optional cell size. PySide6 is already a plugin
+dependency (matplotlib QtAgg backend); the QApplication created here is
+reused by matplotlib afterwards.
+"""
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+from PySide6.QtCore import Qt
+from PySide6.QtWidgets import (QApplication, QCheckBox, QComboBox, QDialog,
+                               QDialogButtonBox, QFormLayout, QLabel,
+                               QLineEdit, QListWidget, QListWidgetItem,
+                               QVBoxLayout)
+
+from . import config, skin
+
+ALL_LAYERS = "All selected layers"
+AUTO_CONTACT = "(auto: per contact part)"
+MODEL_LABELS = {
+    "uniform": "Uniform injection (conductor pressed on top)",
+    "equipotential": "Equipotential (ideal bonded lug)",
+}
+
+
+@dataclass
+class Selection:
+    net: str
+    layers: list[str]
+    contact1: str                 # "auto", "all" or layer name
+    contact2: str
+    current_a: float
+    cell_um: float | None
+    freq_hz: float = 0.0
+    contact_model: str = "uniform"
+    include_buildup: bool = False
+    extra_cu_um: float = 0.0
+
+
+class _Dialog(QDialog):
+    def __init__(self, candidates: dict[str, list[str]], layer_order: list[str],
+                 default_net: str, e1_label: str, e2_label: str,
+                 contact1: str, contact2: str, buildup_layers: list[str]):
+        super().__init__()
+        self.setWindowTitle("Fill Resistance")
+        self.setWindowFlag(Qt.WindowStaysOnTopHint, True)
+        self._candidates = candidates
+        self._layer_order = layer_order
+
+        form = QFormLayout()
+
+        self.net_box = QComboBox()
+        for net in sorted(candidates):
+            self.net_box.addItem(net)
+        self.net_box.setCurrentText(default_net)
+        form.addRow("Signal (net):", self.net_box)
+
+        self.layer_list = QListWidget()
+        self.layer_list.setMaximumHeight(120)
+        form.addRow("Layers:", self.layer_list)
+
+        self.contact1_box = QComboBox()
+        self.contact2_box = QComboBox()
+        form.addRow(f"V+ ({e1_label}):", self.contact1_box)
+        form.addRow(f"V− ({e2_label}):", self.contact2_box)
+
+        self.model_box = QComboBox()
+        for key in ("uniform", "equipotential"):
+            self.model_box.addItem(MODEL_LABELS[key], key)
+        default_index = 0 if config.CONTACT_MODEL == "uniform" else 1
+        self.model_box.setCurrentIndex(default_index)
+        form.addRow("Contact model:", self.model_box)
+
+        self.current_edit = QLineEdit(f"{config.TEST_CURRENT_A:g}")
+        form.addRow("Test current [A]:", self.current_edit)
+
+        self.freq_edit = QLineEdit("")
+        self.freq_edit.setPlaceholderText("0 = DC   (e.g. 142k, 1.5M)")
+        form.addRow("Frequency [Hz]:", self.freq_edit)
+
+        self.cell_edit = QLineEdit("")
+        self.cell_edit.setPlaceholderText("auto")
+        form.addRow("Cell size [µm]:", self.cell_edit)
+
+        self.buildup_check = QCheckBox(
+            f"{config.SOLDER_THICKNESS_UM:g} µm solder on mask openings"
+            + (f" ({', '.join(buildup_layers)})" if buildup_layers
+               else " (none found)"))
+        self.buildup_check.setChecked(bool(buildup_layers)
+                                      and config.INCLUDE_MASK_BUILDUP)
+        self.buildup_check.setEnabled(bool(buildup_layers))
+        form.addRow("Buildup:", self.buildup_check)
+
+        self.extracu_edit = QLineEdit(f"{config.BUILDUP_EXTRA_CU_UM:g}")
+        self.extracu_edit.setEnabled(bool(buildup_layers))
+        form.addRow("Extra Cu in openings [µm]:", self.extracu_edit)
+
+        buttons = QDialogButtonBox(QDialogButtonBox.Ok | QDialogButtonBox.Cancel)
+        buttons.accepted.connect(self.accept)
+        buttons.rejected.connect(self.reject)
+
+        lay = QVBoxLayout(self)
+        lay.addLayout(form)
+        note = QLabel("Multiple layers are coupled through the net's "
+                      "via/through-pad barrels. At f > 0 the foil-thickness "
+                      "skin effect is applied per layer; lateral (proximity) "
+                      "redistribution is not modeled, so AC results are a "
+                      "lower bound.")
+        note.setWordWrap(True)
+        note.setStyleSheet("color: gray; font-size: 10px;")
+        lay.addWidget(note)
+        lay.addWidget(buttons)
+
+        self._desired1, self._desired2 = contact1, contact2
+        self.net_box.currentTextChanged.connect(self._refresh)
+        self._refresh()
+
+    def _refresh(self):
+        net = self.net_box.currentText()
+        layers = [n for n in self._layer_order
+                  if n in self._candidates.get(net, [])]
+        self.layer_list.clear()
+        for name in layers:
+            item = QListWidgetItem(name)
+            item.setFlags(item.flags() | Qt.ItemIsUserCheckable)
+            item.setCheckState(Qt.Checked)
+            self.layer_list.addItem(item)
+        for box, desired in ((self.contact1_box, self._desired1),
+                             (self.contact2_box, self._desired2)):
+            box.clear()
+            box.addItem(AUTO_CONTACT)
+            box.addItem(ALL_LAYERS)
+            box.addItems(layers)
+            if desired == "all":
+                box.setCurrentText(ALL_LAYERS)
+            elif desired in layers:
+                box.setCurrentText(desired)
+
+    def checked_layers(self) -> list[str]:
+        out = []
+        for i in range(self.layer_list.count()):
+            item = self.layer_list.item(i)
+            if item.checkState() == Qt.Checked:
+                out.append(item.text())
+        return out
+
+    def selection(self) -> Selection | None:
+        layers = self.checked_layers()
+        if not layers:
+            return None
+        try:
+            current = float(self.current_edit.text().replace(",", "."))
+        except ValueError:
+            current = config.TEST_CURRENT_A
+        cell_text = self.cell_edit.text().strip()
+        try:
+            cell = float(cell_text.replace(",", ".")) if cell_text else None
+        except ValueError:
+            cell = None
+
+        def contact(box: QComboBox) -> str:
+            t = box.currentText()
+            if t == AUTO_CONTACT:
+                return "auto"
+            return "all" if t == ALL_LAYERS else t
+
+        try:
+            extra_cu = float(self.extracu_edit.text().replace(",", "."))
+        except ValueError:
+            extra_cu = 0.0
+        return Selection(net=self.net_box.currentText(), layers=layers,
+                         contact1=contact(self.contact1_box),
+                         contact2=contact(self.contact2_box),
+                         current_a=current, cell_um=cell,
+                         freq_hz=skin.parse_frequency(self.freq_edit.text()),
+                         contact_model=self.model_box.currentData(),
+                         include_buildup=self.buildup_check.isChecked(),
+                         extra_cu_um=max(0.0, extra_cu))
+
+
+def ask(candidates: dict[str, list[str]], layer_order: list[str],
+        default_net: str, e1_label: str, e2_label: str,
+        contact1: str, contact2: str,
+        buildup_layers: list[str] | None = None) -> Selection | None:
+    """Show the dialog; returns None on cancel."""
+    app = QApplication.instance() or QApplication([])
+    dlg = _Dialog(candidates, layer_order, default_net, e1_label, e2_label,
+                  contact1, contact2, buildup_layers or [])
+    dlg.raise_()
+    dlg.activateWindow()
+    if dlg.exec() != QDialog.Accepted:
+        return None
+    return dlg.selection()

fill_resistance/errors.py

@@ -0,0 +1,34 @@
+"""User-facing error hierarchy.
+
+Every UserFacingError message is shown both on stdout (KiCad status bar)
+and in a matplotlib error figure, so keep messages self-contained and
+actionable.
+"""
+
+
+class UserFacingError(Exception):
+    pass
+
+
+class ApiVersionError(UserFacingError):
+    pass
+
+
+class SelectionError(UserFacingError):
+    pass
+
+
+class CandidateError(UserFacingError):
+    pass
+
+
+class ElectrodeError(UserFacingError):
+    pass
+
+
+class ConnectivityError(UserFacingError):
+    pass
+
+
+class GridSizeError(UserFacingError):
+    pass

fill_resistance/geometry.py

@@ -0,0 +1,317 @@
+"""Plain geometry data model. No kipy imports here.
+
+Everything is int64 nanometers in KiCad board coordinates (y grows down);
+z grows from the board top surface downwards through the stackup.
+Problem is the complete solver input and doubles as the JSON dump schema,
+so the whole pipeline downstream of board_io runs without KiCad.
+
+Schema v2 is multi-layer: per-layer fills at stackup depths, linked by
+via/through-pad barrels. v1 dumps (single layer, no vias) still load.
+"""
+from __future__ import annotations
+
+import json
+import math
+from dataclasses import dataclass, field
+from pathlib import Path
+
+import numpy as np
+
+JSON_SCHEMA_VERSION = 4
+
+
+@dataclass(frozen=True)
+class Rect:
+    x0: int
+    y0: int
+    x1: int
+    y1: int
+    layer_name: str
+
+    @classmethod
+    def normalized(cls, xa: int, ya: int, xb: int, yb: int, layer_name: str) -> "Rect":
+        return cls(min(xa, xb), min(ya, yb), max(xa, xb), max(ya, yb), layer_name)
+
+    @property
+    def width(self) -> int:
+        return self.x1 - self.x0
+
+    @property
+    def height(self) -> int:
+        return self.y1 - self.y0
+
+
+@dataclass
+class Polygon:
+    outline: np.ndarray                       # (N, 2) int64 nm, open ring
+    holes: list[np.ndarray] = field(default_factory=list)
+
+
+@dataclass
+class LayerFill:
+    layer_name: str
+    thickness_nm: int
+    z_nm: int                                 # copper center depth from board top
+    polygons: list[Polygon]
+
+
+@dataclass
+class SurfaceBuildup:
+    """Solder (plus optional added copper) sitting on an outer copper
+    layer inside solder-mask openings (zones on F.Mask/B.Mask)."""
+    layer_name: str                           # copper layer it sits on
+    polygons: list[Polygon]
+
+
+@dataclass
+class Electrode:
+    """One PART of a current-injection terminal: a drawn rectangle or a
+    selected pad. A terminal (V+ or V-) is a LIST of parts, all merged
+    into one equipotential contact (externally bonded). `polygons`
+    (board nm) is the exact copper shape when known (pads); None means
+    the rectangle itself is the shape. `contact` = 'all' or a layer
+    name: which included layers this part touches."""
+    rect: Rect                                # bounding box (labels/summary)
+    contact: str = "all"
+    polygons: list[Polygon] | None = None
+    label: str = "rect"
+
+
+@dataclass
+class ViaLink:
+    """A conductive barrel (via or plated through-hole pad) linking copper
+    layers whose z lies within [z_top_nm, z_bot_nm]."""
+    x: int
+    y: int
+    drill_nm: int
+    z_top_nm: int
+    z_bot_nm: int
+    kind: str = "via"                         # "via" | "pad"
+
+    def spans(self, z_nm: int) -> bool:
+        return self.z_top_nm - 1 <= z_nm <= self.z_bot_nm + 1
+
+    def barrel_resistance(self, length_nm: int, rho_ohm_m: float,
+                          plating_nm: int) -> float:
+        """Barrel segment resistance over length_nm: thin-wall annulus of
+        plating around the drill."""
+        area_m2 = math.pi * (self.drill_nm * 1e-9) * (plating_nm * 1e-9)
+        return rho_ohm_m * (length_nm * 1e-9) / area_m2
+
+
+@dataclass
+class Problem:
+    board_path: str
+    net_name: str
+    rho_ohm_m: float
+    plating_nm: int
+    layers: list[LayerFill]                   # sorted by z_nm (top first)
+    vias: list[ViaLink]
+    electrodes1: list[Electrode]              # V+ terminal parts (merged)
+    electrodes2: list[Electrode]              # V- terminal parts (merged)
+    thickness_source: str = "stackup"
+    buildups: list[SurfaceBuildup] = field(default_factory=list)
+    solder_thickness_nm: int = 50_000
+    solder_rho_ohm_m: float = 1.32e-7
+    extra_cu_nm: int = 0
+
+    @property
+    def layer_names(self) -> list[str]:
+        return [l.layer_name for l in self.layers]
+
+    def sigma_s(self, layer_index: int) -> float:
+        """Sheet conductance of one layer [S per square]."""
+        return (self.layers[layer_index].thickness_nm * 1e-9) / self.rho_ohm_m
+
+    def copper_bbox(self) -> tuple[int, int, int, int]:
+        xs = np.concatenate([p.outline[:, 0]
+                             for l in self.layers for p in l.polygons])
+        ys = np.concatenate([p.outline[:, 1]
+                             for l in self.layers for p in l.polygons])
+        return int(xs.min()), int(ys.min()), int(xs.max()), int(ys.max())
+
+
+def arc_points(start, mid, end, tol_nm: float) -> np.ndarray:
+    """Tessellate a start/mid/end arc into points from start (inclusive)
+    to end (exclusive), max sagitta <= tol_nm. Collinear input degrades
+    to just the start point (straight segment)."""
+    sx, sy = float(start[0]), float(start[1])
+    mx, my = float(mid[0]), float(mid[1])
+    ex, ey = float(end[0]), float(end[1])
+
+    d = 2.0 * (sx * (my - ey) + mx * (ey - sy) + ex * (sy - my))
+    chord = math.hypot(ex - sx, ey - sy)
+    if abs(d) < 1e-9 * max(chord, 1.0):
+        return np.array([[start[0], start[1]]], dtype=np.int64)
+    ux = ((sx**2 + sy**2) * (my - ey) + (mx**2 + my**2) * (ey - sy)
+          + (ex**2 + ey**2) * (sy - my)) / d
+    uy = ((sx**2 + sy**2) * (ex - mx) + (mx**2 + my**2) * (sx - ex)
+          + (ex**2 + ey**2) * (mx - sx)) / d
+    r = math.hypot(sx - ux, sy - uy)
+
+    a0 = math.atan2(sy - uy, sx - ux)
+    a1 = math.atan2(my - uy, mx - ux)
+    a2 = math.atan2(ey - uy, ex - ux)
+    two_pi = 2.0 * math.pi
+    d01 = (a1 - a0) % two_pi
+    d02 = (a2 - a0) % two_pi
+    sweep = d02 if d01 <= d02 else d02 - two_pi
+
+    tol = min(tol_nm, 0.999 * r)
+    dtheta_max = 2.0 * math.acos(1.0 - tol / r)
+    n = max(2, int(math.ceil(abs(sweep) / dtheta_max)))
+    ks = np.arange(n)
+    angs = a0 + sweep * ks / n
+    pts = np.stack([ux + r * np.cos(angs), uy + r * np.sin(angs)], axis=1)
+    return np.round(pts).astype(np.int64)
+
+
+def linearize_ring(nodes: list, tol_nm: float) -> np.ndarray:
+    """nodes: list of ('pt', (x, y)) or ('arc', (start, mid, end)) tuples,
+    already in board nm. Returns an (N, 2) int64 open ring."""
+    parts = []
+    for kind, data in nodes:
+        if kind == "pt":
+            parts.append(np.array([[data[0], data[1]]], dtype=np.int64))
+        elif kind == "arc":
+            parts.append(arc_points(data[0], data[1], data[2], tol_nm))
+        else:
+            raise ValueError(f"unknown polyline node kind: {kind}")
+    ring = np.concatenate(parts, axis=0)
+    if len(ring) > 1 and (ring[0] == ring[-1]).all():
+        ring = ring[:-1]
+    return ring
+
+
+# --- JSON dump / load -------------------------------------------------------
+
+def _poly_to_json(p: Polygon) -> dict:
+    return {"outline": p.outline.tolist(), "holes": [h.tolist() for h in p.holes]}
+
+
+def _poly_from_json(d: dict) -> Polygon:
+    return Polygon(outline=np.asarray(d["outline"], dtype=np.int64),
+                   holes=[np.asarray(h, dtype=np.int64) for h in d["holes"]])
+
+
+def _electrode_to_json(e: Electrode) -> dict:
+    return {
+        "rect": vars(e.rect) | {},
+        "contact": e.contact,
+        "label": e.label,
+        "polygons": (None if e.polygons is None
+                     else [_poly_to_json(poly) for poly in e.polygons]),
+    }
+
+
+def _electrode_from_json(d: dict) -> Electrode:
+    return Electrode(
+        rect=_rect_from_json(d["rect"]),
+        contact=d.get("contact", "all"),
+        label=d.get("label", "rect"),
+        polygons=(None if d.get("polygons") is None
+                  else [_poly_from_json(pd) for pd in d["polygons"]]),
+    )
+
+
+def problem_to_json(p: Problem) -> dict:
+    return {
+        "schema_version": JSON_SCHEMA_VERSION,
+        "board_path": p.board_path,
+        "net_name": p.net_name,
+        "rho_ohm_m": p.rho_ohm_m,
+        "plating_nm": p.plating_nm,
+        "thickness_source": p.thickness_source,
+        "electrodes1": [_electrode_to_json(e) for e in p.electrodes1],
+        "electrodes2": [_electrode_to_json(e) for e in p.electrodes2],
+        "layers": [
+            {
+                "layer_name": l.layer_name,
+                "thickness_nm": l.thickness_nm,
+                "z_nm": l.z_nm,
+                "polygons": [_poly_to_json(poly) for poly in l.polygons],
+            }
+            for l in p.layers
+        ],
+        "vias": [vars(v) | {} for v in p.vias],
+        "buildups": [
+            {"layer_name": b.layer_name,
+             "polygons": [_poly_to_json(poly) for poly in b.polygons]}
+            for b in p.buildups
+        ],
+        "solder_thickness_nm": p.solder_thickness_nm,
+        "solder_rho_ohm_m": p.solder_rho_ohm_m,
+        "extra_cu_nm": p.extra_cu_nm,
+    }
+
+
+def _rect_from_json(rd: dict) -> Rect:
+    return Rect(int(rd["x0"]), int(rd["y0"]), int(rd["x1"]), int(rd["y1"]),
+                rd["layer_name"])
+
+
+def problem_from_json(d: dict) -> Problem:
+    version = d.get("schema_version", 1)
+    if version == 1:
+        # v1: single layer, no vias, rect electrodes
+        return Problem(
+            board_path=d["board_path"],
+            net_name=d["net_name"],
+            rho_ohm_m=float(d["rho_ohm_m"]),
+            plating_nm=18_000,
+            layers=[LayerFill(
+                layer_name=d["layer_name"],
+                thickness_nm=int(d["thickness_nm"]),
+                z_nm=0,
+                polygons=[_poly_from_json(pd) for pd in d["polygons"]],
+            )],
+            vias=[],
+            electrodes1=[Electrode(rect=_rect_from_json(d["rect1"]))],
+            electrodes2=[Electrode(rect=_rect_from_json(d["rect2"]))],
+            thickness_source=d.get("thickness_source", "unknown"),
+        )
+    return Problem(
+        board_path=d["board_path"],
+        net_name=d["net_name"],
+        rho_ohm_m=float(d["rho_ohm_m"]),
+        plating_nm=int(d["plating_nm"]),
+        layers=[
+            LayerFill(
+                layer_name=ld["layer_name"],
+                thickness_nm=int(ld["thickness_nm"]),
+                z_nm=int(ld["z_nm"]),
+                polygons=[_poly_from_json(pd) for pd in ld["polygons"]],
+            )
+            for ld in d["layers"]
+        ],
+        vias=[
+            ViaLink(x=int(vd["x"]), y=int(vd["y"]), drill_nm=int(vd["drill_nm"]),
+                    z_top_nm=int(vd["z_top_nm"]), z_bot_nm=int(vd["z_bot_nm"]),
+                    kind=vd.get("kind", "via"))
+            for vd in d["vias"]
+        ],
+        electrodes1=(
+            [_electrode_from_json(ed) for ed in d["electrodes1"]]
+            if version >= 3 else [_electrode_from_json(d["electrode1"])]),
+        electrodes2=(
+            [_electrode_from_json(ed) for ed in d["electrodes2"]]
+            if version >= 3 else [_electrode_from_json(d["electrode2"])]),
+        thickness_source=d.get("thickness_source", "unknown"),
+        buildups=[
+            SurfaceBuildup(
+                layer_name=bd["layer_name"],
+                polygons=[_poly_from_json(pd) for pd in bd["polygons"]])
+            for bd in d.get("buildups", [])
+        ],
+        solder_thickness_nm=int(d.get("solder_thickness_nm", 50_000)),
+        solder_rho_ohm_m=float(d.get("solder_rho_ohm_m", 1.32e-7)),
+        extra_cu_nm=int(d.get("extra_cu_nm", 0)),
+    )
+
+
+def save_problem(p: Problem, path: Path) -> None:
+    path.write_text(json.dumps(problem_to_json(p)), encoding="utf-8")
+
+
+def load_problem(path: Path) -> Problem:
+    return problem_from_json(json.loads(Path(path).read_text(encoding="utf-8")))

fill_resistance/main.py

@@ -0,0 +1,108 @@
+"""Top-level orchestration for the KiCad-launched action.
+
+Flow: connect -> read the two selected contacts (rectangles/pads) ->
+gather fills -> selection dialog (net, layers, contacts, current, cell)
+-> extract vias -> solve -> figures + report.
+
+Every failure is reported twice: on stdout (lands in the KiCad status-bar
+warning list) and as a matplotlib error figure, so it cannot be missed.
+"""
+from __future__ import annotations
+
+import sys
+import traceback
+
+from . import config, pipeline, report
+from .errors import CandidateError, UserFacingError
+
+
+def _fail(message: str, outdir) -> None:
+    print(f"ERROR: {message}")
+    from . import plots
+    fig = plots.fig_error(message)
+    plots.save_and_show([(fig, "error")], outdir)
+    sys.exit(1)
+
+
+def main() -> None:
+    outdir = None
+    try:
+        from kipy.errors import ApiError
+
+        from . import board_io, dialog
+        try:
+            kicad, board = board_io.connect()
+            stackup = board_io.get_stackup_info(board)
+            es1, es2, net_hint = board_io.get_electrodes(board)
+            if board_io.any_zone_unfilled(board) or config.ALWAYS_REFILL:
+                board_io.refill(board)
+            fills = board_io.gather_net_fills(board)
+            candidate_nets = board_io.nets_overlapping(fills, es1, es2)
+            buildups = board_io.gather_mask_buildups(board)
+        except ApiError as e:
+            raise UserFacingError(
+                f"KiCad API error: {e}\nIf KiCad is showing a dialog, close "
+                f"it and run again."
+            )
+
+        if not candidate_nets:
+            raise CandidateError(
+                "No copper zone fill overlaps both contacts. Check that both "
+                "sit over (or in) filled pours and that the fills are up to "
+                "date (press B in the board editor)."
+            )
+
+        def group_label(parts):
+            names = [p.label for p in parts[:3]]
+            more = f" +{len(parts) - 3}" if len(parts) > 3 else ""
+            return f"{len(parts)}× " + ", ".join(names) + more
+
+        def group_contact(parts):
+            contacts = {p.contact for p in parts}
+            return contacts.pop() if len(contacts) == 1 else "auto"
+
+        default_net = (net_hint if net_hint in candidate_nets
+                       else candidate_nets[0])
+        selection = dialog.ask(
+            candidates={n: list(fills[n].keys()) for n in candidate_nets},
+            layer_order=stackup.names,
+            default_net=default_net,
+            e1_label=group_label(es1), e2_label=group_label(es2),
+            contact1=group_contact(es1), contact2=group_contact(es2),
+            buildup_layers=sorted(buildups.keys()),
+        )
+        if selection is None:
+            print("cancelled")
+            return
+
+        if selection.contact1 != "auto":
+            for e in es1:
+                e.contact = selection.contact1
+        if selection.contact2 != "auto":
+            for e in es2:
+                e.contact = selection.contact2
+        if selection.cell_um is not None:
+            config.CELL_UM_OVERRIDE = selection.cell_um
+
+        try:
+            problem = board_io.build_problem(
+                board, selection.net, selection.layers, es1, es2, stackup,
+                fills,
+                buildups=(buildups if selection.include_buildup else None),
+                extra_cu_um=selection.extra_cu_um)
+            outdir = report.make_output_dir(board_io.board_dir(board))
+        except ApiError as e:
+            raise UserFacingError(f"KiCad API error: {e}")
+
+        report.write_geometry_dump(outdir, problem)
+        pipeline.run(problem, outdir, show=True, i_test=selection.current_a,
+                     freq_hz=selection.freq_hz,
+                     contact_model=selection.contact_model)
+    except UserFacingError as e:
+        _fail(str(e), outdir)
+    except Exception:
+        _fail(traceback.format_exc(), outdir)
+
+
+if __name__ == "__main__":
+    main()

fill_resistance/pipeline.py

@@ -0,0 +1,51 @@
+"""Geometry-in -> results-out pipeline shared by the KiCad entrypoint and
+the offline standalone runner."""
+from __future__ import annotations
+
+from pathlib import Path
+
+from . import config, plots, raster, report, solver
+from .geometry import Problem
+from .solver import Result
+
+
+def run(problem: Problem, outdir: Path | None, show: bool = True,
+        i_test: float | None = None, freq_hz: float = 0.0,
+        contact_model: str | None = None) -> Result:
+    if i_test is None:
+        i_test = config.TEST_CURRENT_A
+    h = raster.choose_cell_size(problem.copper_bbox(), len(problem.layers))
+    print(f"rasterizing {len(problem.layers)} layer(s) at cell size "
+          f"{h / 1000:.1f} um ...")
+    stack = raster.rasterize_stack(problem, h)
+    print(f"grid {stack.shape2d[1]}x{stack.shape2d[0]}x{stack.nlayers}, "
+          f"{int(stack.masks.sum())} copper cells, {len(problem.vias)} "
+          f"via/pad barrel(s)")
+
+    e1, e2 = raster.electrode_masks(stack, problem)
+    parts1, parts2 = raster.electrode_partition(stack, problem)
+
+    print(f"solving @ {i_test:g} A"
+          + (f", {freq_hz:g} Hz" if freq_hz > 0 else " DC") + " ...")
+    result = solver.run_solve(problem, stack, e1, e2, i_test, freq_hz,
+                              contact_model, parts1, parts2)
+    for prefix, pcs in (("P", result.part_currents1),
+                        ("N", result.part_currents2)):
+        for i, (label, amps) in enumerate(pcs):
+            print(f"  {prefix}{i + 1} ({label}): {amps:.4g} A "
+                  f"({100 * amps / i_test:.1f}%)")
+
+    if outdir is not None:
+        outdir.mkdir(parents=True, exist_ok=True)
+        report.write_summary(outdir, problem, stack, result)
+    print(report.result_line(result, problem, stack))
+
+    figs = [
+        (plots.fig_raster(stack, e1, e2, problem, result), "1_raster_map"),
+        (plots.fig_potential(result, stack, e1, e2, problem), "2_potential"),
+        (plots.fig_current(result, stack, e1, e2, problem),
+         "3_current_density"),
+        (plots.fig_power(result, stack, e1, e2, problem), "4_power_density"),
+    ]
+    plots.save_and_show(figs, outdir, show=show)
+    return result

fill_resistance/plots.py

@@ -0,0 +1,391 @@
+"""Figures: per-layer rasterized maps, potential, current density, power
+density, and the error figure. PNGs are saved BEFORE any window opens.
+
+Backend: interactive if a GUI toolkit exists (tkinter, else Qt), else Agg
+with os.startfile on the saved PNGs so results are never silent.
+"""
+from __future__ import annotations
+
+import os
+import textwrap
+from pathlib import Path
+
+import matplotlib
+import numpy as np
+
+
+def _pick_backend():
+    """matplotlib.use() is lazy and 'succeeds' for backends whose GUI
+    toolkit is missing (KiCad's Python has no tkinter), so probe the
+    toolkits explicitly."""
+    try:
+        import tkinter  # noqa: F401
+        return "TkAgg"
+    except Exception:
+        pass
+    for qt in ("PySide6", "PyQt6", "PyQt5", "PySide2"):
+        try:
+            __import__(qt)
+            return "QtAgg" if qt in ("PySide6", "PyQt6") else "Qt5Agg"
+        except Exception:
+            continue
+    return None
+
+
+INTERACTIVE_BACKEND = _pick_backend()
+matplotlib.use(INTERACTIVE_BACKEND or "Agg")
+
+import matplotlib.pyplot as plt  # noqa: E402  (after backend selection)
+from matplotlib.colors import ListedColormap, LogNorm  # noqa: E402
+from matplotlib.patches import Patch  # noqa: E402
+
+from . import config  # noqa: E402
+
+_BG = "#f5f3f0"
+_COPPER = "#c98b4e"
+_E1_COLOR = "#c8385a"
+_E2_COLOR = "#2f6fb0"
+_VIA_COLOR = "#2d6b45"
+_SOLDER = "#9aa3ad"      # tin-gray: solder buildup areas
+_INK = "#3a3a3a"
+_GRID_INK = "#b8b4ae"
+
+
+def _fmt_si(value: float, unit: str) -> str:
+    for scale, prefix in ((1.0, ""), (1e-3, "m"), (1e-6, "µ")):
+        if abs(value) >= scale:
+            return f"{value / scale:.4g} {prefix}{unit}"
+    return f"{value:.3g} {unit}"
+
+
+def _suptitle(problem, stack, result=None) -> str:
+    ny, nx = stack.shape2d
+    parts = []
+    if result is not None:
+        parts.append(f"R = {result.R_ohm * 1000:.4g} mΩ")
+        parts.append(f"P = {_fmt_si(result.P_total, 'W')} @ "
+                     f"{result.i_test:g} A")
+        if result.freq_hz > 0:
+            parts.append(f"f = {result.freq_hz / 1e3:g} kHz "
+                         f"(δ={result.skin_depth_um:.0f} µm, lower bound)")
+    parts.append(problem.net_name)
+    parts.append(f"{nx}×{ny}×{stack.nlayers} @ {stack.h_nm / 1000:.0f} µm")
+    return "  |  ".join(parts)
+
+
+def _layer_fig(stack, window_title: str):
+    L = stack.nlayers
+    ny, nx = stack.shape2d
+    aspect = ny / nx
+    w = 9.5
+    row_h = min(max(w * aspect * 0.9 + 0.6, 1.8), 8.5 / L)
+    fig, axes = plt.subplots(L, 1, figsize=(w, row_h * L + 1.4),
+                             sharex=True, sharey=True, squeeze=False)
+    axes = axes[:, 0]
+    if INTERACTIVE_BACKEND:
+        fig.canvas.manager.set_window_title(window_title)
+    for ax, name in zip(axes, stack.layer_names):
+        ax.set_ylabel(f"{name}\ny [mm]", fontsize=8)
+        ax.tick_params(colors=_INK, labelsize=8)
+        for s in ax.spines.values():
+            s.set_color(_GRID_INK)
+    axes[-1].set_xlabel("x [mm]")
+    return fig, axes
+
+
+def _electrode_labels(ax, stack, e1_l, e2_l):
+    """Label each connected contact part (multi-part terminals get one
+    label per island, largest first, up to 4)."""
+    from scipy import ndimage
+    for e, label, color in ((e1_l, "V+", _E1_COLOR), (e2_l, "V−", _E2_COLOR)):
+        if not e.any():
+            continue
+        labels, n = ndimage.label(e)
+        sizes = ndimage.sum_labels(np.ones_like(labels), labels,
+                                   range(1, n + 1))
+        order = np.argsort(sizes)[::-1][:4] + 1
+        for comp in order:
+            ii, jj = np.nonzero(labels == comp)
+            cx = (stack.x0_nm + (jj.mean() + 0.5) * stack.h_nm) * 1e-6
+            cy = (stack.y0_nm + (ii.mean() + 0.5) * stack.h_nm) * 1e-6
+            ax.annotate(label, (cx, cy), xytext=(0, 0),
+                        textcoords="offset points", color="white",
+                        fontsize=9, fontweight="bold", ha="center",
+                        va="center",
+                        bbox=dict(boxstyle="round,pad=0.2", fc=color,
+                                  ec="none", alpha=0.9))
+
+
+def _via_markers(ax, problem, layer):
+    xs = [v.x * 1e-6 for v in problem.vias if v.spans(layer.z_nm)]
+    ys = [v.y * 1e-6 for v in problem.vias if v.spans(layer.z_nm)]
+    if xs:
+        ax.plot(xs, ys, ".", ms=2.5, color=_VIA_COLOR, alpha=0.7)
+
+
+def area_tag(sign: str, index: int) -> str:
+    """Short injection-area tag: P1, P2, ... for V+; N1, N2, ... for V-."""
+    return f"{'P' if sign == '+' else 'N'}{index + 1}"
+
+
+def _injection_area_labels(ax, li, layer_name, problem, result):
+    """Mark every injection area with its short tag (currents live in
+    the legend)."""
+    groups = ((problem.electrodes1, "+", _E1_COLOR),
+              (problem.electrodes2, "-", _E2_COLOR))
+    for parts, sign, color in groups:
+        for i, el in enumerate(parts):
+            if el.contact != "all" and el.contact != layer_name:
+                continue
+            cx = (el.rect.x0 + el.rect.x1) / 2e6
+            cy = (el.rect.y0 + el.rect.y1) / 2e6
+            ax.annotate(area_tag(sign, i), (cx, cy), xytext=(0, 0),
+                        textcoords="offset points", color="white",
+                        fontsize=8, fontweight="bold", ha="center",
+                        va="center",
+                        bbox=dict(boxstyle="round,pad=0.15", fc=color,
+                                  ec="none", alpha=0.9))
+
+
+def fig_raster(stack, e1, e2, problem, result=None):
+    fig, axes = _layer_fig(stack, "Fill Resistance - rasterized map")
+    cmap = ListedColormap([_BG, _COPPER, _E1_COLOR, _E2_COLOR, _SOLDER])
+    has_buildup = stack.buildup is not None and stack.buildup.any()
+    for li, ax in enumerate(axes):
+        codes = np.zeros(stack.shape2d, dtype=np.uint8)
+        codes[stack.masks[li]] = 1
+        if has_buildup:
+            codes[stack.buildup[li]] = 4
+        codes[e1[li]] = 2
+        codes[e2[li]] = 3
+        ax.imshow(codes, cmap=cmap, vmin=0, vmax=4, origin="upper",
+                  extent=stack.extent_mm(), interpolation="nearest")
+        _via_markers(ax, problem, problem.layers[li])
+        if result is not None and (result.part_currents1
+                                   or result.part_currents2):
+            _injection_area_labels(ax, li, stack.layer_names[li], problem,
+                                   result)
+        else:
+            _electrode_labels(ax, stack, e1[li], e2[li])
+    handles = [Patch(fc=_COPPER, label="copper"),
+               Patch(fc=_VIA_COLOR, label="vias")]
+    if has_buildup:
+        handles.append(Patch(
+            fc=_SOLDER,
+            label=f"solder buildup "
+                  f"({problem.solder_thickness_nm / 1000:.0f} µm"
+                  + (f" + {problem.extra_cu_nm / 1000:.0f} µm Cu"
+                     if problem.extra_cu_nm else "") + ")"))
+    if result is not None and (result.part_currents1
+                               or result.part_currents2):
+        entries = ([("+", _E1_COLOR, i, amps)
+                    for i, (_, amps) in enumerate(result.part_currents1)]
+                   + [("-", _E2_COLOR, i, amps)
+                      for i, (_, amps) in enumerate(result.part_currents2)])
+        shown = entries[:14]
+        for sign, color, i, amps in shown:
+            handles.append(Patch(
+                fc=color,
+                label=f"{area_tag(sign, i)}: {amps:.3g} A "
+                      f"({100 * amps / result.i_test:.0f}%)"))
+        if len(entries) > len(shown):
+            handles.append(Patch(fc="#00000000",
+                                 label=f"... +{len(entries) - len(shown)} "
+                                       f"more in summary.txt"))
+    else:
+        handles += [Patch(fc=_E1_COLOR, label="V+"),
+                    Patch(fc=_E2_COLOR, label="V−")]
+    axes[0].legend(handles=handles, loc="upper right", fontsize=7,
+                   framealpha=0.9)
+    fig.suptitle("Rasterized fill + electrodes  |  "
+                 + _suptitle(problem, stack, result), fontsize=10, color=_INK)
+    fig.tight_layout()
+    return fig
+
+
+def fig_potential(result, stack, e1, e2, problem):
+    fig, axes = _layer_fig(stack, "Fill Resistance - potential")
+    vmax = float(np.nanmax(result.V))
+    unit, scale = ("mV", 1e3) if vmax < 0.1 else ("V", 1.0)
+    cmap = matplotlib.colormaps[config.CMAP_POTENTIAL].copy()
+    cmap.set_bad(_BG)
+    im = None
+    for li, ax in enumerate(axes):
+        vs = result.V[li] * scale
+        im = ax.imshow(vs, cmap=cmap, vmin=0, vmax=vmax * scale,
+                       origin="upper", extent=stack.extent_mm(),
+                       interpolation="nearest")
+        if np.isfinite(vs).sum() > 4:
+            ext = stack.extent_mm()
+            ny, nx = stack.shape2d
+            xs = np.linspace(ext[0], ext[1], nx, endpoint=False)
+            xs += (xs[1] - xs[0]) / 2
+            ys = np.linspace(ext[3], ext[2], ny, endpoint=False)
+            ys += (ys[1] - ys[0]) / 2
+            with np.errstate(invalid="ignore"):
+                ax.contour(xs, ys, vs, levels=15, colors="white",
+                           linewidths=0.4, alpha=0.5)
+        _electrode_labels(ax, stack, e1[li], e2[li])
+    cb = fig.colorbar(im, ax=axes, shrink=0.85)
+    cb.set_label(f"potential [{unit}] @ {result.i_test:g} A", fontsize=9)
+    fig.suptitle("Potential  |  " + _suptitle(problem, stack, result),
+                 fontsize=10, color=_INK)
+    return fig
+
+
+def _field_fig(result, stack, e1, e2, problem, data3, cmap_name, dyn_range,
+               label, title, window):
+    """Shared per-layer LogNorm field figure (current, power)."""
+    fig, axes = _layer_fig(stack, window)
+    vmax = float(np.nanmax(data3))
+    cmap = matplotlib.colormaps[cmap_name].copy()
+    cmap.set_bad(_BG)
+    if config.LOG_CURRENT_SCALE and vmax > 0:
+        norm = LogNorm(vmin=vmax / dyn_range, vmax=vmax)
+    else:
+        norm = None
+    im = None
+    for li, ax in enumerate(axes):
+        d = data3[li]
+        shown = np.clip(d, vmax / dyn_range, None) if norm is not None else d
+        im = ax.imshow(shown, cmap=cmap, norm=norm, origin="upper",
+                       extent=stack.extent_mm(), interpolation="nearest")
+        _electrode_labels(ax, stack, e1[li], e2[li])
+    if vmax > 0:
+        li, i, j = np.unravel_index(np.nanargmax(data3), data3.shape)
+        mx = (stack.x0_nm + (j + 0.5) * stack.h_nm) * 1e-6
+        my = (stack.y0_nm + (i + 0.5) * stack.h_nm) * 1e-6
+        axes[li].plot(mx, my, "o", ms=9, mfc="none", mec="white", mew=1.4)
+        axes[li].annotate(f"max {vmax:.3g}", (mx, my), xytext=(10, -10),
+                          textcoords="offset points", color="white",
+                          fontsize=8,
+                          bbox=dict(boxstyle="round,pad=0.2", fc="#00000088",
+                                    ec="none"))
+    cb = fig.colorbar(im, ax=axes, shrink=0.85)
+    cb.set_label(label, fontsize=9)
+    fig.suptitle(title + "  |  " + _suptitle(problem, stack, result),
+                 fontsize=10, color=_INK)
+    return fig, axes
+
+
+def fig_current(result, stack, e1, e2, problem):
+    fig, axes = _field_fig(
+        result, stack, e1, e2, problem, result.Jmag * 1e-6,
+        config.CMAP_CURRENT, config.CURRENT_DYNAMIC_RANGE,
+        f"|J| [A/mm²] @ {result.i_test:g} A",
+        "Current density (log)", "Fill Resistance - current density")
+    # mark the hottest via
+    if result.via_reports:
+        v = result.via_reports[0]
+        for ax in axes:
+            ax.plot(v.x_mm, v.y_mm, "s", ms=7, mfc="none", mec="#7fe0a8",
+                    mew=1.2)
+        axes[0].annotate(
+            f"hottest via {v.current_a:.3g} A", (v.x_mm, v.y_mm),
+            xytext=(10, 10), textcoords="offset points", color="white",
+            fontsize=8,
+            bbox=dict(boxstyle="round,pad=0.2", fc="#2d6b45", ec="none"))
+    return fig
+
+
+def fig_power(result, stack, e1, e2, problem):
+    # W/m^2 -> W/mm^2
+    fig, axes = _field_fig(
+        result, stack, e1, e2, problem, result.Parea * 1e-6,
+        config.CMAP_POWER, config.POWER_DYNAMIC_RANGE,
+        f"p [W/mm²] @ {result.i_test:g} A",
+        "Power density (log)", "Fill Resistance - power density")
+    for li, ax in enumerate(axes):
+        ax.set_title(f"P({stack.layer_names[li]}) = "
+                     f"{_fmt_si(result.P_layers[li], 'W')}",
+                     fontsize=8, color=_INK, loc="right", pad=2)
+    return fig
+
+
+def fig_error(message: str):
+    fig, ax = plt.subplots(figsize=(9, 4.5))
+    ax.axis("off")
+    ax.set_title("Fill Resistance — ERROR", color="#b02a2a",
+                 fontsize=14, fontweight="bold", loc="left")
+    wrapped = "\n".join(
+        textwrap.fill(line, width=90) for line in message.splitlines()
+    )
+    ax.text(0.0, 0.95, wrapped, family="monospace", fontsize=9,
+            va="top", ha="left", color=_INK, transform=ax.transAxes)
+    fig.tight_layout()
+    return fig
+
+
+def _resolve_label_overlaps(fig):
+    """Measure every annotation's rendered box and greedily push
+    overlapping labels upward until nothing collides. Runs on the real
+    renderer, so it handles any font/DPI."""
+    from matplotlib.text import Annotation
+    try:
+        fig.canvas.draw()
+        renderer = fig.canvas.get_renderer()
+    except Exception:
+        return
+    for ax in fig.axes:
+        anns = [c for c in ax.get_children() if isinstance(c, Annotation)]
+        placed = []
+        for a in sorted(anns, key=lambda t: t.get_window_extent(renderer).x0):
+            try:
+                bb = a.get_window_extent(renderer)
+            except Exception:
+                continue
+            guard = 50
+            while guard > 0:
+                hit = next((p for p in placed if bb.overlaps(p)), None)
+                if hit is None:
+                    break
+                push_px = (hit.y1 - bb.y0) + 3.0
+                dx, dy = a.xyann
+                a.xyann = (dx, dy + push_px * 72.0 / fig.dpi)
+                bb = a.get_window_extent(renderer)
+                guard -= 1
+            placed.append(bb)
+
+
+def _raise_windows():
+    """Best effort: bring plot windows in front of KiCad (windows spawned
+    by a background process tend to open behind)."""
+    for num in plt.get_fignums():
+        try:
+            win = plt.figure(num).canvas.manager.window
+            if hasattr(win, "attributes"):          # Tk
+                win.attributes("-topmost", True)
+                win.after(300, lambda w=win: w.attributes("-topmost", False))
+            else:                                    # Qt
+                win.raise_()
+                win.activateWindow()
+        except Exception:
+            pass
+
+
+def save_and_show(figs_named: list[tuple], outdir: Path | None,
+                  show: bool = True) -> list[Path]:
+    """figs_named: [(figure, basename), ...]. Saves first, then shows."""
+    saved = []
+    for fig, _ in figs_named:
+        _resolve_label_overlaps(fig)
+    if outdir is not None:
+        outdir.mkdir(parents=True, exist_ok=True)
+        for fig, name in figs_named:
+            p = outdir / f"{name}.png"
+            fig.savefig(p, dpi=config.DPI, facecolor="white",
+                        bbox_inches="tight")
+            saved.append(p)
+            print(f"saved {p}")
+    if show and config.INTERACTIVE:
+        if INTERACTIVE_BACKEND:
+            _raise_windows()
+            plt.show()
+        else:
+            for p in saved:
+                try:
+                    os.startfile(p)  # windows: open in default viewer
+                except Exception:
+                    pass
+    plt.close("all")
+    return saved

fill_resistance/raster.py

@@ -0,0 +1,263 @@
+"""Rasterization of the fill polygons onto a shared multi-layer grid, and
+electrode mask construction.
+
+Grid convention: layer l, row i, col j maps to the cell center
+    x = x0_nm + (j + 0.5) * h_nm
+    y = y0_nm + (i + 0.5) * h_nm
+in KiCad board coordinates (y grows down). Row 0 is the minimum-y row,
+the TOP of the board as drawn in the editor; plots use origin='upper'.
+All layers share the same frame, so cell (i, j) is vertically aligned
+across layers (via links connect equal (i, j) on different layers).
+
+Connectivity restriction lives in solver.py: it needs the via edges.
+"""
+from __future__ import annotations
+
+import math
+from dataclasses import dataclass
+
+import numpy as np
+from matplotlib.path import Path as MplPath
+from scipy import ndimage
+
+from . import config
+from .errors import ElectrodeError, GridSizeError
+from .geometry import Electrode, Problem, Rect
+
+# 4-connectivity: matches the in-plane 5-point stencil of the solver
+_STRUCT4 = ndimage.generate_binary_structure(2, 1)
+
+
+@dataclass
+class RasterStack:
+    masks: np.ndarray         # bool (L, ny, nx), True = copper
+    x0_nm: float              # grid origin (outer corner of cell [., 0, 0])
+    y0_nm: float
+    h_nm: float
+    layer_names: list[str]
+    buildup: np.ndarray | None = None   # bool (L, ny, nx): solder buildup
+                                        # (mask opening ∩ copper)
+
+    @property
+    def nlayers(self) -> int:
+        return self.masks.shape[0]
+
+    @property
+    def shape2d(self) -> tuple[int, int]:
+        return self.masks.shape[1:]
+
+    def cell_centers(self, i0: int, i1: int, j0: int, j1: int):
+        xs = self.x0_nm + (np.arange(j0, j1) + 0.5) * self.h_nm
+        ys = self.y0_nm + (np.arange(i0, i1) + 0.5) * self.h_nm
+        return np.meshgrid(xs, ys)
+
+    def cell_of(self, x_nm: float, y_nm: float) -> tuple[int, int] | None:
+        """(i, j) of the cell containing the point, or None if outside."""
+        ny, nx = self.shape2d
+        j = int((x_nm - self.x0_nm) / self.h_nm)
+        i = int((y_nm - self.y0_nm) / self.h_nm)
+        if 0 <= i < ny and 0 <= j < nx:
+            return i, j
+        return None
+
+    def extent_mm(self) -> tuple[float, float, float, float]:
+        """imshow extent (left, right, bottom, top) for origin='upper',
+        y axis in board orientation (increasing downward)."""
+        ny, nx = self.shape2d
+        return (
+            self.x0_nm * 1e-6,
+            (self.x0_nm + nx * self.h_nm) * 1e-6,
+            (self.y0_nm + ny * self.h_nm) * 1e-6,
+            self.y0_nm * 1e-6,
+        )
+
+
+def choose_cell_size(bbox_nm: tuple[int, int, int, int], nlayers: int) -> float:
+    """Pick the cell size h [nm]; TARGET_CELLS counts TOTAL cells across
+    all layers. Raise if the grid would exceed HARD_MAX_CELLS."""
+    x0, y0, x1, y1 = bbox_nm
+    w, ht = float(x1 - x0), float(y1 - y0)
+    if w <= 0 or ht <= 0:
+        raise GridSizeError("Copper geometry has a degenerate bounding box.")
+
+    if config.CELL_UM_OVERRIDE is not None:
+        h = config.CELL_UM_OVERRIDE * 1000.0
+    else:
+        h = math.sqrt(w * ht * nlayers / config.TARGET_CELLS)
+        h = min(max(h, config.MIN_CELL_UM * 1000.0), config.MAX_CELL_UM * 1000.0)
+
+    ncells = math.ceil(w / h) * math.ceil(ht / h) * nlayers
+    if ncells > config.HARD_MAX_CELLS:
+        raise GridSizeError(
+            f"Grid would need ~{ncells / 1e6:.1f} M cells over {nlayers} "
+            f"layer(s) at cell size {h / 1000:.0f} um (limit "
+            f"{config.HARD_MAX_CELLS / 1e6:.0f} M). Raise MAX_CELL_UM / "
+            f"CELL_UM_OVERRIDE in config.py, deselect layers, or measure a "
+            f"smaller region."
+        )
+    return h
+
+
+def _paint_ring(stack: RasterStack, ring: np.ndarray, value: bool,
+                target: np.ndarray) -> None:
+    """Set target (2D) cells whose center lies inside ring to `value`,
+    testing only cells within the ring's bbox (cheap for small holes)."""
+    ny, nx = stack.shape2d
+    h = stack.h_nm
+    j0 = max(0, int((ring[:, 0].min() - stack.x0_nm) / h) - 1)
+    j1 = min(nx, int((ring[:, 0].max() - stack.x0_nm) / h) + 2)
+    i0 = max(0, int((ring[:, 1].min() - stack.y0_nm) / h) - 1)
+    i1 = min(ny, int((ring[:, 1].max() - stack.y0_nm) / h) + 2)
+    if i0 >= i1 or j0 >= j1:
+        return
+    xg, yg = stack.cell_centers(i0, i1, j0, j1)
+    pts = np.column_stack([xg.ravel(), yg.ravel()])
+    # Path(closed=True) treats the LAST vertex as the CLOSEPOLY dummy, so
+    # the first vertex must be appended or the ring loses its last corner
+    verts = np.vstack([ring, ring[:1]])
+    inside = MplPath(verts, closed=True).contains_points(pts)
+    inside = inside.reshape(i1 - i0, j1 - j0)
+    sub = target[i0:i1, j0:j1]
+    sub[inside] = value
+
+
+def rasterize_stack(problem: Problem, h_nm: float) -> RasterStack:
+    """Rasterize every included layer onto one shared frame."""
+    x0, y0, x1, y1 = problem.copper_bbox()
+    m = config.MARGIN_CELLS
+    nx = math.ceil((x1 - x0) / h_nm) + 2 * m
+    ny = math.ceil((y1 - y0) / h_nm) + 2 * m
+    stack = RasterStack(
+        masks=np.zeros((len(problem.layers), ny, nx), dtype=bool),
+        x0_nm=x0 - m * h_nm,
+        y0_nm=y0 - m * h_nm,
+        h_nm=h_nm,
+        layer_names=problem.layer_names,
+    )
+    for li, layer in enumerate(problem.layers):
+        for poly in layer.polygons:
+            pmask = np.zeros((ny, nx), dtype=bool)
+            _paint_ring(stack, poly.outline, True, pmask)
+            for hole in poly.holes:
+                _paint_ring(stack, hole, False, pmask)
+            stack.masks[li] |= pmask
+
+    if problem.buildups:
+        stack.buildup = np.zeros_like(stack.masks)
+        index = {name: li for li, name in enumerate(stack.layer_names)}
+        for b in problem.buildups:
+            li = index.get(b.layer_name)
+            if li is None:
+                continue
+            for poly in b.polygons:
+                pmask = np.zeros((ny, nx), dtype=bool)
+                _paint_ring(stack, poly.outline, True, pmask)
+                for hole in poly.holes:
+                    _paint_ring(stack, hole, False, pmask)
+                stack.buildup[li] |= pmask
+        stack.buildup &= stack.masks        # solder wets exposed copper only
+    return stack
+
+
+def _rect_cells(stack: RasterStack, rect: Rect) -> np.ndarray:
+    """Bool (ny, nx) mask of cells whose center lies inside the rectangle."""
+    ny, nx = stack.shape2d
+    h = stack.h_nm
+    out = np.zeros((ny, nx), dtype=bool)
+    j0 = max(0, int(math.ceil((rect.x0 - stack.x0_nm) / h - 0.5)))
+    j1 = min(nx, int(math.floor((rect.x1 - stack.x0_nm) / h - 0.5)) + 1)
+    i0 = max(0, int(math.ceil((rect.y0 - stack.y0_nm) / h - 0.5)))
+    i1 = min(ny, int(math.floor((rect.y1 - stack.y0_nm) / h - 0.5)) + 1)
+    if i0 < i1 and j0 < j1:
+        out[i0:i1, j0:j1] = True
+    return out
+
+
+def _electrode_cells2d(stack: RasterStack, e: Electrode) -> np.ndarray:
+    """2D footprint of the electrode shape (pad polygons or rectangle)."""
+    if e.polygons:
+        cells = np.zeros(stack.shape2d, dtype=bool)
+        for poly in e.polygons:
+            pm = np.zeros(stack.shape2d, dtype=bool)
+            _paint_ring(stack, poly.outline, True, pm)
+            for hole in poly.holes:
+                _paint_ring(stack, hole, False, pm)
+            cells |= pm
+        if not cells.any():
+            # shape smaller than one grid cell (small pad): use the cell
+            # containing its center
+            r = e.rect
+            c = stack.cell_of((r.x0 + r.x1) / 2, (r.y0 + r.y1) / 2)
+            if c is not None:
+                cells[c] = True
+        return cells
+    return _rect_cells(stack, e.rect)
+
+
+def electrode_masks(stack: RasterStack, problem: Problem
+                    ) -> tuple[np.ndarray, np.ndarray]:
+    """Terminal mask = OR over its parts; part = shape ∩ copper on the
+    part's contact layer(s). contact 'all' = every included layer (bolted
+    lug / through pad); a layer name = that layer only. Every part must
+    individually land on copper (clear feedback). V+/V- must not overlap;
+    touching is checked later, only for the equipotential contact model."""
+    def build(parts: list[Electrode], which: str) -> np.ndarray:
+        e = np.zeros_like(stack.masks)
+        for el in parts:
+            cells2d = _electrode_cells2d(stack, el)
+            part = np.zeros_like(stack.masks)
+            for li, name in enumerate(stack.layer_names):
+                if el.contact == "all" or el.contact == name:
+                    part[li] = cells2d & stack.masks[li]
+            if not part.any():
+                raise ElectrodeError(
+                    f"A {which} contact part ({el.label}) does not overlap "
+                    f"any copper of the selected fill on contact layer(s) "
+                    f"'{el.contact}' (or is smaller than one grid cell)."
+                )
+            e |= part
+        if not e.any():
+            raise ElectrodeError(f"The {which} terminal has no contact parts.")
+        return e
+
+    e1 = build(problem.electrodes1, "V+")
+    e2 = build(problem.electrodes2, "V-")
+
+    if (e1 & e2).any():
+        raise ElectrodeError(
+            "The V+ and V- contact areas overlap on the copper grid. "
+            "Move them apart."
+        )
+    return e1, e2
+
+
+def electrode_partition(stack: RasterStack, problem: Problem
+                        ) -> tuple[list, list]:
+    """Per-part cell masks for both terminals, as [(label, mask3d), ...].
+    Cells covered by several overlapping parts are attributed to the
+    FIRST part (first-wins partition), so part currents sum exactly to
+    the terminal current."""
+    def build(parts: list[Electrode]) -> list:
+        out = []
+        claimed = np.zeros_like(stack.masks)
+        for el in parts:
+            cells2d = _electrode_cells2d(stack, el)
+            m = np.zeros_like(stack.masks)
+            for li, name in enumerate(stack.layer_names):
+                if el.contact == "all" or el.contact == name:
+                    m[li] = cells2d & stack.masks[li]
+            m &= ~claimed
+            claimed |= m
+            out.append((el.label, m))
+        return out
+
+    return build(problem.electrodes1), build(problem.electrodes2)
+
+
+def electrodes_touch(stack: RasterStack, e1: np.ndarray,
+                     e2: np.ndarray) -> str | None:
+    """Layer name where the terminals are 4-adjacent, or None."""
+    for li in range(stack.nlayers):
+        if (ndimage.binary_dilation(e1[li], structure=_STRUCT4) & e2[li]).any():
+            return stack.layer_names[li]
+    return None

fill_resistance/report.py

@@ -0,0 +1,146 @@
+"""Output directory, summary.txt, geometry dump, stdout one-liner."""
+from __future__ import annotations
+
+from datetime import datetime
+from pathlib import Path
+
+import numpy as np
+
+from . import config
+from .geometry import Problem, save_problem
+from .raster import RasterStack
+from .solver import Result
+
+
+def make_output_dir(board_dir: Path) -> Path:
+    stamp = datetime.now().strftime("%Y%m%d-%H%M%S")
+    out = Path(board_dir) / config.OUTPUT_DIRNAME / stamp
+    out.mkdir(parents=True, exist_ok=True)
+    return out
+
+
+def write_geometry_dump(outdir: Path, problem: Problem) -> Path:
+    p = outdir / "geometry_dump.json"
+    save_problem(problem, p)
+    return p
+
+
+def result_line(result: Result, problem: Problem, stack: RasterStack) -> str:
+    ny, nx = stack.shape2d
+    ac = (f" @ {result.freq_hz / 1e3:g} kHz (lower bound)"
+          if result.freq_hz > 0 else "")
+    return (f"R = {result.R_ohm * 1000:.4g} mOhm{ac}, "
+            f"P = {result.P_total:.4g} W @ {result.i_test:g} A "
+            f"(net {problem.net_name}, {'+'.join(stack.layer_names)}, "
+            f"grid {nx}x{ny}x{stack.nlayers}, cell {stack.h_nm / 1000:.0f} um)")
+
+
+def _electrode_line(e) -> str:
+    r = e.rect
+    return (f"{e.label:12s} contact={e.contact:8s} "
+            f"x [{r.x0 / 1e6:.2f}, {r.x1 / 1e6:.2f}] "
+            f"y [{r.y0 / 1e6:.2f}, {r.y1 / 1e6:.2f}] mm")
+
+
+def write_summary(outdir: Path, problem: Problem, stack: RasterStack,
+                  result: Result) -> Path:
+    ny, nx = stack.shape2d
+    info = result.solve_info
+    lines = [
+        "fill_resistance summary",
+        "=======================",
+        f"board:             {problem.board_path}",
+        f"net:               {problem.net_name}",
+        f"test current:      {result.i_test:g} A",
+        f"resistivity:       {problem.rho_ohm_m:.3e} ohm*m",
+        f"via plating:       {problem.plating_nm / 1000:.0f} um",
+        "",
+        (f"frequency:         "
+         + (f"{result.freq_hz:g} Hz (skin depth {result.skin_depth_um:.0f} um)"
+            if result.freq_hz > 0 else "DC")),
+        f"RESISTANCE:        {result.R_ohm * 1000:.6g} mOhm"
+        + (" (AC LOWER BOUND: lateral/proximity redistribution not modeled)"
+           if result.freq_hz > 0 else ""),
+        f"VOLTAGE DROP:      {result.R_ohm * result.i_test * 1000:.4g} mV "
+        f"@ {result.i_test:g} A",
+        f"TOTAL POWER:       {result.P_total:.6g} W @ {result.i_test:g} A",
+        f"  in vias:         {result.P_vias:.4g} W",
+        f"  power balance:   {result.power_balance_rel:.2e} (consistency)",
+        "",
+        "layers (top to bottom):",
+    ]
+    if problem.buildups and stack.buildup is not None:
+        eq_um = (problem.solder_thickness_nm / 1000
+                 * problem.rho_ohm_m / problem.solder_rho_ohm_m
+                 + problem.extra_cu_nm / 1000)
+        cell_mm2 = (stack.h_nm * 1e-6) ** 2
+        per_layer = {name: float(stack.buildup[li].sum()) * cell_mm2
+                     for li, name in enumerate(stack.layer_names)
+                     if stack.buildup[li].any()}
+        areas = ", ".join(f"{n}: {a:.0f} mm^2" for n, a in per_layer.items())
+        lines.insert(-1, f"solder buildup:    "
+                         f"{problem.solder_thickness_nm / 1000:.0f} um solder"
+                         + (f" + {problem.extra_cu_nm / 1000:.0f} um Cu"
+                            if problem.extra_cu_nm else "")
+                         + f" = {eq_um:.1f} um equivalent Cu  ({areas})")
+    for li, layer in enumerate(problem.layers):
+        ac = (f"  Rs_AC/Rs_DC={result.rs_ratios[li]:.2f}"
+              if result.freq_hz > 0 else "")
+        lines.append(
+            f"  {layer.layer_name:8s} t={layer.thickness_nm / 1000:5.1f} um "
+            f"z={layer.z_nm / 1000:7.1f} um  "
+            f"P={result.P_layers[li]:.4g} W  "
+            f"maxJ={float(np.nanmax(result.Jmag[li])) * 1e-6 if np.isfinite(result.Jmag[li]).any() else 0:.4g} A/mm^2"
+            + ac
+        )
+    lines += [
+        "",
+        f"grid:              {nx} x {ny} x {stack.nlayers} cells @ "
+        f"{stack.h_nm / 1000:.1f} um",
+        f"copper cells:      {int(stack.masks.sum())}",
+        f"free unknowns:     {result.n_free}",
+        f"solver:            {info.method}"
+        + (f", {info.iterations} iters, residual {info.residual:.2e}"
+           if info.iterations is not None else ""),
+        f"I1/I2 @ 1V:        {result.I1_a:.9g} / {result.I2_a:.9g} A "
+        f"(mismatch {result.mismatch_rel:.2e})",
+        f"timings [s]:       "
+        f"{', '.join(f'{k}={v:.2f}' for k, v in result.timings.items())}",
+        "",
+        f"contact model:     {result.contact_model}"
+        + ("  (uniform orthogonal injection; R is the upper contact bound)"
+           if result.contact_model == "uniform" else "  (ideal bonded lug)"),
+        f"terminals:",
+        f"  V+ ({len(problem.electrodes1)} injection area(s)):",
+        *(f"    {_electrode_line(e)}" for e in problem.electrodes1),
+        f"  V- ({len(problem.electrodes2)} injection area(s)):",
+        *(f"    {_electrode_line(e)}" for e in problem.electrodes2),
+    ]
+    if result.part_currents1 or result.part_currents2:
+        how = ("prescribed by area share (uniform model)"
+               if result.contact_model == "uniform"
+               else "computed flux (equipotential model)")
+        lines += ["", f"current per injection area @ {result.i_test:g} A "
+                      f"({how}):"]
+        for sign, pcs in (("+", result.part_currents1),
+                          ("-", result.part_currents2)):
+            for i, (label, amps) in enumerate(pcs):
+                tag = f"{'P' if sign == '+' else 'N'}{i + 1}"
+                lines.append(f"  {tag:4s} {label:24s} {amps:9.4g} A  "
+                             f"({100 * amps / result.i_test:5.1f}%)")
+    if result.via_reports:
+        n_shown = min(10, len(result.via_reports))
+        lines += [
+            "",
+            f"vias/pads carrying current (top {n_shown} of "
+            f"{len(result.via_reports)}, @ {result.i_test:g} A):",
+            "  x [mm]   y [mm]   kind  drill   I [A]     P [W]",
+        ]
+        for v in result.via_reports[:n_shown]:
+            lines.append(
+                f"  {v.x_mm:8.2f} {v.y_mm:8.2f} {v.kind:5s} "
+                f"{v.drill_mm:5.2f}  {v.current_a:8.4g}  {v.power_w:.4g}"
+            )
+    p = outdir / "summary.txt"
+    p.write_text("\n".join(lines), encoding="utf-8")
+    return p

fill_resistance/skin.py

@@ -0,0 +1,78 @@
+"""Skin-effect corrections: frequency-dependent effective sheet
+resistance of a copper foil and via-barrel wall.
+
+1D diffusion through the foil thickness (exact): with tau = (1+j)/delta,
+the internal impedance per square of a foil of thickness t is
+
+    one-sided field (plane over a return plane):  Zs = tau*rho * coth(tau*t)
+    two-sided field (isolated foil):              Zs = tau*rho/2 * coth(tau*t/2)
+
+Both reduce to rho/t at DC and to rho/delta (resp. rho/(2*delta)) at
+high frequency. R_AC = Re(Zs) is used as the effective sheet resistance.
+
+HONESTY NOTE (also in the README): only the through-thickness current
+crowding is modeled. Lateral redistribution (proximity effect - AC
+current following the minimum-inductance path) needs a magneto-
+quasistatic solve and is NOT captured; since the resistance-driven
+distribution is the minimum-dissipation one, the reported AC resistance
+is a rigorous LOWER BOUND at the given frequency.
+"""
+from __future__ import annotations
+
+import cmath
+import math
+
+MU0 = 4e-7 * math.pi
+
+
+def skin_depth_m(freq_hz: float, rho_ohm_m: float) -> float:
+    return math.sqrt(2.0 * rho_ohm_m / (2.0 * math.pi * freq_hz * MU0))
+
+
+def _coth(x: complex) -> complex:
+    return 1.0 / cmath.tanh(x)
+
+
+def sheet_resistance_ac(thickness_m: float, freq_hz: float,
+                        rho_ohm_m: float, sides: int = 1) -> float:
+    """Effective sheet resistance [ohm/sq] of a foil at freq_hz.
+    sides=1: field on one side (plane facing a return plane, conservative);
+    sides=2: symmetric field on both sides (isolated foil)."""
+    if freq_hz <= 0.0:
+        return rho_ohm_m / thickness_m
+    delta = skin_depth_m(freq_hz, rho_ohm_m)
+    tau = (1.0 + 1.0j) / delta
+    if sides == 2:
+        zs = tau * rho_ohm_m / 2.0 * _coth(tau * thickness_m / 2.0)
+    else:
+        zs = tau * rho_ohm_m * _coth(tau * thickness_m)
+    return zs.real
+
+
+def resistance_factor(thickness_m: float, freq_hz: float,
+                      rho_ohm_m: float, sides: int = 1) -> float:
+    """R_AC / R_DC of a foil (or barrel wall) of the given thickness."""
+    if freq_hz <= 0.0:
+        return 1.0
+    return (sheet_resistance_ac(thickness_m, freq_hz, rho_ohm_m, sides)
+            / (rho_ohm_m / thickness_m))
+
+
+def parse_frequency(text: str) -> float:
+    """'0', '100k', '1.5M', '142500' -> Hz. Empty/invalid -> 0 (DC)."""
+    t = text.strip().lower().replace(",", ".").removesuffix("hz").strip()
+    if not t:
+        return 0.0
+    mult = 1.0
+    if t.endswith("meg"):
+        mult, t = 1e6, t[:-3]
+    elif t.endswith("m"):
+        mult, t = 1e6, t[:-1]
+    elif t.endswith("k"):
+        mult, t = 1e3, t[:-1]
+    elif t.endswith("g"):
+        mult, t = 1e9, t[:-1]
+    try:
+        return max(0.0, float(t) * mult)
+    except ValueError:
+        return 0.0

fill_resistance/solver.py

@@ -0,0 +1,549 @@
+"""Coupled multi-layer finite-difference solver.
+
+Each included copper layer is a 2D 5-point sheet with per-layer face
+conductance sigma_s = t/rho [S] (square cells: independent of h); via and
+plated-through-pad barrels add vertical conductances between vertically
+aligned cells of the layers they span AND reach copper on. A barrel
+passing an antipad still bridges the layers above/below it with the full
+barrel length. At freq > 0 the per-layer sheet conductances and the
+barrel walls get the 1D skin-effect correction (see skin.py; AC results
+are a rigorous lower bound - lateral redistribution is not modeled).
+
+Two contact models for the terminals (each terminal = merged parts):
+
+- "uniform" (default): a conductor pressed onto the contact area injects
+  the current orthogonally with UNIFORM surface density: every contact
+  cell sources (sinks) I/N. The in-plane current density ramps across
+  the contact instead of being zero. The pure-Neumann system is grounded
+  at one V- cell (that cell's sink share is exactly the flux that exits
+  through the ground reference, so the solution equals the singular
+  system's). R = (<V over V+ cells> - <V over V- cells>) / I; because
+  the injection and averaging weights coincide, sum(edge powers) = I^2 R
+  holds exactly and remains the consistency check.
+
+- "equipotential": ideal bonded lug; contact cells are Dirichlet
+  (V+ = 1 V, V- = 0). R from the exact discrete electrode flux. Touching
+  terminals are rejected (a direct face would short the Dirichlet
+  regions); with "uniform" contacts touching is physically fine.
+
+The two models bracket a real contact: R_equipotential <= R_real <=
+R_uniform. Missing neighbors give no matrix term = insulated boundary.
+Current density per layer comes from face currents (np.gradient across
+the NaN staircase boundary would pollute the field). Power density per
+layer distributes each in-plane edge's dissipation half to each endpoint
+cell. All reported fields are rescaled to the test current I_test.
+"""
+from __future__ import annotations
+
+import time
+from dataclasses import dataclass, field
+
+import numpy as np
+from scipy import sparse
+from scipy.sparse import csgraph
+from scipy.sparse import linalg as sla
+
+from . import config, skin
+from .errors import ConnectivityError, ElectrodeError
+from .geometry import Problem
+from .raster import RasterStack, electrodes_touch
+
+
+@dataclass
+class SolveInfo:
+    method: str                   # "spsolve" | "cg+jacobi"
+    n_unknowns: int
+    iterations: int | None = None
+    residual: float | None = None
+
+
+@dataclass
+class Edges:
+    a: np.ndarray                 # int64 flat cell ids
+    b: np.ndarray
+    w: np.ndarray                 # conductance [S]
+    via_index: np.ndarray         # int32; -1 = in-plane edge
+
+
+@dataclass
+class ViaReport:
+    x_mm: float
+    y_mm: float
+    kind: str
+    drill_mm: float
+    current_a: float              # max barrel-segment current @ I_test
+    power_w: float                # total barrel dissipation @ I_test
+
+
+@dataclass
+class Result:
+    R_ohm: float
+    i_test: float
+    V: np.ndarray                 # (L, ny, nx) volts @ I_test, NaN off-copper
+    Jmag: np.ndarray              # (L, ny, nx) A/m^2 @ I_test
+    Parea: np.ndarray             # (L, ny, nx) W/m^2 @ I_test
+    layer_names: list[str]
+    P_total: float                # I_test^2 * R
+    P_layers: list[float]         # in-plane dissipation per layer @ I_test
+    P_vias: float                 # total barrel dissipation @ I_test
+    power_balance_rel: float      # |sum(edge powers) - I^2 R| / I^2 R
+    via_reports: list[ViaReport]  # sorted by current, descending
+    I1_a: float                   # electrode currents (unit drive)
+    I2_a: float
+    mismatch_rel: float
+    n_free: int
+    solve_info: SolveInfo
+    # per-part terminal currents @ I_test: [(label, amps), ...];
+    # computed flux for "equipotential", prescribed area share for "uniform"
+    part_currents1: list = field(default_factory=list)
+    part_currents2: list = field(default_factory=list)
+    contact_model: str = "uniform"
+    freq_hz: float = 0.0
+    skin_depth_um: float | None = None
+    rs_ratios: list[float] = field(default_factory=list)  # R_AC/R_DC per layer
+    timings: dict = field(default_factory=dict)
+
+
+def _shifts2d():
+    return [
+        ((slice(None), slice(None, -1)), (slice(None), slice(1, None))),
+        ((slice(None, -1), slice(None)), (slice(1, None), slice(None))),
+    ]
+
+
+def _sigma_2d(stack: RasterStack, li: int, sigma_layer: float,
+              sigma_buildup: float) -> np.ndarray | None:
+    """Per-cell sheet conductance for one layer, or None if uniform."""
+    if stack.buildup is None or sigma_buildup <= 0 \
+            or not stack.buildup[li].any():
+        return None
+    s = np.full(stack.shape2d, sigma_layer)
+    s[stack.buildup[li]] += sigma_buildup
+    return s
+
+
+def build_edges(stack: RasterStack, problem: Problem, sigmas: list[float],
+                via_factor: float = 1.0,
+                sigma_buildup: float = 0.0) -> Edges:
+    """All copper-copper conductances: in-plane faces + via barrels.
+    sigmas: effective (possibly AC) sheet conductance per layer;
+    via_factor: R_AC/R_DC of the barrel wall; sigma_buildup: extra sheet
+    conductance on solder-buildup cells. Faces between cells of unequal
+    conductance use the harmonic mean (series half-cells), which reduces
+    exactly to sigma for uniform regions."""
+    L, ny, nx = stack.masks.shape
+    plane = ny * nx
+    aa, bb, ww, vv = [], [], [], []
+
+    for li in range(L):
+        m = stack.masks[li]
+        sig = sigmas[li]
+        scell = _sigma_2d(stack, li, sig, sigma_buildup)
+        base = li * plane
+        for src, dst in _shifts2d():
+            pair = m[src] & m[dst]
+            ii, jj = np.nonzero(pair)
+            if src[0] == slice(None):            # horizontal: j, j+1
+                a = base + ii * nx + jj
+                b = a + 1
+            else:                                 # vertical: i, i+1
+                a = base + ii * nx + jj
+                b = a + nx
+            aa.append(a.astype(np.int64))
+            bb.append(b.astype(np.int64))
+            if scell is None:
+                ww.append(np.full(len(a), sig))
+            else:
+                s_a = scell[src][pair]
+                s_b = scell[dst][pair]
+                ww.append(2.0 * s_a * s_b / (s_a + s_b))
+            vv.append(np.full(len(a), -1, dtype=np.int32))
+
+    for vi, via in enumerate(problem.vias):
+        cell = stack.cell_of(via.x, via.y)
+        if cell is None:
+            continue
+        i, j = cell
+        present = [li for li, layer in enumerate(problem.layers)
+                   if via.spans(layer.z_nm) and stack.masks[li, i, j]]
+        for la, lb in zip(present[:-1], present[1:]):
+            length = problem.layers[lb].z_nm - problem.layers[la].z_nm
+            if length <= 0:
+                continue
+            r = via.barrel_resistance(length, problem.rho_ohm_m,
+                                      problem.plating_nm) * via_factor
+            aa.append(np.array([la * plane + i * nx + j], dtype=np.int64))
+            bb.append(np.array([lb * plane + i * nx + j], dtype=np.int64))
+            ww.append(np.array([1.0 / r]))
+            vv.append(np.array([vi], dtype=np.int32))
+
+    if not aa:
+        raise ConnectivityError("No copper found on the selected layers.")
+    return Edges(a=np.concatenate(aa), b=np.concatenate(bb),
+                 w=np.concatenate(ww), via_index=np.concatenate(vv))
+
+
+def connected_restrict(stack: RasterStack, e1: np.ndarray, e2: np.ndarray,
+                       edges: Edges) -> bool:
+    """Keep only components (through-plane AND through-via) touching both
+    terminals. Mutates stack.masks / e1 / e2. Returns True if anything
+    was dropped (caller must rebuild edges)."""
+    n = stack.masks.size
+    graph = sparse.coo_matrix(
+        (np.ones(len(edges.a)), (edges.a, edges.b)), shape=(n, n))
+    _, labels = csgraph.connected_components(graph, directed=False)
+    labels3 = labels.reshape(stack.masks.shape)
+    common = np.intersect1d(np.unique(labels3[e1]), np.unique(labels3[e2]))
+    if len(common) == 0:
+        raise ConnectivityError(
+            "The two terminals are not connected by the selected fill "
+            "layers (not even through vias). Check the layer selection and "
+            "that the fills are up to date."
+        )
+    keep = np.isin(labels3, common) & stack.masks
+    changed = bool((stack.masks & ~keep).any())
+    stack.masks &= keep
+    e1 &= keep
+    e2 &= keep
+    return changed
+
+
+def _assemble(state: np.ndarray, edges: Edges, rhs_extra: np.ndarray | None):
+    """Weighted-Laplacian assembly with Dirichlet elimination.
+    state: 0 off, 1 free, 2 Dirichlet@1V, 3 Dirichlet@0V.
+    rhs_extra: per-flat-cell current injection [A] added for free cells."""
+    n = state.size
+    sa, sb = state[edges.a], state[edges.b]
+    short = ((sa == 2) & (sb == 3)) | ((sa == 3) & (sb == 2))
+    if short.any():
+        n_via = int((edges.via_index[short] >= 0).sum())
+        raise ElectrodeError(
+            f"The terminals are directly connected by {int(short.sum())} "
+            f"conductance(s) ({n_via} via barrel(s)) without any free copper "
+            f"in between - move the contacts apart."
+        )
+
+    free = state == 1
+    n_free = int(free.sum())
+    if n_free == 0:
+        raise ElectrodeError(
+            "No free copper cells remain between the terminals - the "
+            "contacts cover the whole fill at this grid resolution."
+        )
+    idx = np.full(n, -1, dtype=np.int64)
+    idx[free] = np.arange(n_free)
+
+    diag = np.zeros(n_free)
+    rhs = np.zeros(n_free)
+    fa, fb = sa == 1, sb == 1
+    np.add.at(diag, idx[edges.a[fa]], edges.w[fa])
+    np.add.at(diag, idx[edges.b[fb]], edges.w[fb])
+    r1a = fa & (sb == 2)
+    r1b = fb & (sa == 2)
+    np.add.at(rhs, idx[edges.a[r1a]], edges.w[r1a])
+    np.add.at(rhs, idx[edges.b[r1b]], edges.w[r1b])
+    if rhs_extra is not None:
+        rhs += rhs_extra[free]
+
+    ff = fa & fb
+    rows = np.concatenate([idx[edges.a[ff]], idx[edges.b[ff]],
+                           np.arange(n_free)])
+    cols = np.concatenate([idx[edges.b[ff]], idx[edges.a[ff]],
+                           np.arange(n_free)])
+    vals = np.concatenate([-edges.w[ff], -edges.w[ff], diag])
+    A = sparse.coo_matrix((vals, (rows, cols)),
+                          shape=(n_free, n_free)).tocsr()
+    return A, rhs, idx
+
+
+def solve_system(A: sparse.csr_matrix, b: np.ndarray) -> tuple[np.ndarray, SolveInfo]:
+    n = A.shape[0]
+    if n <= config.SPSOLVE_MAX_UNKNOWNS:
+        x = sla.spsolve(A.tocsc(), b)
+        return x, SolveInfo(method="spsolve", n_unknowns=n)
+
+    # The matrix is SPD, so CG is guaranteed to converge. Jacobi is the
+    # only preconditioner in scipy that keeps the preconditioned operator
+    # SPD without a factorization that can break down at this scale.
+    d = A.diagonal()
+    M = sla.LinearOperator((n, n), lambda v: v / d)
+    iters = 0
+
+    def count(_):
+        nonlocal iters
+        iters += 1
+
+    try:
+        x, code = sla.cg(A, b, M=M, rtol=config.CG_TOL,
+                         maxiter=config.CG_MAXITER, callback=count)
+    except TypeError:  # scipy < 1.12 uses tol=
+        x, code = sla.cg(A, b, M=M, tol=config.CG_TOL,
+                         maxiter=config.CG_MAXITER, callback=count)
+    if code != 0:
+        raise RuntimeError(
+            f"CG did not converge in {config.CG_MAXITER} iterations "
+            f"(code {code}). Try a coarser grid or raise CG_MAXITER."
+        )
+    res = float(np.linalg.norm(b - A @ x) / np.linalg.norm(b))
+    return x, SolveInfo(method="cg+jacobi", n_unknowns=n, iterations=iters,
+                        residual=res)
+
+
+def _face_current_density(V2: np.ndarray, mask2: np.ndarray, sigma: float,
+                          h_m: float, t_m: float,
+                          sig2d: np.ndarray | None = None,
+                          rho: float | None = None) -> np.ndarray:
+    """|J| (A/m^2) for one layer from face currents; V2 in volts.
+    With a per-cell conductance map (buildup), face currents use the
+    harmonic mean and J is referenced to the conductance-equivalent
+    copper thickness t_eq = sigma_cell * rho (equals the geometric t for
+    plain DC copper)."""
+    ny, nx = mask2.shape
+    face_x = mask2[:, :-1] & mask2[:, 1:]
+    face_y = mask2[:-1, :] & mask2[1:, :]
+    if sig2d is None:
+        wx = wy = sigma
+        teq = np.full((ny, nx), t_m)
+    else:
+        wx = 2.0 * sig2d[:, :-1] * sig2d[:, 1:] / (sig2d[:, :-1] + sig2d[:, 1:])
+        wy = 2.0 * sig2d[:-1, :] * sig2d[1:, :] / (sig2d[:-1, :] + sig2d[1:, :])
+        teq = sig2d * rho
+    with np.errstate(invalid="ignore"):
+        Ix = np.where(face_x, (V2[:, :-1] - V2[:, 1:]) * wx, 0.0)
+        Iy = np.where(face_y, (V2[:-1, :] - V2[1:, :]) * wy, 0.0)
+    IxP = np.zeros((ny, nx + 1))
+    IxP[:, 1:nx] = Ix
+    IyP = np.zeros((ny + 1, nx))
+    IyP[1:ny, :] = Iy
+    Jx = 0.5 * (IxP[:, :-1] + IxP[:, 1:])
+    Jy = 0.5 * (IyP[:-1, :] + IyP[1:, :])
+    Jmag = np.hypot(Jx, Jy) / (h_m * teq)
+    Jmag[~mask2] = np.nan
+    return Jmag
+
+
+def _solve_equipotential(stack, e1, e2, edges):
+    """Dirichlet terminals at 1 V / 0 V. Returns (Vflat_unit, R, I1, I2,
+    mismatch, volts_per_amp, info). Fields at 1 V drive; scale by
+    i_test * R to get volts at I_test."""
+    if (layer := electrodes_touch(stack, e1, e2)) is not None:
+        raise ElectrodeError(
+            f"The terminals touch on {layer}. With the equipotential "
+            f"contact model at least one cell of copper must separate "
+            f"them; the uniform-injection model allows touching contacts."
+        )
+    state = np.zeros(stack.masks.size, dtype=np.uint8)
+    state[stack.masks.ravel()] = 1
+    state[e1.ravel()] = 2
+    state[e2.ravel()] = 3
+
+    A, rhs, idx = _assemble(state, edges, None)
+    x, info = solve_system(A, rhs)
+
+    Vflat = np.zeros(state.size)
+    Vflat[state == 2] = 1.0
+    Vflat[state == 1] = x
+
+    Ie = edges.w * (Vflat[edges.a] - Vflat[edges.b])
+    sa, sb = state[edges.a], state[edges.b]
+    I1 = float(Ie[sa == 2].sum() - Ie[sb == 2].sum())
+    I2 = float(Ie[sb == 3].sum() - Ie[sa == 3].sum())
+    mismatch = abs(I1 - I2) / max(abs(I1), abs(I2), 1e-300)
+    R = 1.0 / (0.5 * (I1 + I2))
+    return Vflat, R, I1, I2, mismatch, R, info
+
+
+def _solve_uniform(stack, e1, e2, edges):
+    """Uniform orthogonal injection: every contact cell sources (sinks)
+    1 A / N. Grounded at one V- cell. Returns like _solve_equipotential;
+    fields are at 1 A drive, so volts_per_amp = 1."""
+    n = stack.masks.size
+    e1f, e2f = e1.ravel(), e2.ravel()
+    n1, n2 = int(e1f.sum()), int(e2f.sum())
+
+    inj = np.zeros(n)
+    inj[e1f] = 1.0 / n1
+    inj[e2f] = -1.0 / n2
+
+    state = np.zeros(n, dtype=np.uint8)
+    state[stack.masks.ravel()] = 1
+    ground = int(np.flatnonzero(e2f)[0])
+    state[ground] = 3                       # single Dirichlet 0 V reference;
+    # its sink share is exactly the flux that exits through the reference,
+    # so the grounded solution equals the pure-Neumann one
+
+    A, rhs, idx = _assemble(state, edges, inj)
+    x, info = solve_system(A, rhs)
+
+    Vflat = np.zeros(n)
+    Vflat[state == 1] = x
+
+    v_plus = float(Vflat[e1f].mean())
+    v_minus = float(Vflat[e2f].mean())
+    R = (v_plus - v_minus) / 1.0
+    Vflat = Vflat - v_minus                 # display reference: <V-> = 0
+
+    # quality: KCL residual of the solved system
+    res = info.residual
+    if res is None:
+        res = float(np.linalg.norm(A @ x - rhs)
+                    / max(np.linalg.norm(rhs), 1e-300))
+    return Vflat, R, 1.0, 1.0, res, 1.0, info
+
+
+def _part_currents(parts, Ie, edges, e_flat, scale,
+                   i_test, contact_model, n_terminal_cells):
+    """Current through each contact part @ I_test. Equipotential: exact
+    discrete flux out of the part's cells (same-terminal internal edges
+    carry zero, opposite-terminal edges are forbidden). Uniform: the
+    injection is prescribed, so a part carries exactly its cell share."""
+    out = []
+    for label, mask3 in parts:
+        pf = mask3.ravel() & e_flat
+        n = int(pf.sum())
+        if contact_model == "uniform":
+            amps = i_test * n / max(n_terminal_cells, 1)
+        else:
+            ina = pf[edges.a]
+            inb = pf[edges.b]
+            amps = abs(float(Ie[ina].sum() - Ie[inb].sum())) * scale
+        out.append((label, amps))
+    return out
+
+
+def run_solve(problem: Problem, stack: RasterStack, e1: np.ndarray,
+              e2: np.ndarray, i_test: float, freq_hz: float = 0.0,
+              contact_model: str | None = None,
+              parts1: list | None = None,
+              parts2: list | None = None) -> Result:
+    timings = {}
+    L, ny, nx = stack.masks.shape
+    h_m = stack.h_nm * 1e-9
+    if contact_model is None:
+        contact_model = config.CONTACT_MODEL
+
+    # effective (AC) sheet conductances and barrel factor
+    sigmas = [
+        1.0 / skin.sheet_resistance_ac(
+            problem.layers[li].thickness_nm * 1e-9, freq_hz,
+            problem.rho_ohm_m, config.SKIN_SIDES)
+        for li in range(L)
+    ]
+    rs_ratios = [
+        skin.resistance_factor(problem.layers[li].thickness_nm * 1e-9,
+                               freq_hz, problem.rho_ohm_m, config.SKIN_SIDES)
+        for li in range(L)
+    ]
+    via_factor = skin.resistance_factor(problem.plating_nm * 1e-9, freq_hz,
+                                        problem.rho_ohm_m, sides=2)
+    sigma_buildup = 0.0
+    if problem.buildups and stack.buildup is not None \
+            and stack.buildup.any():
+        sigma_buildup = 1.0 / skin.sheet_resistance_ac(
+            problem.solder_thickness_nm * 1e-9, freq_hz,
+            problem.solder_rho_ohm_m, config.SKIN_SIDES)
+        if problem.extra_cu_nm > 0:
+            sigma_buildup += 1.0 / skin.sheet_resistance_ac(
+                problem.extra_cu_nm * 1e-9, freq_hz, problem.rho_ohm_m,
+                config.SKIN_SIDES)
+        eq_um = sigma_buildup * problem.rho_ohm_m * 1e6
+        print(f"solder buildup: {problem.solder_thickness_nm / 1000:.0f} um "
+              f"solder + {problem.extra_cu_nm / 1000:.0f} um Cu on "
+              f"{int(stack.buildup.sum())} cells "
+              f"(= {eq_um:.1f} um equivalent copper)")
+    if freq_hz > 0:
+        depth = skin.skin_depth_m(freq_hz, problem.rho_ohm_m)
+        print(f"AC @ {freq_hz:g} Hz: skin depth {depth * 1e6:.0f} um, "
+              f"per-layer Rs ratio "
+              f"{', '.join(f'{r:.2f}' for r in rs_ratios)}, "
+              f"via factor {via_factor:.2f}")
+
+    t0 = time.perf_counter()
+    edges = build_edges(stack, problem, sigmas, via_factor, sigma_buildup)
+    if connected_restrict(stack, e1, e2, edges):
+        edges = build_edges(stack, problem, sigmas, via_factor, sigma_buildup)
+    if stack.buildup is not None:
+        stack.buildup &= stack.masks
+    for _, m in (parts1 or []) + (parts2 or []):
+        m &= stack.masks                     # follow the component restriction
+    timings["edges_s"] = time.perf_counter() - t0
+
+    t0 = time.perf_counter()
+    if contact_model == "equipotential":
+        Vflat, R, I1, I2, mismatch, volts_per_amp, info = \
+            _solve_equipotential(stack, e1, e2, edges)
+    else:
+        Vflat, R, I1, I2, mismatch, volts_per_amp, info = \
+            _solve_uniform(stack, e1, e2, edges)
+    timings["solve_s"] = time.perf_counter() - t0
+
+    t0 = time.perf_counter()
+    s = i_test * volts_per_amp              # unit-drive volts -> volts @ I_test
+
+    # per-edge power @ I_test; distribute in-plane power to endpoint cells
+    Pe = edges.w * ((Vflat[edges.a] - Vflat[edges.b]) * s) ** 2
+    inplane = edges.via_index < 0
+    Pflat = np.zeros(Vflat.size)
+    np.add.at(Pflat, edges.a[inplane], 0.5 * Pe[inplane])
+    np.add.at(Pflat, edges.b[inplane], 0.5 * Pe[inplane])
+    Parea = Pflat.reshape(L, ny, nx) / (h_m * h_m)
+    Parea[~stack.masks] = np.nan
+    plane = ny * nx
+    P_layers = [float(Pflat[li * plane:(li + 1) * plane].sum())
+                for li in range(L)]
+    P_vias = float(Pe[~inplane].sum())
+    P_total = i_test ** 2 * R
+    balance = abs((sum(P_layers) + P_vias) - P_total) / max(P_total, 1e-300)
+
+    # via reports: max segment current + total power per via
+    Ie = edges.w * (Vflat[edges.a] - Vflat[edges.b])   # amps at unit drive
+    via_reports = []
+    if problem.vias:
+        vidx = edges.via_index
+        for vi in np.unique(vidx[vidx >= 0]):
+            sel = vidx == vi
+            via = problem.vias[vi]
+            via_reports.append(ViaReport(
+                x_mm=via.x * 1e-6, y_mm=via.y * 1e-6, kind=via.kind,
+                drill_mm=via.drill_nm * 1e-6,
+                current_a=float(np.abs(Ie[sel]).max()) * s,
+                power_w=float(Pe[sel].sum()),
+            ))
+        via_reports.sort(key=lambda v: v.current_a, reverse=True)
+
+    # per-injection-area currents
+    part_currents1 = _part_currents(
+        parts1 or [], Ie, edges, e1.ravel(), s, i_test,
+        contact_model, int(e1.sum()))
+    part_currents2 = _part_currents(
+        parts2 or [], Ie, edges, e2.ravel(), s, i_test,
+        contact_model, int(e2.sum()))
+
+    # embedded potential + per-layer current density @ I_test
+    V3 = np.full((L, ny, nx), np.nan)
+    V3[stack.masks] = Vflat.reshape(L, ny, nx)[stack.masks] * s
+    J3 = np.stack([
+        _face_current_density(
+            np.nan_to_num(V3[li]), stack.masks[li], sigmas[li],
+            h_m, problem.layers[li].thickness_nm * 1e-9,
+            sig2d=_sigma_2d(stack, li, sigmas[li], sigma_buildup),
+            rho=problem.rho_ohm_m)
+        for li in range(L)
+    ])
+    timings["postprocess_s"] = time.perf_counter() - t0
+
+    return Result(
+        R_ohm=R, i_test=i_test, V=V3, Jmag=J3, Parea=Parea,
+        layer_names=list(stack.layer_names),
+        P_total=P_total, P_layers=P_layers, P_vias=P_vias,
+        power_balance_rel=balance, via_reports=via_reports,
+        I1_a=I1, I2_a=I2, mismatch_rel=mismatch,
+        n_free=info.n_unknowns, solve_info=info,
+        part_currents1=part_currents1, part_currents2=part_currents2,
+        contact_model=contact_model,
+        freq_hz=freq_hz,
+        skin_depth_um=(skin.skin_depth_m(freq_hz, problem.rho_ohm_m) * 1e6
+                       if freq_hz > 0 else None),
+        rs_ratios=rs_ratios,
+        timings=timings,
+    )

fill_resistance/standalone.py

@@ -0,0 +1,80 @@
+"""Offline runner: solve a geometry_dump.json without KiCad.
+
+    python -m fill_resistance.standalone dump.json [--current 40]
+        [--cell-um 50] [--layers F.Cu,In1.Cu] [--no-show] [--out DIR]
+        [--force-iterative]
+
+This is the dev loop and the convergence-study tool (KiCad 10 has no
+headless API server, so the plugin path always needs the GUI).
+"""
+from __future__ import annotations
+
+import argparse
+import sys
+from pathlib import Path
+
+from . import config, pipeline
+from .errors import UserFacingError
+from .geometry import load_problem
+
+
+def main(argv=None) -> int:
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument("dump", type=Path, help="geometry_dump.json from a plugin run")
+    ap.add_argument("--current", type=float, default=None,
+                    help="test current [A] (default: config TEST_CURRENT_A)")
+    ap.add_argument("--freq", type=str, default="0",
+                    help="frequency, e.g. 142k or 1.5M (default: DC). "
+                         "AC results are a lower bound (skin per foil only)")
+    ap.add_argument("--cell-um", type=float, default=None,
+                    help="force grid cell size [um]")
+    ap.add_argument("--layers", type=str, default=None,
+                    help="comma-separated subset of layers to include")
+    ap.add_argument("--out", type=Path, default=None,
+                    help="output directory (default: next to the dump)")
+    ap.add_argument("--no-show", action="store_true",
+                    help="save PNGs only, no windows")
+    ap.add_argument("--contact-model", choices=["uniform", "equipotential"],
+                    default=None, help="contact model (default: config)")
+    ap.add_argument("--strip-buildup", action="store_true",
+                    help="ignore solder buildup stored in the dump")
+    ap.add_argument("--extra-cu-um", type=float, default=None,
+                    help="override the added copper in mask openings [um]")
+    ap.add_argument("--force-iterative", action="store_true",
+                    help="use CG (Jacobi) regardless of problem size")
+    args = ap.parse_args(argv)
+
+    if args.cell_um is not None:
+        config.CELL_UM_OVERRIDE = args.cell_um
+    if args.no_show:
+        config.INTERACTIVE = False
+    if args.force_iterative:
+        config.SPSOLVE_MAX_UNKNOWNS = 0
+
+    problem = load_problem(args.dump)
+    if args.strip_buildup:
+        problem.buildups = []
+    if args.extra_cu_um is not None:
+        problem.extra_cu_nm = int(args.extra_cu_um * 1000)
+    if args.layers:
+        keep = [s.strip() for s in args.layers.split(",")]
+        problem.layers = [l for l in problem.layers if l.layer_name in keep]
+        if not problem.layers:
+            print(f"ERROR: no layer of the dump matches --layers {args.layers}",
+                  file=sys.stderr)
+            return 1
+
+    from .skin import parse_frequency
+    outdir = args.out if args.out is not None else args.dump.parent
+    try:
+        pipeline.run(problem, outdir, show=not args.no_show,
+                     i_test=args.current, freq_hz=parse_frequency(args.freq),
+                     contact_model=args.contact_model)
+    except UserFacingError as e:
+        print(f"ERROR: {e}", file=sys.stderr)
+        return 1
+    return 0
+
+
+if __name__ == "__main__":
+    sys.exit(main())

plugin.json

@@ -0,0 +1,21 @@
+{
+    "$schema": "https://go.kicad.org/api/schemas/v1",
+    "identifier": "th.co.b4l.fill-resistance",
+    "name": "Fill Resistance",
+    "description": "DC resistance of a copper zone fill between two rectangle electrodes",
+    "runtime": {
+        "type": "python"
+    },
+    "actions": [
+        {
+            "identifier": "fill-resistance-run",
+            "name": "Fill Resistance",
+            "description": "Select two rectangles marking the contact areas, then run to compute the fill resistance between them",
+            "entrypoint": "fill_res_action.py",
+            "show-button": true,
+            "scopes": ["pcb"],
+            "icons-light": ["icons/fill_res_24_light.png"],
+            "icons-dark": ["icons/fill_res_24_dark.png"]
+        }
+    ]
+}

requirements.txt

@@ -0,0 +1,5 @@
+kicad-python>=0.7.0
+numpy
+scipy
+matplotlib
+PySide6

smoke/smoke_probe.py

@@ -0,0 +1,100 @@
+"""M1 smoke probe: verify the IPC API surface against a live KiCad.
+
+Run from the dev venv while KiCad is open with the board loaded:
+    .venv\\Scripts\\python.exe smoke\\smoke_probe.py
+
+Deliberately uses kipy directly (not board_io) so it works even if
+board_io has a bug. Prints: version, board path, selection contents,
+shapes summary, zones + filled polygon stats, stackup table.
+"""
+import sys
+import traceback
+
+from kipy import KiCad
+from kipy.board_types import BoardRectangle, BoardShape
+from kipy.proto.board.board_pb2 import BoardStackupLayerType
+from kipy.proto.board.board_types_pb2 import ZoneType
+from kipy.util.board_layer import canonical_name
+
+
+def mm(nm):
+    return nm / 1e6
+
+
+def main():
+    print("== connect ==")
+    kicad = KiCad()
+    kicad.ping()
+    print("version:", kicad.get_version())
+    try:
+        print("check_version:", kicad.check_version())
+    except Exception as e:
+        print("check_version raised:", e)
+
+    board = kicad.get_board()
+    print("board.name:", board.name)
+    print("board_filename:", getattr(board.document, "board_filename", "?"))
+
+    print("\n== selection ==")
+    sel = list(board.get_selection())
+    print(f"{len(sel)} item(s) selected")
+    for item in sel:
+        line = f"  {type(item).__name__}"
+        if isinstance(item, BoardRectangle):
+            tl, br = item.top_left, item.bottom_right
+            line += (f"  layer={canonical_name(item.layer)}"
+                     f"  tl=({mm(tl.x):.2f}, {mm(tl.y):.2f})mm"
+                     f"  br=({mm(br.x):.2f}, {mm(br.y):.2f})mm")
+        elif isinstance(item, BoardShape):
+            line += f"  layer={canonical_name(item.layer)}"
+        print(line)
+
+    print("\n== shapes (board-wide rectangles) ==")
+    shapes = list(board.get_shapes())
+    rect_shapes = [s for s in shapes if isinstance(s, BoardRectangle)]
+    print(f"{len(shapes)} shapes total, {len(rect_shapes)} rectangles")
+    for s in rect_shapes[:20]:
+        tl, br = s.top_left, s.bottom_right
+        print(f"  rect on {canonical_name(s.layer)}: "
+              f"({mm(tl.x):.2f}, {mm(tl.y):.2f}) - ({mm(br.x):.2f}, {mm(br.y):.2f}) mm")
+
+    print("\n== zones ==")
+    for zone in board.get_zones():
+        ztype = ZoneType.Name(zone.type)
+        net = zone.net.name if zone.net is not None else "<none>"
+        layers = [canonical_name(l) for l in zone.layers]
+        print(f"  zone '{zone.name}' type={ztype} net={net} "
+              f"layers={layers} filled={zone.filled}")
+        try:
+            for layer, polys in zone.filled_polygons.items():
+                narcs = 0
+                nnodes = 0
+                nholes = 0
+                for p in polys:
+                    nnodes += len(p.outline.nodes)
+                    nholes += len(p.holes)
+                    narcs += sum(1 for n in p.outline.nodes if n.has_arc)
+                print(f"    fill on {canonical_name(layer)}: {len(polys)} "
+                      f"poly(s), {nnodes} outline nodes, {nholes} holes, "
+                      f"{narcs} arc nodes")
+        except Exception:
+            print("    filled_polygons FAILED:")
+            traceback.print_exc()
+
+    print("\n== stackup ==")
+    try:
+        for sl in board.get_stackup().layers:
+            tname = BoardStackupLayerType.Name(sl.type)
+            lname = canonical_name(sl.layer) if sl.type == \
+                BoardStackupLayerType.BSLT_COPPER else "-"
+            print(f"  {tname:18s} layer={lname:8s} thickness={sl.thickness} nm"
+                  f"  enabled={sl.enabled}")
+    except Exception:
+        traceback.print_exc()
+
+    print("\nsmoke probe DONE")
+    return 0
+
+
+if __name__ == "__main__":
+    sys.exit(main())

tests/test_buildup.py

@@ -0,0 +1,106 @@
+"""Solder/mask-opening buildup tests. Uniform-coverage and split-coverage
+strips are 1D-exact, validating the harmonic-mean face weights and the
+parallel-sheet conductance model to solver precision."""
+import numpy as np
+import pytest
+
+from fill_resistance import raster, solver
+from fill_resistance.geometry import (Polygon, SurfaceBuildup, load_problem,
+                                      save_problem)
+from tests.util import NM, make_problem, ring_mm, sigma_s, strip_problem
+
+RHO_CU = 1.68e-8
+RHO_SN = 1.32e-7
+
+
+def _with_buildup(p, polys_mm, layer="F.Cu", solder_um=50.0, extra_um=0.0):
+    p.buildups = [SurfaceBuildup(
+        layer_name=layer,
+        polygons=[Polygon(outline=ring_mm(pts)) for pts in polys_mm])]
+    p.solder_thickness_nm = int(solder_um * 1000)
+    p.solder_rho_ohm_m = RHO_SN
+    p.extra_cu_nm = int(extra_um * 1000)
+    return p
+
+
+def _solve(problem, h_mm):
+    stack = raster.rasterize_stack(problem, h_mm * NM)
+    e1, e2 = raster.electrode_masks(stack, problem)
+    return solver.run_solve(problem, stack, e1, e2, 1.0,
+                            contact_model="equipotential"), stack
+
+
+def _sigma_buildup(solder_um=50.0, extra_um=0.0):
+    return solder_um * 1e-6 / RHO_SN + extra_um * 1e-6 / RHO_CU
+
+
+def test_full_coverage_exact():
+    """Buildup over the whole strip: uniform parallel sheet, exact."""
+    plain = strip_problem(length=50, width=10, e_len=5)
+    covered = _with_buildup(strip_problem(length=50, width=10, e_len=5),
+                            [[(0, 0), (50, 0), (50, 10), (0, 10)]])
+    r0, _ = _solve(plain, 0.5)
+    r1, stack = _solve(covered, 0.5)
+    sig = sigma_s() + _sigma_buildup()
+    assert r1.R_ohm == pytest.approx(81 / 20 / sig, rel=1e-9)
+    assert r1.R_ohm < r0.R_ohm
+    assert stack.buildup is not None and stack.buildup.any()
+
+
+def test_half_coverage_series_exact():
+    """Buildup over the right half: plain faces + one harmonic-mean
+    interface face + buildup faces in series, exact."""
+    p = _with_buildup(strip_problem(length=50, width=10, e_len=5),
+                      [[(25, 0), (50, 0), (50, 10), (25, 10)]])
+    res, _ = _solve(p, 0.5)
+    s1 = sigma_s()
+    s2 = s1 + _sigma_buildup()
+    r_row = 40 / s1 + (s1 + s2) / (2 * s1 * s2) + 40 / s2
+    assert res.R_ohm == pytest.approx(r_row / 20, rel=1e-9)
+
+
+def test_buildup_only_over_hole_is_inert():
+    """Solder wets copper only: an opening over a hole changes nothing."""
+    holed = [([(0, 0), (50, 0), (50, 10), (0, 10)],
+              [[(20, 2), (30, 2), (30, 8), (20, 8)]])]
+    plain = make_problem(holed, rect1_mm=(0, 0, 5, 10),
+                         rect2_mm=(45, 0, 50, 10))
+    masked = _with_buildup(
+        make_problem(holed, rect1_mm=(0, 0, 5, 10),
+                     rect2_mm=(45, 0, 50, 10)),
+        [[(21, 3), (29, 3), (29, 7), (21, 7)]])   # strictly inside the hole
+    r0, _ = _solve(plain, 0.5)
+    r1, _ = _solve(masked, 0.5)
+    assert r1.R_ohm == pytest.approx(r0.R_ohm, rel=1e-12)
+
+
+def test_extra_copper_helps_more_than_solder():
+    base = strip_problem(length=50, width=10, e_len=5)
+    solder_only = _with_buildup(strip_problem(length=50, width=10, e_len=5),
+                                [[(0, 0), (50, 0), (50, 10), (0, 10)]])
+    with_cu = _with_buildup(strip_problem(length=50, width=10, e_len=5),
+                            [[(0, 0), (50, 0), (50, 10), (0, 10)]],
+                            extra_um=70.0)
+    r0, _ = _solve(base, 0.5)
+    r1, _ = _solve(solder_only, 0.5)
+    r2, _ = _solve(with_cu, 0.5)
+    assert r2.R_ohm < r1.R_ohm < r0.R_ohm
+    # 50 um SAC solder ~ 6.4 um Cu: expect a modest (<15%) improvement
+    assert r1.R_ohm > 0.85 * r0.R_ohm
+    # +70 um Cu roughly halves R (2x thickness + solder)
+    assert r2.R_ohm < 0.55 * r0.R_ohm
+
+
+def test_json_v4_roundtrip(tmp_path):
+    p = _with_buildup(strip_problem(), [[(0, 0), (50, 0), (50, 10), (0, 10)]],
+                      extra_um=35.0)
+    f = tmp_path / "d.json"
+    save_problem(p, f)
+    q = load_problem(f)
+    assert len(q.buildups) == 1 and q.buildups[0].layer_name == "F.Cu"
+    assert q.solder_thickness_nm == 50_000
+    assert q.extra_cu_nm == 35_000
+    assert q.solder_rho_ohm_m == pytest.approx(RHO_SN)
+    r_p, _ = _solve(p, 0.5)
+    r_q, _ = _solve(q, 0.5)
+    assert r_q.R_ohm == pytest.approx(r_p.R_ohm, rel=1e-12)

tests/test_contacts.py

@@ -0,0 +1,172 @@
+"""Contact-model (uniform vs equipotential) and multi-part terminal tests."""
+import numpy as np
+import pytest
+
+from fill_resistance import raster, solver
+from fill_resistance.errors import ElectrodeError
+from fill_resistance.geometry import Electrode
+from tests.util import NM, make_problem, rect_mm, sigma_s, strip_problem
+
+
+def _solve(problem, h_mm, model, i_test=1.0):
+    stack = raster.rasterize_stack(problem, h_mm * NM)
+    e1, e2 = raster.electrode_masks(stack, problem)
+    parts1, parts2 = raster.electrode_partition(stack, problem)
+    return solver.run_solve(problem, stack, e1, e2, i_test,
+                            contact_model=model,
+                            parts1=parts1, parts2=parts2), stack
+
+
+def _uniform_1d_reference(m_cols, n1, n2, sig, rows):
+    """Independent 1D reference: uniform injection over the first n1
+    columns, extraction over the last n2, unit total current. R from
+    mean potentials, per row conductance sig, `rows` parallel rows."""
+    inj = np.zeros(m_cols)
+    inj[:n1] += 1.0 / n1
+    inj[m_cols - n2:] -= 1.0 / n2
+    face_current = np.cumsum(inj)[:-1]          # current through face k,k+1
+    v = np.zeros(m_cols)
+    v[1:] = -np.cumsum(face_current) / sig      # per single row of cells
+    v_plus = v[:n1].mean()
+    v_minus = v[m_cols - n2:].mean()
+    return (v_plus - v_minus) / 1.0 / rows      # rows in parallel
+
+
+def test_uniform_strip_exact_1d():
+    """Full-width contacts on a uniform strip: rows are identical 1D
+    chains; compare with an independent 1D computation, exact."""
+    p = strip_problem(length=50, width=10, e_len=5)
+    res, _ = _solve(p, 0.5, "uniform")
+    sig = sigma_s()
+    r_ref = _uniform_1d_reference(m_cols=100, n1=10, n2=10, sig=sig, rows=20)
+    assert res.R_ohm == pytest.approx(r_ref, rel=1e-9)
+    assert res.contact_model == "uniform"
+    assert res.power_balance_rel < 1e-9         # P = b^T V = I^2 R identity
+
+
+def test_uniform_higher_than_equipotential():
+    p = strip_problem(length=50, width=10, e_len=5)
+    r_uni, _ = _solve(p, 0.5, "uniform")
+    r_equ, _ = _solve(p, 0.5, "equipotential")
+    assert r_uni.R_ohm > r_equ.R_ohm
+
+
+def test_uniform_current_density_ramps_inside_contact():
+    """Inside the V+ contact, |J| must ramp: ~0 at the outer edge,
+    ~full sheet current at the inner (leading) edge; the equipotential
+    model shows ~0 throughout the contact interior."""
+    p = strip_problem(length=50, width=10, e_len=5)
+    res_u, stack = _solve(p, 0.5, "uniform")
+    ny, nx = stack.shape2d
+    row = ny // 2
+    # contact columns are the first 10 copper columns (margin = 2)
+    j_outer = res_u.Jmag[0, row, 2]              # first contact column
+    j_inner = res_u.Jmag[0, row, 11]             # last contact column
+    j_free = res_u.Jmag[0, row, nx // 2]         # mid strip = I/(W t)
+    assert j_inner > 0.8 * j_free                # ramped up to ~full
+    assert j_outer < 0.2 * j_free                # near zero at outer edge
+    assert j_inner > 5 * max(j_outer, 1e-30)
+
+    res_e, _ = _solve(p, 0.5, "equipotential")
+    j_center_e = res_e.Jmag[0, row, 6]           # deep inside Dirichlet region
+    assert j_center_e < 0.05 * j_free
+
+
+def test_multipart_terminal_equals_single_rect():
+    """V+ split into two half-height rectangles == one full rectangle,
+    for both contact models (exact)."""
+    whole = strip_problem(length=50, width=10, e_len=5)
+    split = strip_problem(length=50, width=10, e_len=5)
+    split.electrodes1 = [
+        Electrode(rect=rect_mm((0, 0, 5, 5))),
+        Electrode(rect=rect_mm((0, 5, 5, 10))),
+    ]
+    for model in ("uniform", "equipotential"):
+        r_whole, _ = _solve(whole, 0.5, model)
+        r_split, _ = _solve(split, 0.5, model)
+        assert r_split.R_ohm == pytest.approx(r_whole.R_ohm, rel=1e-9), model
+
+
+def test_multipart_asymmetric_parts():
+    """Two separated V+ parts feeding one V-: sane R, balance holds."""
+    p = make_problem([([(0, 0), (50, 0), (50, 10), (0, 10)], [])],
+                     rect1_mm=(0, 0, 2, 3), rect2_mm=(45, 0, 50, 10))
+    p.electrodes1 = [
+        Electrode(rect=rect_mm((0, 0, 2, 3)), label="top lug"),
+        Electrode(rect=rect_mm((0, 7, 2, 10)), label="bottom lug"),
+    ]
+    single, _ = _solve(
+        make_problem([([(0, 0), (50, 0), (50, 10), (0, 10)], [])],
+                     rect1_mm=(0, 0, 2, 3), rect2_mm=(45, 0, 50, 10)),
+        0.25, "uniform")
+    multi, _ = _solve(p, 0.25, "uniform")
+    assert multi.R_ohm < single.R_ohm            # more contact area helps
+    assert multi.power_balance_rel < 1e-9
+
+
+def test_part_off_copper_raises_with_label():
+    p = strip_problem(length=50, width=10, e_len=5)
+    p.electrodes1 = [
+        Electrode(rect=rect_mm((0, 0, 5, 10))),
+        Electrode(rect=rect_mm((100, 100, 105, 105)), label="stray part"),
+    ]
+    stack = raster.rasterize_stack(p, 0.5 * NM)
+    with pytest.raises(ElectrodeError, match="stray part"):
+        raster.electrode_masks(stack, p)
+
+
+def test_injection_area_currents_equipotential_flux():
+    """Two V+ lugs at different distances: the nearer one carries more;
+    the flux split sums exactly to the test current."""
+    p = make_problem([([(0, 0), (50, 0), (50, 10), (0, 10)], [])],
+                     rect1_mm=(0, 0, 2, 10), rect2_mm=(48, 0, 50, 10))
+    p.electrodes1 = [
+        Electrode(rect=rect_mm((0, 4, 2, 6)), label="far lug"),
+        Electrode(rect=rect_mm((10, 4, 12, 6)), label="near lug"),
+    ]
+    res, _ = _solve(p, 0.25, "equipotential", i_test=10.0)
+    pc = dict(res.part_currents1)
+    assert pc["near lug"] > pc["far lug"]
+    assert pc["near lug"] + pc["far lug"] == pytest.approx(10.0, rel=1e-9)
+    # V- side: single part carries everything
+    assert res.part_currents2[0][1] == pytest.approx(10.0, rel=1e-9)
+
+
+def test_injection_area_currents_uniform_area_share():
+    """Uniform model: each injection area carries exactly its cell share."""
+    p = make_problem([([(0, 0), (50, 0), (50, 10), (0, 10)], [])],
+                     rect1_mm=(0, 0, 2, 10), rect2_mm=(48, 0, 50, 10))
+    p.electrodes1 = [
+        Electrode(rect=rect_mm((0, 0, 2, 6)), label="big"),    # 2x6 mm
+        Electrode(rect=rect_mm((0, 6, 2, 9)), label="small"),  # 2x3 mm
+    ]
+    res, _ = _solve(p, 0.25, "uniform", i_test=9.0)
+    pc = dict(res.part_currents1)
+    # cell counts: 8x24 = 192 and 8x12 = 96 at h=0.25 -> shares 2/3, 1/3
+    assert pc["big"] == pytest.approx(6.0, rel=1e-12)
+    assert pc["small"] == pytest.approx(3.0, rel=1e-12)
+
+
+def test_injection_area_partition_first_wins():
+    """Overlapping parts: shared cells attributed to the first part, so
+    the shares still sum to the terminal current."""
+    p = make_problem([([(0, 0), (50, 0), (50, 10), (0, 10)], [])],
+                     rect1_mm=(0, 0, 2, 10), rect2_mm=(48, 0, 50, 10))
+    p.electrodes1 = [
+        Electrode(rect=rect_mm((0, 0, 2, 6)), label="first"),
+        Electrode(rect=rect_mm((0, 4, 2, 10)), label="second"),  # overlaps
+    ]
+    res, _ = _solve(p, 0.25, "uniform", i_test=1.0)
+    total = sum(a for _, a in res.part_currents1)
+    assert total == pytest.approx(1.0, rel=1e-12)
+
+
+def test_touching_ok_uniform_error_equipotential():
+    p = make_problem([([(0, 0), (10, 0), (10, 10), (0, 10)], [])],
+                     rect1_mm=(0, 0, 5, 10), rect2_mm=(5, 0, 10, 10))
+    res, _ = _solve(p, 0.5, "uniform")           # touching is fine here
+    assert res.R_ohm > 0
+    p2 = make_problem([([(0, 0), (10, 0), (10, 10), (0, 10)], [])],
+                      rect1_mm=(0, 0, 5, 10), rect2_mm=(5, 0, 10, 10))
+    with pytest.raises(ElectrodeError, match="touch"):
+        _solve(p2, 0.5, "equipotential")

tests/test_geometry.py

@@ -0,0 +1,88 @@
+import json
+import math
+
+import numpy as np
+
+from fill_resistance.geometry import (arc_points, linearize_ring,
+                                      load_problem, problem_from_json,
+                                      save_problem)
+from tests.util import make_multilayer, strip_problem
+
+
+def test_arc_points_quarter_circle():
+    r = 10_000_000  # 10 mm in nm
+    start = (r, 0)
+    mid = (int(r / math.sqrt(2)), int(r / math.sqrt(2)))
+    end = (0, r)
+    tol = 50_000  # 50 um
+    pts = arc_points(start, mid, end, tol)
+    assert len(pts) >= 3
+    radii = np.hypot(pts[:, 0].astype(float), pts[:, 1].astype(float))
+    assert np.allclose(radii, r, rtol=1e-6)
+    allpts = np.vstack([pts, [end]]).astype(float)
+    for a, b in zip(allpts[:-1], allpts[1:]):
+        half_chord = np.hypot(*(b - a)) / 2
+        sagitta = r - math.sqrt(max(r**2 - half_chord**2, 0.0))
+        assert sagitta <= tol * 1.01
+
+
+def test_arc_points_collinear_degrades_to_segment():
+    pts = arc_points((0, 0), (5_000_000, 0), (10_000_000, 0), 1000)
+    assert len(pts) == 1
+    assert tuple(pts[0]) == (0, 0)
+
+
+def test_linearize_ring_mixed_nodes_and_closure():
+    nodes = [
+        ("pt", (0, 0)),
+        ("pt", (10, 0)),
+        ("arc", ((10, 0), (17, 7), (10, 14))),
+        ("pt", (0, 14)),
+        ("pt", (0, 0)),
+    ]
+    ring = linearize_ring(nodes, tol_nm=1)
+    assert (ring[0] != ring[-1]).any()
+    assert len(ring) > 4
+
+
+def test_problem_json_roundtrip_v2(tmp_path):
+    p = make_multilayer(
+        [[([(0, 0), (10, 0), (10, 1), (0, 1)], [])],
+         [([(0, 0), (10, 0), (10, 1), (0, 1)], [])]],
+        rect1_mm=(0, 0, 1, 1), rect2_mm=(9, 0, 10, 1),
+        contact1="L0", contact2="L1", vias_mm=[(5.5, 0.5)])
+    f = tmp_path / "dump.json"
+    save_problem(p, f)
+    q = load_problem(f)
+    assert q.layer_names == ["L0", "L1"]
+    assert q.electrodes1[0].contact == "L0"
+    assert q.electrodes2[0].contact == "L1"
+    assert len(q.vias) == 1 and q.vias[0].drill_nm == p.vias[0].drill_nm
+    assert q.plating_nm == p.plating_nm
+    assert np.array_equal(q.layers[0].polygons[0].outline,
+                          p.layers[0].polygons[0].outline)
+    assert abs(q.sigma_s(0) - p.sigma_s(0)) < 1e-12 * p.sigma_s(0)
+
+
+def test_v1_schema_still_loads():
+    p = strip_problem()
+    v1 = {
+        "schema_version": 1,
+        "board_path": "old",
+        "layer_name": "F.Cu",
+        "net_name": "GND",
+        "thickness_nm": 70000,
+        "thickness_source": "stackup",
+        "rho_ohm_m": 1.68e-8,
+        "rect1": {"x0": 0, "y0": 0, "x1": 1000, "y1": 1000,
+                  "layer_name": "User.1"},
+        "rect2": {"x0": 5000, "y0": 0, "x1": 6000, "y1": 1000,
+                  "layer_name": "User.1"},
+        "polygons": [{"outline": p.layers[0].polygons[0].outline.tolist(),
+                      "holes": []}],
+    }
+    q = problem_from_json(json.loads(json.dumps(v1)))
+    assert q.layer_names == ["F.Cu"]
+    assert q.vias == []
+    assert q.electrodes1[0].contact == "all"
+    assert q.layers[0].thickness_nm == 70000

tests/test_multilayer.py

@@ -0,0 +1,148 @@
+"""Multi-layer / via solver tests. The 1-cell-wide strip cases are pure
+series chains, so the discrete solution is exact and validates the via
+barrel model, layer coupling, and flux integration to solver precision."""
+import math
+
+import numpy as np
+import pytest
+
+from fill_resistance import raster, solver
+from fill_resistance.errors import ConnectivityError, ElectrodeError
+from tests.util import NM, make_multilayer, sigma_s
+
+
+def _solve(problem, h_mm, i_test=1.0):
+    stack = raster.rasterize_stack(problem, h_mm * NM)
+    e1, e2 = raster.electrode_masks(stack, problem)
+    return solver.run_solve(problem, stack, e1, e2, i_test,
+                            contact_model="equipotential"), stack
+
+
+STRIP = [(0, 0), (10, 0), (10, 1), (0, 1)]     # 10 x 1 mm; h=1 -> 1 row
+
+
+def _r_via(length_mm, drill_mm=0.3, plating_um=18.0, rho=1.68e-8):
+    area = math.pi * (drill_mm * 1e-3) * (plating_um * 1e-6)
+    return rho * (length_mm * 1e-3) / area
+
+
+def test_two_identical_layers_parallel():
+    """Both electrodes contact both layers, no vias needed: two identical
+    independent sheets in parallel -> exactly half the single-layer R."""
+    one = make_multilayer([[(STRIP, [])]], (0, 0, 1, 1), (9, 0, 10, 1))
+    two = make_multilayer([[(STRIP, [])], [(STRIP, [])]],
+                          (0, 0, 1, 1), (9, 0, 10, 1))
+    r1, _ = _solve(one, 1.0)
+    r2, _ = _solve(two, 1.0)
+    assert r2.R_ohm == pytest.approx(r1.R_ohm / 2, rel=1e-9)
+
+
+def test_via_chain_1d_exact():
+    """e1 on L0 left end, e2 on L1 right end, one through-via at x=5.5:
+    R = faces_L0/sigma + R_via + faces_L1/sigma, exact."""
+    p = make_multilayer(
+        [[(STRIP, [])], [(STRIP, [])]],
+        rect1_mm=(0, 0, 1, 1), rect2_mm=(9, 0, 10, 1),
+        contact1="L0", contact2="L1",
+        vias_mm=[(5.5, 0.5)], gap_mm=1.0)
+    res, stack = _solve(p, 1.0)
+    # cells at x centers 0.5..9.5 -> cols 0..9 (plus margins); electrode
+    # cells: col of 0.5 (e1), col of 9.5 (e2); via cell: col of 5.5
+    sig = sigma_s()
+    faces_l0 = 5          # cols 0->5: faces between 0|1 .. 4|5
+    faces_l1 = 4          # cols 5->9
+    r_exact = (faces_l0 + faces_l1) / sig + _r_via(1.0)
+    assert res.R_ohm == pytest.approx(r_exact, rel=1e-9)
+    assert res.mismatch_rel < 1e-10
+    assert len(res.via_reports) == 1
+    # the single via carries the full test current
+    assert res.via_reports[0].current_a == pytest.approx(1.0, rel=1e-9)
+    assert res.via_reports[0].power_w == pytest.approx(_r_via(1.0), rel=1e-9)
+
+
+def test_parallel_vias_halve_barrel_resistance():
+    base = dict(rect1_mm=(0, 0, 1, 1), rect2_mm=(9, 0, 10, 1),
+                contact1="L0", contact2="L1", gap_mm=1.0)
+    one = make_multilayer([[(STRIP, [])], [(STRIP, [])]],
+                          vias_mm=[(5.5, 0.5)], **base)
+    two = make_multilayer([[(STRIP, [])], [(STRIP, [])]],
+                          vias_mm=[(5.5, 0.5), (5.5, 0.5)], **base)
+    r_one, _ = _solve(one, 1.0)
+    r_two, _ = _solve(two, 1.0)
+    assert (r_one.R_ohm - r_two.R_ohm) == pytest.approx(_r_via(1.0) / 2,
+                                                        rel=1e-9)
+
+
+def test_antipad_bridging():
+    """3 layers; the middle layer has an antipad hole at the via cell, so
+    the barrel bridges L0 -> L2 directly with DOUBLE the length."""
+    mid_with_hole = [(STRIP, [[(5, 0), (6, 0), (6, 1), (5, 1)]])]
+    p = make_multilayer(
+        [[(STRIP, [])], mid_with_hole, [(STRIP, [])]],
+        rect1_mm=(0, 0, 1, 1), rect2_mm=(9, 0, 10, 1),
+        contact1="L0", contact2="L2",
+        vias_mm=[(5.5, 0.5)], gap_mm=1.0)
+    res, _ = _solve(p, 1.0)
+    sig = sigma_s()
+    r_exact = (5 + 4) / sig + _r_via(2.0)      # barrel length 2 mm
+    assert res.R_ohm == pytest.approx(r_exact, rel=1e-9)
+
+
+def test_via_short_between_electrodes_raises():
+    """Both electrodes over the SAME cell on different layers with a via
+    there = direct short, no free copper -> error."""
+    p = make_multilayer(
+        [[(STRIP, [])], [(STRIP, [])]],
+        rect1_mm=(5, 0, 6, 1), rect2_mm=(5, 0, 6, 1),
+        contact1="L0", contact2="L1",
+        vias_mm=[(5.5, 0.5)], gap_mm=1.0)
+    stack = raster.rasterize_stack(p, 1.0 * NM)
+    e1, e2 = raster.electrode_masks(stack, p)
+    with pytest.raises(ElectrodeError, match="directly connected"):
+        solver.run_solve(p, stack, e1, e2, 1.0,
+                         contact_model="equipotential")
+
+
+def test_layers_without_via_disconnected():
+    p = make_multilayer(
+        [[(STRIP, [])], [(STRIP, [])]],
+        rect1_mm=(0, 0, 1, 1), rect2_mm=(9, 0, 10, 1),
+        contact1="L0", contact2="L1", gap_mm=1.0)   # no vias
+    stack = raster.rasterize_stack(p, 1.0 * NM)
+    e1, e2 = raster.electrode_masks(stack, p)
+    with pytest.raises(ConnectivityError, match="not connected"):
+        solver.run_solve(p, stack, e1, e2, 1.0,
+                         contact_model="equipotential")
+
+
+def test_power_split_layers_and_vias():
+    """Power accounting: layer + via powers sum to I^2 R."""
+    p = make_multilayer(
+        [[(STRIP, [])], [(STRIP, [])]],
+        rect1_mm=(0, 0, 1, 1), rect2_mm=(9, 0, 10, 1),
+        contact1="L0", contact2="L1",
+        vias_mm=[(5.5, 0.5)], gap_mm=1.0)
+    res, _ = _solve(p, 1.0, i_test=10.0)
+    assert res.power_balance_rel < 1e-9
+    assert res.P_vias == pytest.approx(100 * _r_via(1.0), rel=1e-9)
+    sig = sigma_s()
+    assert res.P_layers[0] == pytest.approx(100 * 5 / sig, rel=1e-9)
+    assert res.P_layers[1] == pytest.approx(100 * 4 / sig, rel=1e-9)
+
+
+def test_pad_polygon_electrode():
+    """A polygon-shaped electrode (pad) restricted to one layer."""
+    from fill_resistance.geometry import Electrode, Polygon
+    from tests.util import rect_mm, ring_mm
+    p = make_multilayer([[(STRIP, [])]], (0, 0, 1, 1), (9, 0, 10, 1))
+    # replace terminal 1 with a small polygon pad covering the same cell
+    p.electrodes1 = [Electrode(
+        rect=rect_mm((0.2, 0.2, 0.8, 0.8)),
+        contact="all",
+        polygons=[Polygon(outline=ring_mm(
+            [(0.2, 0.2), (0.8, 0.2), (0.8, 0.8), (0.2, 0.8)]))],
+        label="pad TP1.1",
+    )]
+    res, _ = _solve(p, 1.0)
+    sig = sigma_s()
+    assert res.R_ohm == pytest.approx(9 / sig, rel=1e-9)  # cols 0..9

tests/test_raster.py

@@ -0,0 +1,102 @@
+import numpy as np
+import pytest
+
+from fill_resistance import config, raster, solver
+from fill_resistance.errors import (ConnectivityError, ElectrodeError,
+                                    GridSizeError)
+from tests.util import NM, make_problem, strip_problem
+
+
+def _stack(problem, h_mm):
+    return raster.rasterize_stack(problem, h_mm * NM)
+
+
+def test_exact_cell_count_square_with_hole():
+    # 10x10 mm square, centered 4x4 mm hole, h=1 mm: cell centers at
+    # half-integers, no boundary ambiguity -> exactly 100 - 16 cells
+    p = make_problem(
+        [([(0, 0), (10, 0), (10, 10), (0, 10)],
+          [[(3, 3), (7, 3), (7, 7), (3, 7)]])],
+        rect1_mm=(0, 0, 1, 10), rect2_mm=(9, 0, 10, 10))
+    stack = _stack(p, 1.0)
+    assert int(stack.masks[0].sum()) == 100 - 16
+
+
+def test_margin_cells_are_empty():
+    p = strip_problem()
+    stack = _stack(p, 0.5)
+    m = stack.masks[0]
+    assert not m[0, :].any() and not m[-1, :].any()
+    assert not m[:, 0].any() and not m[:, -1].any()
+
+
+def test_electrode_masks_and_counts():
+    p = strip_problem(length=50, width=10, e_len=5)
+    stack = _stack(p, 0.5)
+    e1, e2 = raster.electrode_masks(stack, p)
+    # electrodes: 5 mm / 0.5 mm = 10 columns x 20 rows on 1 layer
+    assert int(e1.sum()) == 200 and int(e2.sum()) == 200
+
+
+def test_electrode_off_copper_raises():
+    p = make_problem([([(0, 0), (10, 0), (10, 10), (0, 10)], [])],
+                     rect1_mm=(20, 20, 25, 25), rect2_mm=(8, 0, 10, 10))
+    stack = _stack(p, 0.5)
+    with pytest.raises(ElectrodeError, match="does not overlap"):
+        raster.electrode_masks(stack, p)
+
+
+def test_touching_electrodes_raise_equipotential():
+    p = make_problem([([(0, 0), (10, 0), (10, 10), (0, 10)], [])],
+                     rect1_mm=(0, 0, 5, 10), rect2_mm=(5, 0, 10, 10))
+    stack = _stack(p, 0.5)
+    e1, e2 = raster.electrode_masks(stack, p)   # touch is fine at mask level
+    with pytest.raises(ElectrodeError, match="touch"):
+        solver.run_solve(p, stack, e1, e2, 1.0,
+                         contact_model="equipotential")
+
+
+def test_disconnected_regions_raise():
+    p = make_problem(
+        [([(0, 0), (10, 0), (10, 10), (0, 10)], []),
+         ([(20, 0), (30, 0), (30, 10), (20, 10)], [])],
+        rect1_mm=(0, 0, 2, 10), rect2_mm=(28, 0, 30, 10))
+    stack = _stack(p, 0.5)
+    e1, e2 = raster.electrode_masks(stack, p)
+    with pytest.raises(ConnectivityError, match="not connected"):
+        solver.run_solve(p, stack, e1, e2, 1.0,
+                         contact_model="equipotential")
+
+
+def test_islands_dropped():
+    # island square not touching the main strip disappears from the mask
+    p = make_problem(
+        [([(0, 0), (50, 0), (50, 10), (0, 10)], []),
+         ([(20, 20), (30, 20), (30, 30), (20, 30)], [])],
+        rect1_mm=(0, 0, 5, 10), rect2_mm=(45, 0, 50, 10))
+    stack = _stack(p, 0.5)
+    e1, e2 = raster.electrode_masks(stack, p)
+    before = int(stack.masks.sum())
+    solver.run_solve(p, stack, e1, e2, 1.0, contact_model="equipotential")
+    after = int(stack.masks.sum())
+    assert after < before
+    assert after == 100 * 20  # only the strip remains
+
+
+def test_hard_max_cells_guard(monkeypatch):
+    monkeypatch.setattr(config, "CELL_UM_OVERRIDE", 1.0)  # 1 um cells
+    p = strip_problem()
+    with pytest.raises(GridSizeError, match="M cells"):
+        raster.choose_cell_size(p.copper_bbox(), len(p.layers))
+
+
+def test_auto_cell_size_hits_target():
+    # large plane: unclamped regime, cell count tracks TARGET_CELLS
+    p = strip_problem(length=200, width=100, e_len=5)
+    h = raster.choose_cell_size(p.copper_bbox(), 1)
+    ncells = (200.0 * NM / h) * (100.0 * NM / h)
+    assert 0.5 * config.TARGET_CELLS < ncells < 2.0 * config.TARGET_CELLS
+    # small board: MIN_CELL_UM clamp kicks in instead
+    q = strip_problem()  # 50x10 mm
+    hq = raster.choose_cell_size(q.copper_bbox(), 1)
+    assert hq == pytest.approx(config.MIN_CELL_UM * 1000)

tests/test_skin.py

@@ -0,0 +1,103 @@
+"""Skin-effect model tests. The single-layer AC solve scales ALL in-plane
+conductances identically, so R_AC = R_DC * resistance_factor EXACTLY -
+which turns the analytic foil formula into an end-to-end exact test."""
+import math
+
+import numpy as np
+import pytest
+
+from fill_resistance import raster, skin, solver
+from tests.util import NM, make_multilayer, strip_problem
+
+RHO = 1.68e-8
+
+
+def _solve(problem, h_mm, i_test=1.0, freq=0.0):
+    stack = raster.rasterize_stack(problem, h_mm * NM)
+    e1, e2 = raster.electrode_masks(stack, problem)
+    return solver.run_solve(problem, stack, e1, e2, i_test, freq,
+                            contact_model="equipotential"), stack
+
+
+def test_skin_depth_value():
+    # copper @ 1 MHz: ~65-66 um
+    assert skin.skin_depth_m(1e6, RHO) * 1e6 == pytest.approx(65.2, rel=0.01)
+
+
+def test_sheet_resistance_dc_limit():
+    t = 70e-6
+    assert skin.sheet_resistance_ac(t, 0.0, RHO) == pytest.approx(RHO / t)
+    # low frequency: within 0.1% of DC
+    assert skin.sheet_resistance_ac(t, 100.0, RHO) == pytest.approx(
+        RHO / t, rel=1e-3)
+
+
+def test_sheet_resistance_high_f_limits():
+    t = 70e-6
+    f = 1e9                                  # delta << t
+    delta = skin.skin_depth_m(f, RHO)
+    assert skin.sheet_resistance_ac(t, f, RHO, sides=1) == pytest.approx(
+        RHO / delta, rel=0.01)
+    assert skin.sheet_resistance_ac(t, f, RHO, sides=2) == pytest.approx(
+        RHO / (2 * delta), rel=0.01)
+
+
+def test_resistance_factor_monotonic():
+    t = 70e-6
+    factors = [skin.resistance_factor(t, f, RHO)
+               for f in (0, 1e4, 1e5, 1e6, 1e7, 1e8)]
+    assert all(b >= a - 1e-12 for a, b in zip(factors, factors[1:]))
+    assert factors[0] == 1.0
+
+
+def test_parse_frequency():
+    assert skin.parse_frequency("") == 0.0
+    assert skin.parse_frequency("0") == 0.0
+    assert skin.parse_frequency("142k") == 142_000.0
+    assert skin.parse_frequency("1.5M") == 1_500_000.0
+    assert skin.parse_frequency("2meg") == 2_000_000.0
+    assert skin.parse_frequency("100000") == 100_000.0
+    assert skin.parse_frequency("100 kHz") == 100_000.0
+    assert skin.parse_frequency("junk") == 0.0
+
+
+def test_single_layer_ac_scales_exactly():
+    """Uniform conductance scaling leaves the field shape unchanged:
+    R_AC = R_DC * factor to solver precision."""
+    p = strip_problem(length=50, width=10, e_len=5)
+    f = 2e6                                    # delta=46um < t=70um
+    r_dc, _ = _solve(p, 0.5)
+    r_ac, _ = _solve(p, 0.5, freq=f)
+    factor = skin.resistance_factor(70e-6, f, RHO, sides=1)
+    assert factor > 1.2                        # real crowding at 2 MHz
+    assert r_ac.R_ohm == pytest.approx(r_dc.R_ohm * factor, rel=1e-9)
+    assert r_ac.rs_ratios[0] == pytest.approx(factor, rel=1e-12)
+    assert r_ac.skin_depth_um == pytest.approx(
+        skin.skin_depth_m(f, RHO) * 1e6, rel=1e-12)
+
+
+def test_via_chain_ac_exact():
+    """1D chain: layers scale by the foil factor, the barrel by the
+    plating-wall factor - exact composition."""
+    STRIP = [(0, 0), (10, 0), (10, 1), (0, 1)]
+    p = make_multilayer(
+        [[(STRIP, [])], [(STRIP, [])]],
+        rect1_mm=(0, 0, 1, 1), rect2_mm=(9, 0, 10, 1),
+        contact1="L0", contact2="L1",
+        vias_mm=[(5.5, 0.5)], gap_mm=1.0)
+    f = 2e6
+    sig_ac = 1.0 / skin.sheet_resistance_ac(70e-6, f, RHO, sides=1)
+    via_factor = skin.resistance_factor(18e-6, f, RHO, sides=2)
+    r_via_dc = RHO * 1e-3 / (math.pi * 0.3e-3 * 18e-6)
+    r_exact = (5 + 4) / sig_ac + r_via_dc * via_factor
+    res, _ = _solve(p, 1.0, freq=f)
+    assert res.R_ohm == pytest.approx(r_exact, rel=1e-9)
+
+
+def test_dc_default_unchanged():
+    """freq omitted -> identical to the pre-skin behavior."""
+    p = strip_problem(length=50, width=10, e_len=5)
+    res, _ = _solve(p, 0.5)
+    assert res.freq_hz == 0.0
+    assert res.skin_depth_um is None
+    assert all(r == 1.0 for r in res.rs_ratios)

tests/test_solver.py

@@ -0,0 +1,124 @@
+import numpy as np
+import pytest
+
+from fill_resistance import config, raster, solver
+from tests.util import NM, make_problem, strip_problem
+
+
+def _solve(problem, h_mm, i_test=1.0):
+    stack = raster.rasterize_stack(problem, h_mm * NM)
+    e1, e2 = raster.electrode_masks(stack, problem)
+    return solver.run_solve(problem, stack, e1, e2, i_test,
+                            contact_model="equipotential"), stack
+
+
+def test_uniform_strip_exact_discrete():
+    """Full-width electrodes on a uniform strip: every row is an identical
+    series chain, so the discrete solution is exact:
+    R = (n_free_columns + 1) / (n_rows * sigma_s)."""
+    p = strip_problem(length=50, width=10, e_len=5)
+    res, stack = _solve(p, 0.5)
+    n_free_cols = int(round((50 - 2 * 5) / 0.5))   # 80
+    n_rows = int(round(10 / 0.5))                  # 20
+    r_exact = (n_free_cols + 1) / n_rows / p.sigma_s(0)
+    assert res.R_ohm == pytest.approx(r_exact, rel=1e-9)
+    assert res.mismatch_rel < 1e-10
+    r_cont = p.rho_ohm_m * 0.0405 / (0.010 * 70e-6)
+    assert res.R_ohm == pytest.approx(r_cont, rel=1e-6)
+
+
+def test_strip_R_independent_of_h():
+    p = strip_problem(length=50, width=10, e_len=5)
+    for h in (1.0, 0.5, 0.25):
+        res, _ = _solve(p, h)
+        m = int(round(40 / h))
+        rows = int(round(10 / h))
+        assert res.R_ohm == pytest.approx((m + 1) / rows / p.sigma_s(0),
+                                          rel=1e-9)
+
+
+def test_partial_electrode_constriction():
+    full = strip_problem(length=50, width=10, e_len=5)
+    partial = make_problem(
+        [([(0, 0), (50, 0), (50, 10), (0, 10)], [])],
+        rect1_mm=(0, 4, 5, 6),
+        rect2_mm=(45, 4, 50, 6))
+    r_full, _ = _solve(full, 0.25)
+    r_a, _ = _solve(partial, 0.25)
+    r_b, _ = _solve(partial, 0.125)
+    assert r_a.R_ohm > r_full.R_ohm * 1.05
+    assert abs(r_a.R_ohm - r_b.R_ohm) < 0.01 * r_b.R_ohm
+
+
+def test_l_shape_corner_squares():
+    """Right-angle bend of equal-width arms: corner square counts as
+    ~0.559 squares (conformal-mapping result), within 5% at a fine grid."""
+    w = 10.0
+    outline = [(0, 0), (30, 0), (30, 30), (20, 30), (20, 10), (0, 10)]
+    p = make_problem([(outline, [])],
+                     rect1_mm=(0, 0, 2, 10),
+                     rect2_mm=(20, 28, 30, 30))
+    res, _ = _solve(p, 0.125)
+    a_sq = (20 - 2) / w
+    b_sq = (28 - 10) / w
+    r_expect = (a_sq + b_sq + 0.559) / p.sigma_s(0)
+    assert res.R_ohm == pytest.approx(r_expect, rel=0.05)
+
+
+def test_hole_increases_resistance_and_converges():
+    solid = make_problem([([(0, 0), (40, 0), (40, 20), (0, 20)], [])],
+                         rect1_mm=(0, 0, 2, 20), rect2_mm=(38, 0, 40, 20))
+    holed = make_problem(
+        [([(0, 0), (40, 0), (40, 20), (0, 20)],
+          [[(15, 5), (25, 5), (25, 15), (15, 15)]])],
+        rect1_mm=(0, 0, 2, 20), rect2_mm=(38, 0, 40, 20))
+    r_solid, _ = _solve(solid, 0.25)
+    r_a, _ = _solve(holed, 0.25)
+    r_b, _ = _solve(holed, 0.125)
+    assert r_a.R_ohm > r_solid.R_ohm * 1.1
+    assert abs(r_a.R_ohm - r_b.R_ohm) < 0.01 * r_b.R_ohm
+
+
+def test_cg_path_matches_direct(monkeypatch):
+    p = strip_problem(length=50, width=10, e_len=5)
+    r_direct, _ = _solve(p, 0.25)
+    monkeypatch.setattr(config, "SPSOLVE_MAX_UNKNOWNS", 0)
+    r_cg, _ = _solve(p, 0.25)
+    assert r_cg.solve_info.method == "cg+jacobi"
+    assert r_cg.R_ohm == pytest.approx(r_direct.R_ohm, rel=1e-6)
+    assert r_cg.mismatch_rel < 1e-5
+
+
+def test_current_density_and_potential_scale():
+    """Uniform strip at 1 A: |J| in the free region equals I/(W t); the
+    potential span equals R * I."""
+    p = strip_problem(length=50, width=10, e_len=5)
+    res, stack = _solve(p, 0.5)
+    j_expect = 1.0 / (0.010 * 70e-6)
+    ny, nx = stack.shape2d
+    assert res.Jmag[0, ny // 2, nx // 2] == pytest.approx(j_expect, rel=1e-6)
+    assert np.nanmax(res.V) == pytest.approx(res.R_ohm, rel=1e-9)
+
+
+def test_test_current_scaling():
+    """V and J scale linearly with I_test, power quadratically; R fixed."""
+    p = strip_problem(length=50, width=10, e_len=5)
+    r1, _ = _solve(p, 0.5, i_test=1.0)
+    r10, _ = _solve(p, 0.5, i_test=10.0)
+    assert r10.R_ohm == pytest.approx(r1.R_ohm, rel=1e-12)
+    assert np.nanmax(r10.V) == pytest.approx(10 * np.nanmax(r1.V), rel=1e-9)
+    assert np.nanmax(r10.Jmag) == pytest.approx(10 * np.nanmax(r1.Jmag),
+                                                rel=1e-9)
+    assert r10.P_total == pytest.approx(100 * r1.P_total, rel=1e-9)
+
+
+def test_power_identity():
+    """Sum of edge powers equals I^2 R exactly for the direct solve."""
+    p = make_problem(
+        [([(0, 0), (40, 0), (40, 20), (0, 20)],
+          [[(15, 5), (25, 5), (25, 15), (15, 15)]])],
+        rect1_mm=(0, 0, 2, 20), rect2_mm=(38, 0, 40, 20))
+    res, _ = _solve(p, 0.25, i_test=40.0)
+    assert res.power_balance_rel < 1e-9
+    assert res.P_total == pytest.approx(40.0 ** 2 * res.R_ohm, rel=1e-12)
+    assert res.P_vias == 0.0

tests/util.py

@@ -0,0 +1,74 @@
+"""Synthetic Problem builders for tests. Dimensions in mm here, nm inside."""
+import numpy as np
+
+from fill_resistance.geometry import (Electrode, LayerFill, Polygon, Problem,
+                                      Rect, ViaLink)
+
+NM = 1_000_000  # nm per mm
+
+
+def ring_mm(points_mm) -> np.ndarray:
+    return (np.asarray(points_mm, dtype=float) * NM).astype(np.int64)
+
+
+def _polys(polygons_mm) -> list[Polygon]:
+    return [
+        Polygon(outline=ring_mm(outline), holes=[ring_mm(h) for h in holes])
+        for outline, holes in polygons_mm
+    ]
+
+
+def rect_mm(r, layer="User.1") -> Rect:
+    return Rect.normalized(int(r[0] * NM), int(r[1] * NM),
+                           int(r[2] * NM), int(r[3] * NM), layer)
+
+
+def make_multilayer(layers_mm, rect1_mm, rect2_mm, contact1="all",
+                    contact2="all", vias_mm=(), t_um=70.0, gap_mm=1.0,
+                    drill_mm=0.3, plating_um=18.0, rho=1.68e-8) -> Problem:
+    """layers_mm: one list of (outline_pts, [holes]) per layer; layer i is
+    named 'L{i}' at z = i * gap_mm. vias_mm: (x, y) through-barrels."""
+    nlayers = len(layers_mm)
+    return Problem(
+        board_path="synthetic",
+        net_name="TEST",
+        rho_ohm_m=rho,
+        plating_nm=int(plating_um * 1000),
+        layers=[
+            LayerFill(layer_name=f"L{i}", thickness_nm=int(t_um * 1000),
+                      z_nm=int(i * gap_mm * NM), polygons=_polys(polys_mm))
+            for i, polys_mm in enumerate(layers_mm)
+        ],
+        vias=[
+            ViaLink(x=int(x * NM), y=int(y * NM),
+                    drill_nm=int(drill_mm * NM),
+                    z_top_nm=-1, z_bot_nm=int((nlayers - 1) * gap_mm * NM) + 1)
+            for x, y in vias_mm
+        ],
+        electrodes1=[Electrode(rect=rect_mm(rect1_mm), contact=contact1)],
+        electrodes2=[Electrode(rect=rect_mm(rect2_mm), contact=contact2)],
+        thickness_source="override",
+    )
+
+
+def make_problem(polygons_mm, rect1_mm, rect2_mm, t_um=70.0,
+                 rho=1.68e-8) -> Problem:
+    """Single-layer problem (the v1 test surface)."""
+    p = make_multilayer([polygons_mm], rect1_mm, rect2_mm, t_um=t_um, rho=rho)
+    p.layers[0].layer_name = "F.Cu"
+    return p
+
+
+def strip_problem(length=50.0, width=10.0, e_len=5.0, t_um=70.0):
+    """Uniform strip with full-width electrodes at both ends."""
+    outline = [(0, 0), (length, 0), (length, width), (0, width)]
+    return make_problem(
+        [(outline, [])],
+        rect1_mm=(0, 0, e_len, width),
+        rect2_mm=(length - e_len, 0, length, width),
+        t_um=t_um,
+    )
+
+
+def sigma_s(t_um=70.0, rho=1.68e-8) -> float:
+    return t_um * 1e-6 / rho