Magnetics add-on: template shapes and hand formulas

/**
 * templates.js — ready-made magnet studies (the Magnetics add-on, 0.8 SG.7+; DOM-free). Each one is the cross-section of a long device, in mm,
 * as closed polygons with a role per polygon (air, iron, magnet, coil: the shapes of PartCraft's magnet-study.js), so a study can be set up and
 * solved without drawing sketches first. Five of them, three with a hand formula the result is compared against:
 *
 *   ccore   C-core electromagnet: an iron C with an air gap, a coil round its back leg (go and return)        hand: μ0·NI / (g + l/μr) in the gap
 *   frame   a permanent magnet in one leg of a closed iron frame                                             hand: Br·(lm/μrm) / (lm/μrm + L/μr)
 *   keeper  a holding magnet: U yoke with a magnet in its base, a keeper across the poles over a small gap   (no hand formula; force through a thin gap is rough)
 *   wire    one round conductor in air                                                                      hand: B = μ0·I / 2πr at r = 2a
 *   wires   two parallel conductors with opposite currents                                                  hand: F = μ0·I² / 2πd per metre
 *
 *   TEMPLATES                 { id → { params: [{ key, def, min, max }], pad? (the air box margin it wants), build(p) → { loops, specs, names }, hand?(p, specs) → { kind, … } } }
 *   build(id, params)         → { loops: [[[x, y] …] …] (mm), specs: [spec], names: [language key], hand: … | null, params (clamped) }
 *   circle(cx, cy, r, n)      → a polygon with n corners (counter-clockwise)
 * A spec is magnet-study.js's: { role, mur, curve, br, angle, murMag, current (total A through the profile), force }.
 * Every material number here is an example (iron μr 1000–2000, magnet Br 1.2 T, μr 1.05), not a data sheet.
 */
export const MU0 = 4e-7 * Math.PI;

export const circle = (cx, cy, r, n = 48) => Array.from({ length: n }, (_, i) => [cx + r * Math.cos(2 * Math.PI * i / n), cy + r * Math.sin(2 * Math.PI * i / n)]);

const { w, h, tk } = p, g = Math.min(p.gap, h - 2 * tk - 2), l = 2 * (w - tk) + 2 * (h - tk) - g, NI = Math.abs(Number(specs[1]?.current) || 0), mur = Number(specs[0]?.mur) || 1;
return { kind: 'meanB', box: [w - tk, h / 2 - g / 2, w, h / 2 + g / 2], value: MU0 * NI / ((g + l / mur) * 1e-3), what: 'hand.ccore', tol: 0.15 };

const { w, h, tk } = p, lm = h - 2 * tk, L = 2 * (w - tk) + 2 * (h - tk) - lm, Br = Number(specs[2]?.br) || 0, murm = Number(specs[2]?.murMag) || 1, mur = Number(specs[0]?.mur) || 1;
return { kind: 'meanB', region: 3, value: Br * (lm / murm) / (lm / murm + L / mur), what: 'hand.frame', tol: 0.02 };

const I = Math.abs(Number(specs[0]?.current) || 0), r = 2 * p.r;
return { kind: 'ringB', at: [0, 0], r0: 1.8 * p.r, r1: 2.2 * p.r, r, value: MU0 * I / (2 * Math.PI * r * 1e-3), what: 'hand.wire', tol: 0.02 };

const I1 = Number(specs[0]?.current) || 0, I2 = Number(specs[1]?.current) || 0;
return { kind: 'force', body: 1, value: MU0 * Math.abs(I1 * I2) / (2 * Math.PI * p.d * 1e-3), what: 'hand.wires', tol: 0.06, perMetre: true };

export function cleanParams(id, params = {}) {
  const T = TEMPLATES[id];
  const out = {};
  for (const q of T.params) { const v = Number(params[q.key]); out[q.key] = Number.isFinite(v) ? Math.min(q.max, Math.max(q.min, v)) : q.def; }
  if (id === 'ccore' || id === 'frame' || id === 'keeper') { out.tk = Math.min(out.tk, (Math.min(out.w, out.h) - 6) / 2); }
  return out;
}