import * as THREE from 'three'; import { chargePair, carrierModel, number, plateModel, wireModel, type ExperimentId, type Parameters } from '../experiments'; import { electricField, type Charge, type Point } from '../physics/electricField'; import { forceOn, pairEnergy, potential } from '../physics/models'; import { arrow, box, colours, grid, label, line, sphere } from './primitives'; import { buildTestScene } from './test4'; export type Animate = (delta: number) => void; const still: Animate = () => {}; function signedCharge(group: THREE.Group, charge: Charge) { const colour = charge.coulombs >= 0 ? colours.positive : colours.negative; sphere(group, charge, 0.2, colour); label(group, String.raw`$${charge.coulombs >= 0 ? '+' : '-'}${Math.abs(charge.coulombs * 1e9).toFixed(1)}\,\mathrm{nC}$`, { ...charge, y: charge.y + 0.55 }, colour, 1.25); } function compressedFieldArrow(group: THREE.Group, position: Point, direction: Point, colour = colours.field) { const strength = Math.hypot(direction.x, direction.y, direction.z); if (strength < 1e-8) return; arrow(group, position, direction, 0.12 + 0.32 * strength / (strength + 4), colour); } function fieldScene(group: THREE.Group, p: Parameters) { grid(group); const charges = chargePair(p); charges.forEach(charge => signedCharge(group, charge)); for (let x = -5; x <= 5; x += 0.6) for (let z = -5; z <= 5; z += 0.6) { const point = { x, y: 0, z }; if (charges.some(q => Math.hypot(q.x - x, q.z - z) < 0.42)) continue; compressedFieldArrow(group, point, electricField(point, charges)); } const force = forceOn(charges[1], [charges[0]]); arrow(group, { ...charges[1], y: 0.8 }, force, 1.3, colours.gold); label(group, String.raw`$\vec F$ on right charge`, { x: charges[1].x, y: 1.5, z: 0 }, colours.gold, 2); sphere(group, { x: 0, y: 0, z: 0 }, 0.06, colours.gold); label(group, 'Origin', { x: 0, y: 0, z: 0.45 }, colours.muted, 0.9); } function fluxScene(group: THREE.Group, p: Parameters) { const radius = number(p, 'radius'); const charge: Charge = { x: number(p, 'position'), y: 0, z: 0, coulombs: number(p, 'charge') * 1e-9 }; grid(group, -3.4); signedCharge(group, charge); const surface = new THREE.Mesh(new THREE.SphereGeometry(radius, 40, 24), new THREE.MeshBasicMaterial({ color: colours.negative, wireframe: true, transparent: true, opacity: 0.11, depthWrite: false })); group.add(surface); for (let i = 0; i < 150; i++) { const y = 1 - 2 * (i + 0.5) / 150; const r = Math.sqrt(1 - y * y); const theta = i * Math.PI * (3 - Math.sqrt(5)); const normal = { x: r * Math.cos(theta), y, z: r * Math.sin(theta) }; const point = { x: normal.x * radius, y: y * radius, z: normal.z * radius }; if (Math.hypot(point.x - charge.x, point.y, point.z) < 0.3) continue; const e = electricField(point, [charge]); const dot = e.x * normal.x + e.y * normal.y + e.z * normal.z; compressedFieldArrow(group, point, e, dot >= 0 ? colours.field : colours.positive); } label(group, 'Gaussian surface', { x: 0, y: radius + 0.6, z: 0 }, colours.negative, 2.5); line(group, [{ x: -4.7, y: 0, z: 0 }, { x: 4.7, y: 0, z: 0 }], colours.muted, 0.4); } function energyScene(group: THREE.Group, p: Parameters) { grid(group, -4.3); const r = number(p, 'distance'); const q = number(p, 'testCharge') * 1e-9; const source: Charge = { x: -3, y: 0, z: 1.5, coulombs: 3e-9 }; const moving: Charge = { x: -3 + r, y: 0, z: 1.5, coulombs: q }; signedCharge(group, source); signedCharge(group, moving); line(group, [source, moving], colours.muted); arrow(group, { ...moving, y: 0.7 }, forceOn(moving, [source]), 1.1, colours.gold); const curve: Point[] = []; for (let distance = 0.75; distance <= 6; distance += 0.05) curve.push({ x: -3 + distance, y: pairEnergy(3e-9, q, distance) * 1e9 / 20, z: -1.5 }); line(group, curve, colours.field); line(group, [{ x: -2.5, y: 0, z: -1.5 }, { x: 3.5, y: 0, z: -1.5 }], colours.muted); line(group, [{ x: -3, y: -5.5, z: -1.5 }, { x: -3, y: 5.5, z: -1.5 }], colours.muted, 0.5); sphere(group, { x: -3 + r, y: pairEnergy(3e-9, q, r) * 1e9 / 20, z: -1.5 }, 0.12, colours.gold); label(group, String.raw`$U(r)$ · 20 nJ per height unit`, { x: 0, y: 5.7, z: -1.5 }, colours.field, 3.9); label(group, '0 energy', { x: 4, y: 0, z: -1.5 }, colours.muted, 1.5); label(group, String.raw`$r = ${r.toFixed(2)}\,\mathrm m$`, { x: 0, y: -0.65, z: 1.5 }, colours.muted, 2); } function potentialScene(group: THREE.Group, p: Parameters) { const charges = chargePair(p); const geometry = new THREE.PlaneGeometry(10, 10, 64, 64); geometry.rotateX(-Math.PI / 2); const positions = geometry.getAttribute('position'); const values: number[] = []; const colourValues: number[] = []; const negative = new THREE.Color(colours.negative); const positive = new THREE.Color(colours.positive); const neutral = new THREE.Color('#203847'); for (let i = 0; i < positions.count; i++) { const point = { x: positions.getX(i), y: 0, z: positions.getZ(i) }; const v = potential(point, charges); const height = Number.isFinite(v) ? Math.tanh(v / 15) : NaN; values.push(height); positions.setY(i, Number.isFinite(height) ? 2 * height : 0); const colour = neutral.clone().lerp(height >= 0 ? positive : negative, Math.abs(Number.isFinite(height) ? height : 0)); colourValues.push(colour.r, colour.g, colour.b); } const indices = geometry.getIndex()!; const kept: number[] = []; for (let i = 0; i < indices.count; i += 3) { const a = indices.getX(i), b = indices.getX(i + 1), c = indices.getX(i + 2); if ([a, b, c].every(index => Number.isFinite(values[index]))) kept.push(a, b, c); } geometry.setIndex(kept); geometry.setAttribute('color', new THREE.Float32BufferAttribute(colourValues, 3)); geometry.computeVertexNormals(); group.add(new THREE.Mesh(geometry, new THREE.MeshStandardMaterial({ vertexColors: true, side: THREE.DoubleSide, roughness: 0.7, transparent: true, opacity: 0.88 }))); for (let x = -4.5; x <= 4.5; x += 0.75) for (let z = -4.5; z <= 4.5; z += 0.75) { const point = { x, y: 0, z }; if (charges.some(q => Math.hypot(q.x - x, q.z - z) < 0.6)) continue; const v = potential(point, charges); if (!Number.isFinite(v)) continue; compressedFieldArrow(group, { ...point, y: 2 * Math.tanh(v / 15) + 0.12 }, electricField(point, charges)); } const probe = { x: number(p, 'probe'), y: 0, z: 1 }; const v = potential(probe, charges); sphere(group, { ...probe, y: 2 * Math.tanh(v / 15) + 0.2 }, 0.13, colours.gold); label(group, 'Probe', { ...probe, y: 2 * Math.tanh(v / 15) + 0.8 }, colours.gold, 1.3); charges.forEach(charge => signedCharge(group, { ...charge, y: Math.sign(charge.coulombs) * 2.2 })); grid(group, -2.4); } function plateScene(group: THREE.Group, p: Parameters, dielectric: boolean) { const c = plateModel(p); const halfGap = number(p, 'gap') * 0.75; const side = Math.sqrt(number(p, 'area')) * 0.3; // Uniform magnification maps lateral metres to 30 scene units/m and gap // metres to 1500 units/m: gap is enlarged 50x relative to plate width. for (const sign of [1, -1]) { const x = -sign * halfGap; const colour = sign === 1 ? colours.positive : colours.negative; box(group, { x, y: 0, z: 0 }, { x: 0.05, y: side, z: side }, colour, 0.65); label(group, sign === 1 ? '+ plate' : '− plate', { x, y: side / 2 + 0.45, z: 0 }, colour, 1.2); for (let y = -0.35; y <= 0.35; y += 0.35) for (let z = -0.35; z <= 0.35; z += 0.35) { sphere(group, { x: x + sign * 0.035, y: y * side, z: z * side }, 0.025, colour); } } for (let y = -0.3; y <= 0.3; y += 0.3) for (let z = -0.3; z <= 0.3; z += 0.3) { const length = Math.max(0.1, 2 * halfGap - 0.1); // Repeated arrows are direction cues; readouts provide field magnitude. arrow(group, { x: -halfGap + 0.05, y: y * side, z: z * side }, { x: 1, y: 0, z: 0 }, length, colours.field); } if (dielectric) { box(group, { x: 0, y: 0, z: 0 }, { x: Math.max(0.04, 2 * halfGap - 0.08), y: side * 0.92, z: side * 0.92 }, colours.gold, 0.1); const kappa = number(p, 'permittivity'); if (kappa > 1) { const boundOffset = Math.min(halfGap * 0.65, 0.12) * (kappa - 1) / kappa; for (let y = -0.32; y <= 0.32; y += 0.32) for (let z = -0.32; z <= 0.32; z += 0.32) { const center = { x: 0, y: y * side, z: z * side }; sphere(group, { ...center, x: -boundOffset }, 0.035, colours.negative); sphere(group, { ...center, x: boundOffset }, 0.035, colours.positive); line(group, [{ ...center, x: -boundOffset }, { ...center, x: boundOffset }], colours.gold); } } } line(group, [{ x: -halfGap, y: -side, z: 0 }, { x: halfGap, y: -side, z: 0 }], colours.muted); label(group, String.raw`$d = ${number(p, 'gap').toFixed(1)}\,\mathrm{mm}$ (gap $\times50$)`, { x: 0, y: -side - 0.45, z: 0 }, colours.muted, 2.5); label(group, String.raw`$${c.voltage.toFixed(2)}\,\mathrm V$ · ${p.connection === 'isolated' ? 'isolated' : 'supply connected'}`, { x: 0, y: side + 0.8, z: 0 }, colours.field, 3); grid(group, -3.2); } function currentScene(group: THREE.Group, p: Parameters): Animate { grid(group, -2); const model = wireModel(p); const length = number(p, 'length') * 3; const radius = Math.sqrt(number(p, 'area')) * 0.4; const wire = new THREE.Mesh(new THREE.CylinderGeometry(radius, radius, length, 28, 1, true), new THREE.MeshStandardMaterial({ color: '#bf8158', transparent: true, opacity: 0.12, side: THREE.DoubleSide, depthWrite: false })); wire.rotation.z = Math.PI / 2; group.add(wire); for (let i = 0; i < 6; i++) { const x = length * ((i + 0.5) / 6 - 0.5); for (let j = 0; j < 6; j++) { const angle = j * Math.PI / 3; sphere(group, { x, y: radius * 0.8 * Math.cos(angle), z: radius * 0.8 * Math.sin(angle) }, 0.055, colours.gold); } } const carriers: THREE.Mesh[] = []; for (let i = 0; i < 32; i++) { const angle = i * 2.39996; const r = radius * 0.65 * Math.sqrt((i % 7 + 1) / 8); carriers.push(sphere(group, { x: length * (i / 32 - 0.5), y: r * Math.cos(angle), z: r * Math.sin(angle) }, 0.065, colours.negative)); } arrow(group, { x: -Math.sign(model.current) * 1.1, y: radius + 0.8, z: 0 }, { x: model.current, y: 0, z: 0 }, 2.2, colours.field); label(group, model.current === 0 ? 'No net current' : 'Conventional current', { x: 0, y: radius + 1.5, z: 0 }, colours.field, 2.8); arrow(group, { x: -Math.sign(model.electronDrift) * 1.1, y: -radius - 0.65, z: 0 }, { x: model.electronDrift, y: 0, z: 0 }, 2.2, colours.negative); label(group, String.raw`Electron drift · displayed $\times600$`, { x: 0, y: -radius - 1.1, z: 0 }, colours.negative, 3.3); const velocity = model.electronDrift * 600 * 3; return delta => { for (const electron of carriers) { electron.position.x = ((electron.position.x + length / 2 + delta * velocity) % length + length) % length - length / 2; } }; } function semiconductorScene(group: THREE.Group, p: Parameters): Animate { grid(group, -3.5); const s = carrierModel(p); // 3 display units per eV; approximate intrinsic level at midgap. const bandEdge = 1.12 / 2 * 3; box(group, { x: 0, y: bandEdge + 0.4, z: 0 }, { x: 7, y: 0.8, z: 3 }, colours.negative, 0.12); box(group, { x: 0, y: -bandEdge - 0.4, z: 0 }, { x: 7, y: 0.8, z: 3 }, colours.positive, 0.12); line(group, [{ x: -3.5, y: 0, z: 1.6 }, { x: 3.5, y: 0, z: 1.6 }], colours.muted, 0.7); line(group, [{ x: -3.6, y: s.fermiShift * 3, z: 1.65 }, { x: 3.6, y: s.fermiShift * 3, z: 1.65 }], colours.gold); label(group, String.raw`$E_F$`, { x: 4, y: s.fermiShift * 3, z: 1.65 }, colours.gold, 0.7); label(group, String.raw`$E_i\approx\text{midgap}$`, { x: -4.4, y: 0, z: 1.65 }, colours.muted, 1.7); label(group, 'Conduction band', { x: 0, y: bandEdge + 1.1, z: 0 }, colours.negative, 2.8); label(group, 'Valence band', { x: 0, y: -bandEdge - 1.1, z: 0 }, colours.positive, 2.8); label(group, String.raw`$E_g=1.12\,\mathrm{eV}$`, { x: 4.1, y: 0, z: -1.3 }, colours.muted, 1.8); line(group, [{ x: 3.8, y: -bandEdge, z: -1.3 }, { x: 3.8, y: bandEdge, z: -1.3 }], colours.muted); const particles: { mesh: THREE.Mesh; base: THREE.Vector3; phase: number }[] = []; for (const [density, sign] of [[s.electrons, 1], [s.holes, -1]]) { const count = Math.round(3 + Math.max(0, Math.log10(density) - 8) * 2.5); for (let i = 0; i < count; i++) { const x = 6.4 * ((i * 0.618034) % 1 - 0.5); const z = 2.5 * ((i * 0.414214) % 1 - 0.5); const mesh = sphere(group, { x, y: sign * (bandEdge + 0.4), z }, 0.075, sign === 1 ? colours.negative : colours.positive); if (sign === -1) { (mesh.material as THREE.MeshStandardMaterial).wireframe = true; } particles.push({ mesh, base: mesh.position.clone(), phase: i * 2.4 + sign }); } } let time = 0; return delta => { time += delta; for (const particle of particles) { particle.mesh.position.x = particle.base.x + 0.12 * Math.sin(time * 1.3 + particle.phase); particle.mesh.position.z = particle.base.z + 0.12 * Math.cos(time * 1.7 + particle.phase); } }; } export function buildExperiment(group: THREE.Group, id: ExperimentId, p: Parameters): Animate { switch (id) { case 'field': fieldScene(group, p); break; case 'flux': fluxScene(group, p); break; case 'energy': energyScene(group, p); break; case 'potential': potentialScene(group, p); break; case 'capacitance': plateScene(group, p, false); break; case 'dielectric': plateScene(group, p, true); break; case 'current': return currentScene(group, p); case 'semiconductor': return semiconductorScene(group, p); default: return buildTestScene(group, id, p); } return still; }