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Diffstat (limited to 'src/scene/experiments.ts')
| -rw-r--r-- | src/scene/experiments.ts | 245 |
1 files changed, 245 insertions, 0 deletions
diff --git a/src/scene/experiments.ts b/src/scene/experiments.ts new file mode 100644 index 0000000..67d0322 --- /dev/null +++ b/src/scene/experiments.ts @@ -0,0 +1,245 @@ +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'; + +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, `${charge.coulombs >= 0 ? '+' : '−'}${Math.abs(charge.coulombs * 1e9).toFixed(1)} 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, '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, '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, `r = ${r.toFixed(2)} 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, `d = ${number(p, 'gap').toFixed(1)} mm (gap ×50)`, { x: 0, y: -side - 0.45, z: 0 }, colours.muted, 2.5); + label(group, `${c.voltage.toFixed(2)} 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, 'Electron drift · displayed ×600', { 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, 'EF', { x: 4, y: s.fermiShift * 3, z: 1.65 }, colours.gold, 0.7); + label(group, 'Ei ≈ 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, 'Eg = 1.12 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); + } + return still; +} |