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1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 | /** * Render influence highlight: a prominent glowing ring around the most * influential given point when hovering over a derived point, with a * connecting line, preview arrow, and motion trail during drag. * * Features smooth fade-in/fade-out transitions. */ import type { ConstructionState, EuclidViewportState } from '../types' import { getPoint } from '../engine/constructionState' import { worldToScreen2D } from '../../shared/coordinateConversions' import { constrainedDragStep } from '../engine/jacobianInfluence' // ── Visual constants ── const HIGHLIGHT_COLOR = '#4E79A7' // Byrne blue const LINE_COLOR_BASE = 'rgba(78, 121, 167, 0.35)' const OUTER_RING_RADIUS = 20 const INNER_RING_RADIUS = 14 const GLOW_RADIUS = 28 const OUTER_RING_WIDTH = 2 const INNER_RING_WIDTH = 3 const DASH_PATTERN: [number, number] = [6, 4] const FADE_DURATION_MS = 500 const PREVIEW_ARROW_COLOR = '#4E79A7' const PREVIEW_ARROW_SCALE = 40 // pixels per unit of Jacobian response const PREVIEW_ARROW_MAX_LEN = 60 // max arrow length in pixels const PREVIEW_ARROW_HEAD = 8 // arrowhead size const PREVIEW_ARROW_FADE_START = 15 // screen px from derived point: arrow fully visible beyond this const PREVIEW_ARROW_FADE_END = 5 // screen px from derived point: arrow fully hidden below this const TENSION_START_RADIUS = 40 // screen px: tension visuals begin const BREAK_FREE_RADIUS = 250 // screen px: constraint snaps const TENSION_DAMPEN = 0.95 // at max tension, cursor influence reduced to 1 - this const TENSION_COLOR = '#D98D2F' // amber for strained state const TENSION_COLOR_RGB = '217, 141, 47' const HIGHLIGHT_COLOR_RGB = '78, 121, 167' const BREAK_FREE_FLASH_DURATION_MS = 400 const BREAK_FREE_SHOCKWAVE_MAX_RADIUS = 80 const TRAIL_COLOR = 'rgba(78, 121, 167, 0.6)' const TRAIL_MAX_POINTS = 20 const TRAIL_MAX_WIDTH = 4 const TRAIL_MIN_WIDTH = 0.5 // ── State types ── /** Persistent state for smooth highlight transitions. */ export interface InfluenceHighlightState { opacity: number targetOpacity: number derivedPointId: string | null givenPointId: string | null fadeStartTime: number fadeStartOpacity: number /** Sub-Jacobian for preview arrow: [∂tx/∂gx, ∂tx/∂gy, ∂ty/∂gx, ∂ty/∂gy] */ subJacobian: [number, number, number, number] | null /** 0..1 tension during constrained drag (0 = relaxed, 1 = about to break) */ tension: number /** Cursor screen position during constrained drag (for rubber band line) */ cursorScreen: { x: number; y: number } | null /** * Field targets — derived points whose constraint-response field * contributes to the background. Each is rendered with its own * proximity factor based on cursor distance, so as the cursor moves * between two derived points their fields naturally crossfade * (one's prox shrinks while the other's grows) — no hard switch. * Updated on every pointer move; entries with negligible proximity * are dropped to bound cost. */ fieldTargets: FieldTarget[] } export interface FieldTarget { derivedPointId: string givenPointId: string subJacobian: [number, number, number, number] } export function createInfluenceHighlightState(): InfluenceHighlightState { return { opacity: 0, targetOpacity: 0, derivedPointId: null, givenPointId: null, fadeStartTime: 0, fadeStartOpacity: 0, subJacobian: null, tension: 0, cursorScreen: null, fieldTargets: [], } } /** Visual flash when the constraint breaks free during a drag. */ export interface BreakFreeFlash { startTime: number /** Screen position of the influential given point at the moment of break */ givenScreen: { x: number; y: number } /** Screen position of the derived point at the moment of break */ derivedScreen: { x: number; y: number } } /** Motion trail state: ring buffer of recent positions for each tracked point. */ export interface MotionTrailState { /** Point ID being trailed */ pointId: string | null /** Ring buffer of recent screen positions */ positions: Array<{ x: number; y: number }> /** Write index into the ring buffer */ writeIdx: number /** Number of valid entries */ count: number /** Fade-out opacity (1 while dragging, decays after release) */ opacity: number } export function createMotionTrailState(): MotionTrailState { return { pointId: null, positions: new Array(TRAIL_MAX_POINTS).fill({ x: 0, y: 0 }), writeIdx: 0, count: 0, opacity: 0, } } /** Record a new position in the trail. Call each drag frame. */ export function recordTrailPosition( trail: MotionTrailState, pointId: string, screenX: number, screenY: number ): void { if (trail.pointId !== pointId) { // New drag target — reset trail.pointId = pointId trail.count = 0 trail.writeIdx = 0 } trail.positions[trail.writeIdx] = { x: screenX, y: screenY } trail.writeIdx = (trail.writeIdx + 1) % TRAIL_MAX_POINTS if (trail.count < TRAIL_MAX_POINTS) trail.count++ trail.opacity = 1 } /** Call when drag ends to begin fade-out. */ export function clearTrail(trail: MotionTrailState): void { trail.pointId = null trail.count = 0 trail.writeIdx = 0 trail.opacity = 0 } // ── Highlight target update ── export function updateInfluenceTarget( state: InfluenceHighlightState, derivedPointId: string | null, givenPointId: string | null, now: number ): void { const hasTarget = derivedPointId != null && givenPointId != null if (hasTarget) { state.derivedPointId = derivedPointId state.givenPointId = givenPointId if (state.targetOpacity !== 1) { state.targetOpacity = 1 state.fadeStartTime = now state.fadeStartOpacity = state.opacity } } else { if (state.targetOpacity !== 0) { state.targetOpacity = 0 state.fadeStartTime = now state.fadeStartOpacity = state.opacity } } } // ── Helpers ── function toScreen(wx: number, wy: number, vp: EuclidViewportState, w: number, h: number) { return worldToScreen2D(wx, wy, vp.center.x, vp.center.y, vp.pixelsPerUnit, vp.pixelsPerUnit, w, h) } function easeOutCubic(t: number): number { return 1 - (1 - t) ** 3 } /** * Distance-based proximity multiplier. Softened inverse-square falloff: * f(d) = R² / (R² + d²). At d = 0 the factor is 1; at d = R it's ½; for * d ≫ R it decays as 1/d² (true inverse-square asymptote). */ const PROXIMITY_HALF_RADIUS_PX = 220 function proximityFromDistance(d: number): number { const r = PROXIMITY_HALF_RADIUS_PX return (r * r) / (r * r + d * d) } /** * Width (px) of the soft Voronoi boundary between adjacent field targets. * Targets at distance > d_min + this contribute weight 0; at distance = * d_min they get weight 1; linearly interpolated in between. Larger → * wider blend zone near bisectors. Smaller → harder Voronoi cells. */ const VORONOI_TRANSITION_PX = 70 interface FieldRenderItem { target: FieldTarget derivedScreen: { x: number; y: number } distance: number weight: number } /** * Compute the cursor-relative weighting for each field target. Returns the * minimum distance to any target plus a per-target weight that's 1 on the * nearest, falls linearly to 0 for any target farther than VORONOI_TRANSITION_PX * past the nearest, and is normalized so the weights sum to 1. This gives: * - Firmly near point A: only A's field renders (weight ≈ 1, neighbors 0) * - Near a bisector between A & B: smooth crossfade (weights split) * - Far from all: dMin large, caller can use proximity falloff to fade out */ function computeFieldRenderItems( state: ConstructionState, viewport: EuclidViewportState, w: number, h: number, pointerWorld: { x: number; y: number } | null, fieldTargets: FieldTarget[] ): { dMin: number; items: FieldRenderItem[] } | null { if (!pointerWorld || fieldTargets.length === 0) return null const cursor = toScreen(pointerWorld.x, pointerWorld.y, viewport, w, h) const items: Array<FieldRenderItem & { rawWeight: number }> = [] let dMin = Infinity for (const target of fieldTargets) { const pt = getPoint(state, target.derivedPointId) if (!pt) continue const ds = toScreen(pt.x, pt.y, viewport, w, h) const dx = cursor.x - ds.x const dy = cursor.y - ds.y const d = Math.sqrt(dx * dx + dy * dy) if (d < dMin) dMin = d items.push({ target, derivedScreen: ds, distance: d, weight: 0, rawWeight: 0 }) } if (items.length === 0) return null let sumRaw = 0 for (const it of items) { it.rawWeight = Math.max(0, 1 - (it.distance - dMin) / VORONOI_TRANSITION_PX) sumRaw += it.rawWeight } const out: FieldRenderItem[] = items.map((it) => ({ target: it.target, derivedScreen: it.derivedScreen, distance: it.distance, weight: sumRaw > 0 ? it.rawWeight / sumRaw : 0, })) return { dMin, items: out } } /** Lerp between two RGB color strings based on t (0..1). Returns CSS rgba(). */ function lerpColor( r1: number, g1: number, b1: number, r2: number, g2: number, b2: number, t: number, a: number ): string { const r = Math.round(r1 + (r2 - r1) * t) const g = Math.round(g1 + (g2 - g1) * t) const b = Math.round(b1 + (b2 - b1) * t) return `rgba(${r}, ${g}, ${b}, ${a})` } /** Lerp between Byrne blue and tension amber. */ function tensionColor(tension: number, alpha: number): string { return lerpColor(78, 121, 167, 217, 141, 47, tension, alpha) } /** Hex color lerped between blue and amber based on tension. */ function tensionHex(tension: number): string { const r = Math.round(78 + (217 - 78) * tension) const g = Math.round(121 + (141 - 121) * tension) const b = Math.round(167 + (47 - 167) * tension) return `rgb(${r}, ${g}, ${b})` } function drawArrowhead( ctx: CanvasRenderingContext2D, tipX: number, tipY: number, angle: number, size: number ): void { ctx.beginPath() ctx.moveTo(tipX, tipY) ctx.lineTo( tipX - size * Math.cos(angle - Math.PI / 6), tipY - size * Math.sin(angle - Math.PI / 6) ) ctx.moveTo(tipX, tipY) ctx.lineTo( tipX - size * Math.cos(angle + Math.PI / 6), tipY - size * Math.sin(angle + Math.PI / 6) ) ctx.stroke() } // ── Constraint response field ── /** * Paint a per-direction encoding of the constrained-drag response over the * entire canvas, anchored at the derived point. The user can read it before * dragging to discover how the controlling given will react to each possible * cursor direction. * * The 2×2 sub-Jacobian J is locally constant, so the response is radially * symmetric around the derived point — every pixel along a ray from D * produces the same Δg direction and gain. We encode that into 120 angular * stops on a conic gradient and fill the whole canvas in a single draw. * * Coordinate handling: J is in world coords (y-up); the canvas is screen * coords (y-down). The screen-effective Jacobian J' = (1/det) [[d, b],[c, a]] * (derived from J⁻¹ with a y-flip on each side) takes a screen-space * Δd_unit directly to a screen-space Δg vector — so screen-angle math * produces the rotation the user actually perceives. * * Encoding: * • Hue from green (intuitive, Δg ‖ Δd) through yellow (sideways) to * red (anti-aligned, Δg ‖ -Δd) — based on |rotation|. * • Lightness from gain |Δg| / |Δd|, normalized within the frame so the * two principal-axis lobes always pop visually (bright = high mechanical * advantage in this direction; dim = the constraint resists motion). * * @returns true if a field was drawn (caller may want to redraw) */ export function renderConstraintField( ctx: CanvasRenderingContext2D, state: ConstructionState, viewport: EuclidViewportState, w: number, h: number, highlightState: InfluenceHighlightState, pointerWorld: { x: number; y: number } | null ): boolean { if (highlightState.fieldTargets.length === 0) return false const result = computeFieldRenderItems( state, viewport, w, h, pointerWorld, highlightState.fieldTargets ) if (!result) return false const globalProx = proximityFromDistance(result.dMin) if (globalProx < 0.005) return false let drewAny = false for (const item of result.items) { const alphaMultiplier = globalProx * item.weight if (alphaMultiplier < 0.005) continue if (renderConstraintFieldForTarget(ctx, viewport, w, h, item, alphaMultiplier)) { drewAny = true } } return drewAny } function renderConstraintFieldForTarget( ctx: CanvasRenderingContext2D, viewport: EuclidViewportState, w: number, h: number, item: FieldRenderItem, alphaMultiplier: number ): boolean { const [a, b, c, d] = item.target.subJacobian const det = a * d - b * c if (Math.abs(det) < 1e-9) return false // degenerate — nothing to show const derivedScreen = item.derivedScreen const N = 120 const gains = new Float32Array(N + 1) const rotations = new Float32Array(N + 1) let maxGain = 0 for (let i = 0; i <= N; i++) { const θ = (i / N) * 2 * Math.PI const sx = Math.cos(θ) const sy = Math.sin(θ) // Screen-effective J': Δg_screen = (1/det) · [[d, b],[c, a]] · Δd_screen const gx = (d * sx + b * sy) / det const gy = (c * sx + a * sy) / det const gain = Math.sqrt(gx * gx + gy * gy) if (gain > maxGain) maxGain = gain gains[i] = gain let rot = Math.atan2(gy, gx) - θ while (rot > Math.PI) rot -= 2 * Math.PI while (rot < -Math.PI) rot += 2 * Math.PI rotations[i] = rot } // Build conic gradient anchored at the derived point in screen space. // Canvas conic angles measure clockwise from +x — same as our screen θ. const grad = ctx.createConicGradient(0, derivedScreen.x, derivedScreen.y) const fieldAlpha = 0.18 * alphaMultiplier for (let i = 0; i <= N; i++) { const t = i / N const absRot = Math.abs(rotations[i]) // 0 rotation → 120 (green), π/2 → 60 (yellow), π → 0 (red) const hue = 120 * (1 - absRot / Math.PI) const normGain = maxGain > 0 ? gains[i] / maxGain : 0 // Bias lightness toward the bright end of high-gain lobes so the // principal axes are unmistakable; dim sectors stay readable. const lightness = 32 + 38 * normGain grad.addColorStop(t, `hsla(${hue}, 75%, ${lightness}%, ${fieldAlpha})`) } ctx.save() ctx.fillStyle = grad ctx.fillRect(0, 0, w, h) ctx.restore() return true } // ── LIC (Line Integral Convolution) ── // Continuous flow visualization: smear a noise texture along the field's // streamlines so coherent flow direction shows up as smeared streaks. Output // is grayscale, drawn with `multiply` blend so it darkens the existing color // (the conic gradient from renderConstraintField) without overwriting it. // // Computed at low resolution (LIC_W × LIC_H), upscaled to canvas size — the // upscale's bilinear smoothing is what makes the result feel like a smooth // gradient rather than a discrete tile pattern. // Target offscreen pixel count — LIC dimensions adapt to the main canvas // aspect ratio so a square or 4:3 canvas doesn't stretch streaks horizontally. const LIC_TARGET_PIXELS = 22000 const NOISE_SIZE = 256 // power-of-two so wrapping uses bitmask; large enough that the table doesn't visibly tile across the canvas const NOISE_MASK = NOISE_SIZE - 1 let licCanvas: HTMLCanvasElement | null = null let licCtx2D: CanvasRenderingContext2D | null = null let licImage: ImageData | null = null let licW = 0 let licH = 0 let noiseTable: Float32Array | null = null function computeLicDims(w: number, h: number): { lw: number; lh: number } { const aspect = w / h let lw = Math.round(Math.sqrt(LIC_TARGET_PIXELS * aspect)) let lh = Math.round(lw / aspect) if (lw < 32) lw = 32 if (lh < 32) lh = 32 return { lw, lh } } function ensureLicResources(targetW: number, targetH: number): void { if (!noiseTable) { noiseTable = new Float32Array(NOISE_SIZE * NOISE_SIZE) let s = 0x9e3779b9 for (let i = 0; i < noiseTable.length; i++) { s = ((s * 1103515245) >>> 0) + 12345 noiseTable[i] = ((s >>> 8) & 0xffff) / 65535 } } if (typeof document === 'undefined') return if (!licCanvas) { licCanvas = document.createElement('canvas') licCtx2D = licCanvas.getContext('2d')! } if (licW !== targetW || licH !== targetH || !licImage) { licW = targetW licH = targetH licCanvas.width = licW licCanvas.height = licH licImage = licCtx2D!.createImageData(licW, licH) } } function sampleNoise(x: number, y: number): number { const t = noiseTable! const xfm = x - Math.floor(x) const yfm = y - Math.floor(y) const xi = Math.floor(x) & NOISE_MASK const yi = Math.floor(y) & NOISE_MASK const xn = (xi + 1) & NOISE_MASK const yn = (yi + 1) & NOISE_MASK const r0 = yi * NOISE_SIZE const r1 = yn * NOISE_SIZE const n00 = t[r0 + xi] const n10 = t[r0 + xn] const n01 = t[r1 + xi] const n11 = t[r1 + xn] const a = n00 + (n10 - n00) * xfm const b = n01 + (n11 - n01) * xfm return a + (b - a) * yfm } /** * Continuous flow visualization for the constraint response field * Δg(P) = J' · (P − D). Rendered via Line Integral Convolution: at every * output pixel, walk forward and backward along Δg in small steps, sampling * a smooth noise texture; average the samples. The result is high autocorr- * elation along streamlines (smooth) and decorrelation across them (sharp), * producing a brushed-flow texture without discrete lines. * * Drawn after the conic gradient (renderConstraintField) with `multiply` * blend, so the LIC darkens the colored field rather than replacing it. */ export function renderConstraintFieldFlow( ctx: CanvasRenderingContext2D, state: ConstructionState, viewport: EuclidViewportState, w: number, h: number, highlightState: InfluenceHighlightState, pointerWorld: { x: number; y: number } | null ): boolean { if (highlightState.fieldTargets.length === 0) return false const result = computeFieldRenderItems( state, viewport, w, h, pointerWorld, highlightState.fieldTargets ) if (!result) return false const globalProx = proximityFromDistance(result.dMin) if (globalProx < 0.005) return false let drewAny = false for (const item of result.items) { const alphaMultiplier = globalProx * item.weight if (alphaMultiplier < 0.005) continue if (renderConstraintFieldFlowForTarget(ctx, viewport, w, h, item, alphaMultiplier)) { drewAny = true } } return drewAny } function renderConstraintFieldFlowForTarget( ctx: CanvasRenderingContext2D, viewport: EuclidViewportState, w: number, h: number, item: FieldRenderItem, alphaMultiplier: number ): boolean { const [a, b, c, d] = item.target.subJacobian const det = a * d - b * c if (Math.abs(det) < 1e-9) return false const dims = computeLicDims(w, h) ensureLicResources(dims.lw, dims.lh) if (!licCanvas || !licCtx2D || !licImage) return false const D = item.derivedScreen // Map derived-point screen position into LIC pixel space. const sxk = licW / w const syk = licH / h const Dlx = D.x * sxk const Dly = D.y * syk // Tunables. Step/half scaled with LIC resolution so streak length on the // final canvas stays comparable across resolution changes. const STEP = 1.6 // LIC px per integration step const HALF = 16 // steps each direction const NOISE_SCALE = 0.45 // LIC-px-to-noise-px scale (smaller = chunkier streaks) const CONTRAST = 1.9 // amplify deviation from 0.5 → more visible streaks const NEAR_D_LIC = 2 // skip only the very pixel at D — blur covers residue // Magnitude reference: |Δg| at (P−D) of length halfDiagLic in the worst // direction is bounded by Frobenius(J')·halfDiagLic. We use this to map // local |Δg(P)| into a 0..1 "intensity" so far-from-D pixels darken more // (= bigger required given-point move). Both numerator and denominator // carry the same |det| factor below, so it cancels — no need to divide. const halfDiagLic2 = (licW * licW + licH * licH) / 4 const frobSquared = a * a + b * b + c * c + d * d const refMag2 = frobSquared * halfDiagLic2 const data = licImage.data let idx = 0 for (let py = 0; py < licH; py++) { for (let px = 0; px < licW; px++) { const xC = px + 0.5 const yC = py + 0.5 const dxN = xC - Dlx const dyN = yC - Dly let v = 0.5 let intensity = 0 if (dxN * dxN + dyN * dyN >= NEAR_D_LIC * NEAR_D_LIC) { let sum = 0 let count = 0 // Forward walk let cx = xC let cy = yC for (let i = 0; i < HALF; i++) { const ex = cx - Dlx const ey = cy - Dly // Field direction (J' · e) — we normalize by m below, so direction // matters but absolute scale doesn't here. const gx = d * ex + b * ey const gy = c * ex + a * ey const m = Math.sqrt(gx * gx + gy * gy) if (m < 1e-9) break cx += (gx / m) * STEP cy += (gy / m) * STEP sum += sampleNoise(cx * NOISE_SCALE, cy * NOISE_SCALE) count++ } // Backward walk cx = xC cy = yC for (let i = 0; i < HALF; i++) { const ex = cx - Dlx const ey = cy - Dly const gx = d * ex + b * ey const gy = c * ex + a * ey const m = Math.sqrt(gx * gx + gy * gy) if (m < 1e-9) break cx -= (gx / m) * STEP cy -= (gy / m) * STEP sum += sampleNoise(cx * NOISE_SCALE, cy * NOISE_SCALE) count++ } if (count > 0) v = sum / count // Local |J' · (P−D)|² (proportional to |Δg(P)|², |det|² factor // cancels with refMag2 below). const lgx = d * dxN + b * dyN const lgy = c * dxN + a * dyN const localMag2 = lgx * lgx + lgy * lgy intensity = Math.sqrt(localMag2 / refMag2) if (intensity > 1) intensity = 1 } // Stretch contrast around 0.5 → streak value in [0,1]. let streak = 0.5 + (v - 0.5) * CONTRAST if (streak < 0) streak = 0 else if (streak > 1) streak = 1 // Lerp from white (1.0 = no multiply effect) to the streak value, // weighted by intensity. Near D: pixels stay white → multiply leaves // canvas alone → light region. Far from D: full streak → multiply // darkens streaks → "expensive zone" reads as denser, busier canvas. const final = 1 + (streak - 1) * intensity const g = (final * 255) | 0 data[idx++] = g data[idx++] = g data[idx++] = g data[idx++] = 255 } } licCtx2D.putImageData(licImage, 0, 0) // Composite LIC onto main canvas: multiply darkens (streaks become darker // brush strokes against the conic gradient). Bilinear upscale alone leaves // a Minecraft-grid look at ~7-10× factor, so we layer a Gaussian blur via // ctx.filter on top — the radius scales with the upscale factor, large // enough to dissolve cell boundaries while still preserving streak shape. const upscaleFactor = w / licW const blurPx = Math.max(1.5, upscaleFactor * 1.4) ctx.save() ctx.globalAlpha = 0.2 * alphaMultiplier ctx.globalCompositeOperation = 'multiply' ctx.imageSmoothingEnabled = true ctx.imageSmoothingQuality = 'high' ctx.filter = `blur(${blurPx.toFixed(2)}px)` ctx.drawImage(licCanvas, 0, 0, w, h) ctx.restore() return true } // ── Main render ── /** * @returns true if still animating (needs redraw) */ export function renderInfluenceHighlight( ctx: CanvasRenderingContext2D, state: ConstructionState, viewport: EuclidViewportState, w: number, h: number, highlightState: InfluenceHighlightState, time: number, pointerWorld: { x: number; y: number } | null ): boolean { const now = time * 1000 // Animate opacity if (highlightState.opacity !== highlightState.targetOpacity) { const elapsed = now - highlightState.fadeStartTime const t = Math.min(1, elapsed / FADE_DURATION_MS) const eased = easeOutCubic(t) highlightState.opacity = highlightState.fadeStartOpacity + (highlightState.targetOpacity - highlightState.fadeStartOpacity) * eased if (t >= 1) { highlightState.opacity = highlightState.targetOpacity if (highlightState.targetOpacity === 0) { highlightState.derivedPointId = null highlightState.givenPointId = null highlightState.subJacobian = null } } } if (highlightState.opacity <= 0.001) return false if (!highlightState.derivedPointId || !highlightState.givenPointId) return false const derivedPt = getPoint(state, highlightState.derivedPointId) const givenPt = getPoint(state, highlightState.givenPointId) if (!derivedPt || !givenPt) return false const derivedScreen = toScreen(derivedPt.x, derivedPt.y, viewport, w, h) const givenScreen = toScreen(givenPt.x, givenPt.y, viewport, w, h) const alpha = highlightState.opacity const tension = highlightState.tension const pulse = 0.75 + 0.25 * Math.sin(time * 3.5) // Tension-driven ring vibration: random offset scaled by tension const vibeX = tension > 0.01 ? (Math.random() - 0.5) * tension * 8 : 0 const vibeY = tension > 0.01 ? (Math.random() - 0.5) * tension * 8 : 0 const ringX = givenScreen.x + vibeX const ringY = givenScreen.y + vibeY // Color that shifts with tension const lineColor = tensionColor(tension, 0.35 + tension * 0.4) const ringColor = tensionHex(tension) ctx.save() // ── Rubber band line (cursor → derived point, visible during tension) ── if (tension > 0.01 && highlightState.cursorScreen) { const rbAlpha = alpha * tension * 0.8 const rbWidth = 1 + tension * 2.5 ctx.beginPath() ctx.moveTo(highlightState.cursorScreen.x, highlightState.cursorScreen.y) ctx.lineTo(derivedScreen.x, derivedScreen.y) ctx.strokeStyle = tensionColor(tension, 1) ctx.lineWidth = rbWidth ctx.globalAlpha = rbAlpha ctx.lineCap = 'round' ctx.stroke() } // ── Connecting dashed line ── ctx.beginPath() ctx.setLineDash(DASH_PATTERN) ctx.moveTo(derivedScreen.x, derivedScreen.y) ctx.lineTo(ringX, ringY) ctx.strokeStyle = lineColor ctx.lineWidth = 1.5 + tension * 1.5 ctx.globalAlpha = alpha * 0.8 ctx.stroke() ctx.setLineDash([]) // ── Soft glow ── const gradient = ctx.createRadialGradient(ringX, ringY, 0, ringX, ringY, GLOW_RADIUS * pulse) gradient.addColorStop(0, tensionColor(tension, 0.4)) gradient.addColorStop(0.5, tensionColor(tension, 0.15)) gradient.addColorStop(1, tensionColor(tension, 0)) ctx.beginPath() ctx.arc(ringX, ringY, GLOW_RADIUS * pulse, 0, Math.PI * 2) ctx.fillStyle = gradient ctx.globalAlpha = alpha ctx.fill() // ── Outer ring ── ctx.beginPath() ctx.arc(ringX, ringY, OUTER_RING_RADIUS, 0, Math.PI * 2) ctx.strokeStyle = ringColor ctx.lineWidth = OUTER_RING_WIDTH ctx.globalAlpha = alpha * 0.4 * pulse ctx.stroke() // ── Inner ring ── ctx.beginPath() ctx.arc(ringX, ringY, INNER_RING_RADIUS, 0, Math.PI * 2) ctx.strokeStyle = ringColor ctx.lineWidth = INNER_RING_WIDTH ctx.globalAlpha = alpha * pulse ctx.stroke() // ── Center disc ── ctx.beginPath() ctx.arc(ringX, ringY, 5, 0, Math.PI * 2) ctx.fillStyle = ringColor ctx.globalAlpha = alpha * 0.7 ctx.fill() // ── Diamond marker on derived point ── const s = 5 ctx.beginPath() ctx.moveTo(derivedScreen.x, derivedScreen.y - s) ctx.lineTo(derivedScreen.x + s, derivedScreen.y) ctx.lineTo(derivedScreen.x, derivedScreen.y + s) ctx.lineTo(derivedScreen.x - s, derivedScreen.y) ctx.closePath() ctx.strokeStyle = ringColor ctx.lineWidth = 1.5 ctx.globalAlpha = alpha * 0.6 ctx.stroke() // ── Preview arrow: shows where given point would move ── if (pointerWorld && highlightState.subJacobian) { // Compute cursor-to-derived-point distance in SCREEN pixels for fade const pointerScreen = toScreen(pointerWorld.x, pointerWorld.y, viewport, w, h) const dxScreen = pointerScreen.x - derivedScreen.x const dyScreen = pointerScreen.y - derivedScreen.y const cursorScreenDist = Math.sqrt(dxScreen * dxScreen + dyScreen * dyScreen) // Fade arrow based on proximity: full at FADE_START, zero at FADE_END const proximityAlpha = cursorScreenDist <= PREVIEW_ARROW_FADE_END ? 0 : cursorScreenDist >= PREVIEW_ARROW_FADE_START ? 1 : (cursorScreenDist - PREVIEW_ARROW_FADE_END) / (PREVIEW_ARROW_FADE_START - PREVIEW_ARROW_FADE_END) // Vector from derived point to cursor in world coords const dxWorld = pointerWorld.x - derivedPt.x const dyWorld = pointerWorld.y - derivedPt.y const cursorDist = Math.sqrt(dxWorld * dxWorld + dyWorld * dyWorld) if (proximityAlpha > 0.01 && cursorDist > 0.01) { // Normalize to unit direction, then compute given-point response const scale = 1 / cursorDist const unitDx = dxWorld * scale const unitDy = dyWorld * scale const response = constrainedDragStep( { x: 0, y: 0 }, // we only care about the delta { x: unitDx, y: unitDy }, highlightState.subJacobian ) if (response) { // Convert response to screen pixels const respScreenX = response.x * viewport.pixelsPerUnit const respScreenY = -response.y * viewport.pixelsPerUnit // Y flipped in screen let arrowLen = Math.sqrt(respScreenX * respScreenX + respScreenY * respScreenY) arrowLen *= PREVIEW_ARROW_SCALE if (arrowLen > 2) { const clampedLen = Math.min(arrowLen, PREVIEW_ARROW_MAX_LEN) const normFactor = clampedLen / Math.sqrt(respScreenX * respScreenX + respScreenY * respScreenY) const ax = respScreenX * normFactor const ay = respScreenY * normFactor const tipX = givenScreen.x + ax const tipY = givenScreen.y + ay const angle = Math.atan2(ay, ax) const arrowAlpha = alpha * 0.7 * proximityAlpha // Arrow shaft ctx.beginPath() ctx.moveTo(givenScreen.x, givenScreen.y) ctx.lineTo(tipX, tipY) ctx.strokeStyle = PREVIEW_ARROW_COLOR ctx.lineWidth = 2.5 ctx.globalAlpha = arrowAlpha ctx.lineCap = 'round' ctx.stroke() // Arrowhead ctx.lineWidth = 2.5 drawArrowhead(ctx, tipX, tipY, angle, PREVIEW_ARROW_HEAD) } } } } ctx.restore() return highlightState.opacity !== highlightState.targetOpacity || highlightState.opacity > 0 } // ── Motion trail rendering ── /** * Render the motion trail for a given point during/after drag. * @returns true if still animating */ export function renderMotionTrail(ctx: CanvasRenderingContext2D, trail: MotionTrailState): boolean { if (trail.count < 2 || trail.opacity <= 0.01) return false ctx.save() // Read positions in order from oldest to newest const startIdx = trail.count < TRAIL_MAX_POINTS ? 0 : trail.writeIdx // oldest is at writeIdx when buffer is full for (let i = 0; i < trail.count - 1; i++) { const idx0 = (startIdx + i) % TRAIL_MAX_POINTS const idx1 = (startIdx + i + 1) % TRAIL_MAX_POINTS const p0 = trail.positions[idx0] const p1 = trail.positions[idx1] // Age: 0 = oldest, 1 = newest const age = i / (trail.count - 1) const segAlpha = age * trail.opacity const segWidth = TRAIL_MIN_WIDTH + (TRAIL_MAX_WIDTH - TRAIL_MIN_WIDTH) * age ctx.beginPath() ctx.moveTo(p0.x, p0.y) ctx.lineTo(p1.x, p1.y) ctx.strokeStyle = TRAIL_COLOR ctx.lineWidth = segWidth ctx.globalAlpha = segAlpha ctx.lineCap = 'round' ctx.stroke() } ctx.restore() return trail.opacity > 0 } // ── Break-free flash rendering ── /** * Render the break-free flash: expanding shockwave ring + line fragment burst. * @returns true if still animating */ export function renderBreakFreeFlash( ctx: CanvasRenderingContext2D, flash: BreakFreeFlash, now: number ): boolean { const elapsed = now - flash.startTime if (elapsed >= BREAK_FREE_FLASH_DURATION_MS) return false const t = elapsed / BREAK_FREE_FLASH_DURATION_MS const eased = easeOutCubic(t) ctx.save() // ── Expanding shockwave ring from given point ── const shockRadius = INNER_RING_RADIUS + (BREAK_FREE_SHOCKWAVE_MAX_RADIUS - INNER_RING_RADIUS) * eased const shockAlpha = (1 - eased) * 0.8 ctx.beginPath() ctx.arc(flash.givenScreen.x, flash.givenScreen.y, shockRadius, 0, Math.PI * 2) ctx.strokeStyle = TENSION_COLOR ctx.lineWidth = 3 * (1 - eased) + 0.5 ctx.globalAlpha = shockAlpha ctx.stroke() // ── Bright flash on given point (white → amber, fast fade) ── const flashT = Math.min(1, elapsed / 100) // 100ms flash const flashAlpha = (1 - flashT) * 0.9 if (flashAlpha > 0.01) { const flashGrad = ctx.createRadialGradient( flash.givenScreen.x, flash.givenScreen.y, 0, flash.givenScreen.x, flash.givenScreen.y, 20 ) flashGrad.addColorStop(0, `rgba(255, 255, 255, ${flashAlpha})`) flashGrad.addColorStop(0.4, `rgba(${TENSION_COLOR_RGB}, ${flashAlpha * 0.6})`) flashGrad.addColorStop(1, `rgba(${TENSION_COLOR_RGB}, 0)`) ctx.beginPath() ctx.arc(flash.givenScreen.x, flash.givenScreen.y, 20, 0, Math.PI * 2) ctx.fillStyle = flashGrad ctx.globalAlpha = 1 ctx.fill() } // ── Line fragment burst from midpoint of the old constraint line ── const midX = (flash.givenScreen.x + flash.derivedScreen.x) / 2 const midY = (flash.givenScreen.y + flash.derivedScreen.y) / 2 const lineAngle = Math.atan2( flash.derivedScreen.y - flash.givenScreen.y, flash.derivedScreen.x - flash.givenScreen.x ) const perpAngle = lineAngle + Math.PI / 2 const fragAlpha = (1 - eased) * 0.7 if (fragAlpha > 0.01) { ctx.strokeStyle = TENSION_COLOR ctx.lineWidth = 2 ctx.globalAlpha = fragAlpha ctx.lineCap = 'round' // 4 fragments: 2 pairs going in opposite perpendicular directions const fragLen = 8 const driftDist = 30 * eased for (let i = 0; i < 4; i++) { const side = i < 2 ? 1 : -1 const offset = (i % 2 === 0 ? -0.3 : 0.3) * fragLen const fx = midX + offset * Math.cos(lineAngle) + side * driftDist * Math.cos(perpAngle) const fy = midY + offset * Math.sin(lineAngle) + side * driftDist * Math.sin(perpAngle) ctx.beginPath() ctx.moveTo(fx, fy) ctx.lineTo( fx + fragLen * Math.cos(lineAngle + side * 0.3), fy + fragLen * Math.sin(lineAngle + side * 0.3) ) ctx.stroke() } } ctx.restore() return true } /** Exported constants for use by the drag handler. */ export { TENSION_START_RADIUS, BREAK_FREE_RADIUS, TENSION_DAMPEN } |