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1171 lines (1078 loc) · 43.1 KB
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<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>方案 10 · 桥端藏到方块内侧</title>
<style>
:root {
color-scheme: light dark;
--bg-center: #ffffff;
--bg-edge: #edf2f8;
--ui-bg: rgba(255, 255, 255, 0.72);
--ui-border: rgba(15, 35, 70, 0.10);
--ui-text: #1e293b;
--ui-muted: #64748b;
--focus: #2c74be;
}
@media (prefers-color-scheme: dark) {
:root {
--bg-center: #16213a;
--bg-edge: #0a101d;
--ui-bg: rgba(15, 23, 42, 0.66);
--ui-border: rgba(148, 180, 230, 0.16);
--ui-text: #e2e8f0;
--ui-muted: #94a3b8;
--focus: #5aa9ef;
}
}
html, body {
margin: 0;
height: 100%;
overflow: hidden;
font-family: system-ui, -apple-system, "Segoe UI", "Microsoft YaHei", sans-serif;
background: radial-gradient(ellipse at 50% 45%, var(--bg-center) 0%, var(--bg-edge) 100%);
}
canvas {
display: block;
width: 100%;
height: 100%;
touch-action: none;
cursor: grab;
outline: none;
}
canvas.dragging { cursor: grabbing; }
canvas:focus-visible { box-shadow: inset 0 0 0 2px var(--focus); }
.ui {
position: fixed;
left: 50%;
bottom: 20px;
transform: translateX(-50%);
display: flex;
align-items: center;
gap: 12px;
padding: 6px 6px 6px 16px;
border: 1px solid var(--ui-border);
border-radius: 999px;
background: var(--ui-bg);
backdrop-filter: blur(12px);
-webkit-backdrop-filter: blur(12px);
font-size: 13px;
color: var(--ui-muted);
white-space: nowrap;
}
.hint { transition: opacity 0.6s ease; }
.hint.faded { opacity: 0.45; }
button {
display: inline-flex;
align-items: center;
gap: 6px;
font: inherit;
padding: 7px 14px;
border: 0;
border-radius: 999px;
background: transparent;
color: var(--ui-text);
cursor: pointer;
}
button:hover { background: var(--ui-border); }
button:focus-visible { outline: 2px solid var(--focus); outline-offset: 2px; }
button svg { width: 15px; height: 15px; }
@media (max-width: 480px) {
.hint { display: none; }
.ui { padding: 4px; }
}
.lights {
position: fixed;
top: 20px;
right: 20px;
display: grid;
grid-template-columns: auto minmax(100px, 160px) 3.5em;
align-items: center;
gap: 8px 10px;
margin: 0;
padding: 12px 14px 8px;
border: 1px solid var(--ui-border);
border-radius: 14px;
background: var(--ui-bg);
backdrop-filter: blur(12px);
-webkit-backdrop-filter: blur(12px);
font-size: 13px;
color: var(--ui-text);
}
.lights legend {
float: left;
grid-column: 1 / -1;
padding: 0;
color: var(--ui-muted);
}
.lights input[type="range"] {
width: 100%;
margin: 0;
accent-color: var(--focus);
}
.lights input[type="range"]:focus-visible { outline: 2px solid var(--focus); outline-offset: 3px; }
.lights output {
text-align: right;
font-variant-numeric: tabular-nums;
color: var(--ui-muted);
}
.lights button {
grid-column: 1 / -1;
justify-self: end;
padding: 5px 10px;
}
@media (max-width: 480px) {
.lights { top: 10px; right: 10px; left: 10px; grid-template-columns: auto 1fr 3.5em; }
}
.error {
position: fixed;
inset: 0;
display: none;
align-items: center;
justify-content: center;
color: #b91c1c;
}
</style>
</head>
<body>
<canvas id="scene" tabindex="0" role="img"
aria-label="8 个蓝色立方体组成的等轴测场景，上下两层均由十字桥接，四组上下方块之间保留内侧百分之七十五截面积的半透明连接。拖拽旋转，滚轮或双指缩放，方向键旋转，加减号缩放，R 键重置视角。"></canvas>
<div class="ui">
<span class="hint" id="hint">拖拽旋转 · 滚轮缩放 · 双击重置</span>
<button id="reset" type="button">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true">
<path d="M3 12a9 9 0 1 0 9-9 9.75 9.75 0 0 0-6.74 2.74L3 8"/><path d="M3 3v5h5"/>
</svg>
重置视角
</button>
<button id="export-svg" type="button" title="按默认机位和当前光照导出">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true">
<path d="M12 3v12"/><path d="m7 10 5 5 5-5"/><path d="M5 21h14"/>
</svg>
导出 SVG
</button>
</div>
<fieldset class="lights" id="lights">
<legend>光照俯仰角</legend>
<label for="key-pitch">主光</label>
<input id="key-pitch" type="range" min="-90" max="90" step="1" value="0" aria-describedby="key-pitch-out">
<output id="key-pitch-out" for="key-pitch">0°</output>
<label for="inner-pitch">内侧光</label>
<input id="inner-pitch" type="range" min="-90" max="90" step="1" value="0" aria-describedby="inner-pitch-out">
<output id="inner-pitch-out" for="inner-pitch">0°</output>
<button id="lights-reset" type="button">恢复默认</button>
</fieldset>
<div class="error" id="error" role="alert">当前浏览器不支持 WebGL2</div>
<script>
(() => {
'use strict';
// ---- Scene definition ----------------------------------------------------
// 2x2x2 lattice. Cube edge = 1, center spacing = 1.5 (gap 0.5).
// Box: [cx, cy, cz, sx, sy, sz, layer (1 upper / 0 lower), gradientBaseY, kind].
//
// Shading is kept SVG-friendly for the default view: every visible face (or half face) is a
// flat color times a vertical linear gradient, and glass is plain alpha-over compositing.
const KIND_CUBE = 0;
const KIND_FILL = 1; // opaque
const KIND_GLASS_SIDES = 2; // glass, side faces only (top/bottom would be coplanar with cubes)
const A = 0.75;
const OUTER = A + 0.5; // 1.25
const INNER = A - 0.5; // 0.25
const HALF = 0.5;
const box = (min, max, layer, kind) => [
(min[0] + max[0]) / 2, (min[1] + max[1]) / 2, (min[2] + max[2]) / 2,
max[0] - min[0], max[1] - min[1], max[2] - min[2],
layer, min[1], kind,
];
const cube = (x, y, z, layer) =>
box([x - 0.5, y - 0.5, z - 0.5], [x + 0.5, y + 0.5, z + 0.5], layer, KIND_CUBE);
const UPPER_BOTTOM = INNER; // 0.25
const LOWER_TOP = -INNER; // -0.25
const COLUMNS = [[A, A], [-A, A], [A, -A], [-A, -A]];
// 保留四号方块与连接柱，通过桥接长度和厚度调整遮挡关系。
const BRIDGE_UPPER = OUTER * 0.6;
const BRIDGE_LOWER = OUTER * 0.6;
const BRIDGE_HEIGHT = 0.5;
const OPAQUE_BOXES = [
...COLUMNS.map(([x, z]) => cube(x, A, z, 1)),
...COLUMNS.map(([x, z]) => cube(x, -A, z, 0)),
box([-BRIDGE_UPPER, UPPER_BOTTOM, -INNER], [BRIDGE_UPPER, UPPER_BOTTOM + BRIDGE_HEIGHT, INNER], 1, KIND_FILL),
box([-INNER, UPPER_BOTTOM, INNER], [INNER, UPPER_BOTTOM + BRIDGE_HEIGHT, BRIDGE_UPPER], 1, KIND_FILL),
box([-INNER, UPPER_BOTTOM, -BRIDGE_UPPER], [INNER, UPPER_BOTTOM + BRIDGE_HEIGHT, -INNER], 1, KIND_FILL),
box([-BRIDGE_LOWER, LOWER_TOP - BRIDGE_HEIGHT, -INNER], [BRIDGE_LOWER, LOWER_TOP, INNER], 0, KIND_FILL),
box([-INNER, LOWER_TOP - BRIDGE_HEIGHT, INNER], [INNER, LOWER_TOP, BRIDGE_LOWER], 0, KIND_FILL),
box([-INNER, LOWER_TOP - BRIDGE_HEIGHT, -BRIDGE_LOWER], [INNER, LOWER_TOP, -INNER], 0, KIND_FILL),
];
OPAQUE_BOXES.filter(b => b[8] === KIND_FILL && b[6] === 0).forEach(b => { b[7] = -A - HALF; });
// 四根连接柱以内侧角为锚点保留百分之七十五截面积，高度与半透明材质不变。
const LINK_AREA_RATIO = 0.75;
const LINK_WIDTH = Math.sqrt(LINK_AREA_RATIO);
const GLASS_BOXES = COLUMNS.map(([x, z]) => {
const innerX = x - Math.sign(x) * HALF;
const innerZ = z - Math.sign(z) * HALF;
const outerX = innerX + Math.sign(x) * LINK_WIDTH;
const outerZ = innerZ + Math.sign(z) * LINK_WIDTH;
return box(
[Math.min(outerX, innerX), LOWER_TOP, Math.min(outerZ, innerZ)],
[Math.max(outerX, innerX), UPPER_BOTTOM, Math.max(outerZ, innerZ)],
1, KIND_GLASS_SIDES,
);
});
// Default camera: true isometric, orthographic, looking along -(1,1,1) at the origin.
const DEFAULT_VIEW = {
azimuth: Math.PI / 4,
elevation: Math.atan(1 / Math.SQRT2), // 35.264 deg
// Reference: projected edge = 152px of 800px; isometric foreshortening is sqrt(2/3),
// so one world unit = 152 / 0.8165 = 186px and the half view = 400 / 186 (tuned to 2.13 by overlay).
halfExtent: 2.13,
};
const TARGET = [0, 0, 0];
const CAMERA_DISTANCE = 10;
const hex = (h) => [1, 3, 5].map((i) => parseInt(h.slice(i, i + 2), 16) / 255);
const PALETTE = {
topUpper: hex('#3ab0e6'),
sideUpperHi: hex('#2c74be'),
sideUpperLo: hex('#20438a'),
topLower: hex('#26497a'),
sideLowerHi: hex('#1c3964'),
sideLowerLo: hex('#122341'),
fillTint: [0.88, 0.93, 0.98], // cross fill: a touch deeper and cooler than the cubes
// Inner light on side faces facing the central channel (sampled from the reference's top cube).
innerHi: hex('#2192d3'), // at the top edge of the face
innerLo: hex('#28a0e2'), // at the bottom edge, slightly brighter near the fill
innerTop: hex('#4ec8f8'), // on top faces, once the inner light is pitched upward
glassTop: hex('#55b4f4'),
glassHi: hex('#4a9cf0'),
glassLo: hex('#2a68cc'),
glassAlpha: 0.48,
glassBackdrop: hex('#122a55'), // stands in for the page wherever nothing opaque is behind glass
};
const reducedMotion = window.matchMedia('(prefers-reduced-motion: reduce)');
// ---- WebGL setup ---------------------------------------------------------
const canvas = document.getElementById('scene');
const gl = canvas.getContext('webgl2', { antialias: true, alpha: true, premultipliedAlpha: true });
if (!gl) {
document.getElementById('error').style.display = 'flex';
return;
}
const VS = `#version 300 es
layout(location = 0) in vec3 aPos;
layout(location = 1) in vec3 aNormal;
layout(location = 2) in vec3 aOffset;
layout(location = 3) in vec3 aScale;
layout(location = 4) in vec3 aStyle; // layer, gradient base height, kind
uniform mat4 uViewProj;
out vec3 vNormal;
out vec3 vWorld;
out vec3 vLocal;
flat out vec3 vScale;
flat out vec3 vStyle;
flat out vec3 vFaceCenter;
void main() {
vec3 world = aPos * aScale + aOffset;
vNormal = aNormal;
vWorld = world;
vLocal = aPos;
vScale = aScale;
vStyle = aStyle;
vFaceCenter = aOffset + aNormal * aScale * 0.5;
gl_Position = uViewProj * vec4(world, 1.0);
}`;
// Shared shading terms. Depth cue is evaluated once per face so each face stays a plain
// linear gradient (exportable as an SVG <linearGradient>).
const COMMON_GLSL = `
uniform vec3 uToCamera;
uniform vec3 uTarget;
uniform vec3 uKeyDir; // toward the key light; pitch 0 = horizontal (the reference look)
float keyLight(vec3 n) {
return 0.6 + 0.4 * max(dot(n, uKeyDir), 0.0);
}
// Palette top/bottom colors are what a horizontal key light gives (factor 0.6), so they are
// rescaled relative to that: pitch 0 reproduces the palette exactly.
float capLight(vec3 n) {
return keyLight(n) / 0.6;
}
float depthCue(vec3 faceCenter) {
return 1.0 + 0.06 * dot(faceCenter - uTarget, uToCamera);
}
// Brightens past 1.0 without washing the hue out to white.
vec3 fitRange(vec3 c) {
c = max(c, vec3(0.0));
return c / max(1.0, max(c.r, max(c.g, c.b)));
}`;
const OPAQUE_FS = `#version 300 es
precision highp float;
in vec3 vNormal;
in vec3 vWorld;
in vec3 vLocal;
flat in vec3 vScale;
flat in vec3 vStyle;
flat in vec3 vFaceCenter;
uniform vec3 uTopUpper, uSideUpperHi, uSideUpperLo;
uniform vec3 uTopLower, uSideLowerHi, uSideLowerLo;
uniform vec3 uFillTint;
uniform vec3 uInnerHi, uInnerLo, uInnerTop;
uniform vec2 uInnerPitch; // (sin, cos) of the inner light's pitch
out vec4 outColor;
${COMMON_GLSL}
void main() {
vec3 n = normalize(vNormal);
float layer = vStyle.x;
bool fill = vStyle.z > 0.5;
float t = clamp(vWorld.y - vStyle.y, 0.0, 1.0);
vec3 color;
vec3 inner;
float lam; // how squarely this face faces the inner light
if (n.y > 0.5) {
color = mix(uTopLower, uTopUpper, layer) * capLight(n);
inner = uInnerTop;
lam = uInnerPitch.x;
} else if (n.y < -0.5) {
color = mix(uSideLowerLo, uSideUpperLo, layer) * 0.7 * capLight(n);
inner = uInnerLo * 0.7;
lam = -uInnerPitch.x;
} else {
vec3 hi = mix(uSideLowerHi, uSideUpperHi, layer);
vec3 lo = mix(uSideLowerLo, uSideUpperLo, layer);
color = mix(lo, hi, t) * keyLight(n);
inner = mix(uInnerLo, uInnerHi, t);
// Only side faces that face the central cross channel see the inner light.
lam = step(0.0, dot(n.xz, -vFaceCenter.xz)) * uInnerPitch.y;
}
// Inner light: a cyan light inside the upper layer's cross channel, strongest toward the back
// corner, i.e. the farthest (top) cube in the default view. Its pitch moves it between the
// channel walls (0), the top faces (+90) and the bottom faces (-90). Constant per face, so
// faces stay plain linear gradients.
if (layer > 0.5 && !fill) {
float back = clamp(0.5 + 0.7 * dot(vFaceCenter.xz, vec2(-0.70710678)), 0.0, 1.0);
inner *= 0.9 + 0.1 * max(dot(n, uKeyDir), 0.0);
color = mix(color, inner, back * max(lam, 0.0));
}
if (fill) color *= uFillTint;
color *= depthCue(vFaceCenter);
outColor = vec4(fitRange(color), 1.0);
}`;
const GLASS_FS = `#version 300 es
precision highp float;
in vec3 vNormal;
in vec3 vWorld;
in vec3 vLocal;
flat in vec3 vScale;
flat in vec3 vStyle;
flat in vec3 vFaceCenter;
uniform vec3 uGlassTop, uGlassHi, uGlassLo, uBackdrop;
uniform float uAlpha;
uniform int uPass; // 0 = backdrop where the canvas is still empty, 1 = glass over
out vec4 outColor;
${COMMON_GLSL}
void main() {
if (uPass == 0) {
outColor = vec4(uBackdrop, 1.0);
return;
}
vec3 n = normalize(vNormal);
float t = clamp((vWorld.y - vStyle.y) / vScale.y, 0.0, 1.0);
vec3 color;
if (n.y > 0.5) color = uGlassTop * capLight(n);
else if (n.y < -0.5) color = uGlassLo * 0.7 * capLight(n);
else color = mix(uGlassLo, uGlassHi, t) * keyLight(n);
color *= depthCue(vFaceCenter);
outColor = vec4(fitRange(color), uAlpha);
}`;
function compile(type, src) {
const s = gl.createShader(type);
gl.shaderSource(s, src);
gl.compileShader(s);
if (!gl.getShaderParameter(s, gl.COMPILE_STATUS)) throw new Error(gl.getShaderInfoLog(s));
return s;
}
function createProgram(vs, fs, uniformNames) {
const program = gl.createProgram();
gl.attachShader(program, compile(gl.VERTEX_SHADER, vs));
gl.attachShader(program, compile(gl.FRAGMENT_SHADER, fs));
gl.linkProgram(program);
if (!gl.getProgramParameter(program, gl.LINK_STATUS)) throw new Error(gl.getProgramInfoLog(program));
const u = {};
for (const name of uniformNames) u[name] = gl.getUniformLocation(program, name);
return { program, u };
}
const opaqueProg = createProgram(VS, OPAQUE_FS, [
'uViewProj', 'uToCamera', 'uTarget', 'uKeyDir',
'uTopUpper', 'uSideUpperHi', 'uSideUpperLo', 'uTopLower', 'uSideLowerHi', 'uSideLowerLo',
'uFillTint', 'uInnerHi', 'uInnerLo', 'uInnerTop', 'uInnerPitch',
]);
const glassProg = createProgram(VS, GLASS_FS, [
'uViewProj', 'uToCamera', 'uTarget', 'uKeyDir',
'uGlassTop', 'uGlassHi', 'uGlassLo', 'uBackdrop', 'uAlpha', 'uPass',
]);
// Unit cube, CCW winding seen from outside (u x v = n).
// The four side faces come first so SIDE_VERTEX_COUNT draws a top/bottom-less box.
const CUBE_VERTEX_COUNT = 36;
const SIDE_VERTEX_COUNT = 24;
const FACES = [
{ n: [ 1, 0, 0], u: [0, 0, -1], v: [0, 1, 0] },
{ n: [-1, 0, 0], u: [0, 0, 1], v: [0, 1, 0] },
{ n: [ 0, 0, 1], u: [1, 0, 0], v: [0, 1, 0] },
{ n: [ 0, 0,-1], u: [-1, 0, 0], v: [0, 1, 0] },
{ n: [ 0, 1, 0], u: [1, 0, 0], v: [0, 0, -1] },
{ n: [ 0,-1, 0], u: [1, 0, 0], v: [0, 0, 1] },
];
function buildCube() {
const quad = [[-1, -1], [1, -1], [1, 1], [-1, -1], [1, 1], [-1, 1]];
const data = [];
for (const { n, u, v } of FACES) {
for (const [su, sv] of quad) {
for (let i = 0; i < 3; i++) data.push(0.5 * (n[i] + su * u[i] + sv * v[i]));
data.push(...n);
}
}
return new Float32Array(data);
}
const cubeBuf = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, cubeBuf);
gl.bufferData(gl.ARRAY_BUFFER, buildCube(), gl.STATIC_DRAW);
function bindCubeGeometry() {
gl.bindBuffer(gl.ARRAY_BUFFER, cubeBuf);
gl.enableVertexAttribArray(0);
gl.vertexAttribPointer(0, 3, gl.FLOAT, false, 24, 0);
gl.enableVertexAttribArray(1);
gl.vertexAttribPointer(1, 3, gl.FLOAT, false, 24, 12);
}
// Opaque boxes: one instanced draw.
const opaqueVao = gl.createVertexArray();
gl.bindVertexArray(opaqueVao);
bindCubeGeometry();
gl.bindBuffer(gl.ARRAY_BUFFER, gl.createBuffer());
gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(OPAQUE_BOXES.flat()), gl.STATIC_DRAW);
[[2, 3, 0], [3, 3, 12], [4, 3, 24]].forEach(([loc, size, offset]) => {
gl.enableVertexAttribArray(loc);
gl.vertexAttribPointer(loc, size, gl.FLOAT, false, 9 * 4, offset);
gl.vertexAttribDivisor(loc, 1);
});
// Glass boxes: drawn one by one, back to front, with per-box constant attributes.
const glassVao = gl.createVertexArray();
gl.bindVertexArray(glassVao);
bindCubeGeometry();
gl.bindVertexArray(null);
// Static uniforms.
gl.useProgram(opaqueProg.program);
gl.uniform3fv(opaqueProg.u.uTarget, TARGET);
gl.uniform3fv(opaqueProg.u.uTopUpper, PALETTE.topUpper);
gl.uniform3fv(opaqueProg.u.uSideUpperHi, PALETTE.sideUpperHi);
gl.uniform3fv(opaqueProg.u.uSideUpperLo, PALETTE.sideUpperLo);
gl.uniform3fv(opaqueProg.u.uTopLower, PALETTE.topLower);
gl.uniform3fv(opaqueProg.u.uSideLowerHi, PALETTE.sideLowerHi);
gl.uniform3fv(opaqueProg.u.uSideLowerLo, PALETTE.sideLowerLo);
gl.uniform3fv(opaqueProg.u.uFillTint, PALETTE.fillTint);
gl.uniform3fv(opaqueProg.u.uInnerHi, PALETTE.innerHi);
gl.uniform3fv(opaqueProg.u.uInnerLo, PALETTE.innerLo);
gl.uniform3fv(opaqueProg.u.uInnerTop, PALETTE.innerTop);
gl.useProgram(glassProg.program);
gl.uniform3fv(glassProg.u.uTarget, TARGET);
gl.uniform3fv(glassProg.u.uGlassTop, PALETTE.glassTop);
gl.uniform3fv(glassProg.u.uGlassHi, PALETTE.glassHi);
gl.uniform3fv(glassProg.u.uGlassLo, PALETTE.glassLo);
gl.uniform3fv(glassProg.u.uBackdrop, PALETTE.glassBackdrop);
gl.uniform1f(glassProg.u.uAlpha, PALETTE.glassAlpha);
gl.enable(gl.DEPTH_TEST);
gl.depthFunc(gl.LEQUAL);
gl.enable(gl.CULL_FACE);
gl.cullFace(gl.BACK);
gl.clearColor(0, 0, 0, 0);
// ---- Math ----------------------------------------------------------------
const sub = (a, b) => [a[0] - b[0], a[1] - b[1], a[2] - b[2]];
const dot = (a, b) => a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
const cross = (a, b) => [a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]];
const normalize = (a) => { const l = Math.hypot(a[0], a[1], a[2]); return [a[0] / l, a[1] / l, a[2] / l]; };
const clamp = (v, lo, hi) => Math.min(hi, Math.max(lo, v));
function lookAt(eye, center, up) {
const z = normalize(sub(eye, center));
const x = normalize(cross(up, z));
const y = cross(z, x);
return [
x[0], y[0], z[0], 0,
x[1], y[1], z[1], 0,
x[2], y[2], z[2], 0,
-dot(x, eye), -dot(y, eye), -dot(z, eye), 1,
];
}
function ortho(l, r, b, t, n, f) {
return [
2 / (r - l), 0, 0, 0,
0, 2 / (t - b), 0, 0,
0, 0, -2 / (f - n), 0,
-(r + l) / (r - l), -(t + b) / (t - b), -(f + n) / (f - n), 1,
];
}
function multiply(a, b) {
const out = new Float32Array(16);
for (let c = 0; c < 4; c++) {
for (let r = 0; r < 4; r++) {
let s = 0;
for (let k = 0; k < 4; k++) s += a[k * 4 + r] * b[c * 4 + k];
out[c * 4 + r] = s;
}
}
return out;
}
// ---- Camera state & rendering -------------------------------------------
const MAX_ELEVATION = (89 * Math.PI) / 180;
const MIN_EXTENT = 1.2;
const MAX_EXTENT = 8;
const ROTATE_SPEED = 0.008; // radians per CSS pixel
const INERTIA_DECAY_MS = 220; // time constant of the spin-down after a flick
// Light pitch in degrees: 0 = horizontal, +90 = from straight above, -90 = from below.
// The key light's azimuth is fixed so +z faces stay slightly brighter than +x faces.
const KEY_AZIMUTH = Math.atan2(0.55, 1);
const DEFAULT_LIGHTS = { keyPitch: 0, innerPitch: 0 };
const lights = { ...DEFAULT_LIGHTS };
function keyDirFor(pitchDeg) {
const p = (pitchDeg * Math.PI) / 180;
return [Math.sin(KEY_AZIMUTH) * Math.cos(p), Math.sin(p), Math.cos(KEY_AZIMUTH) * Math.cos(p)];
}
function toCameraFor(v) {
const ce = Math.cos(v.elevation);
return [ce * Math.sin(v.azimuth), Math.sin(v.elevation), ce * Math.cos(v.azimuth)];
}
const view = { ...DEFAULT_VIEW };
const spin = { az: 0, el: 0 }; // radians per ms
let resetAnim = null;
let frameQueued = false;
let lastFrame = 0;
function resize() {
const dpr = Math.min(window.devicePixelRatio || 1, 2);
const w = Math.round(canvas.clientWidth * dpr);
const h = Math.round(canvas.clientHeight * dpr);
if (canvas.width !== w || canvas.height !== h) {
canvas.width = w;
canvas.height = h;
}
}
function step(now) {
const dt = lastFrame ? Math.min(now - lastFrame, 50) : 16;
lastFrame = now;
if (resetAnim) {
const t = clamp((now - resetAnim.start) / resetAnim.duration, 0, 1);
const e = 1 - Math.pow(1 - t, 3);
const from = resetAnim.from;
view.azimuth = from.azimuth + (DEFAULT_VIEW.azimuth - from.azimuth) * e;
view.elevation = from.elevation + (DEFAULT_VIEW.elevation - from.elevation) * e;
view.halfExtent = from.halfExtent * Math.pow(DEFAULT_VIEW.halfExtent / from.halfExtent, e);
if (t >= 1) resetAnim = null;
} else if (spin.az || spin.el) {
view.azimuth += spin.az * dt;
view.elevation = clamp(view.elevation + spin.el * dt, -MAX_ELEVATION, MAX_ELEVATION);
const decay = Math.exp(-dt / INERTIA_DECAY_MS);
spin.az *= decay;
spin.el *= decay;
if (Math.hypot(spin.az, spin.el) < 2e-5) spin.az = spin.el = 0;
}
return Boolean(resetAnim || spin.az || spin.el);
}
function render(now) {
frameQueued = false;
const animating = step(now);
resize();
gl.viewport(0, 0, canvas.width, canvas.height);
gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
const toCamera = toCameraFor(view);
const eye = toCamera.map((d, i) => TARGET[i] + d * CAMERA_DISTANCE);
// Keep the whole cluster visible on both landscape and portrait viewports.
const aspect = canvas.width / canvas.height;
const hh = aspect >= 1 ? view.halfExtent : view.halfExtent / aspect;
const hw = hh * aspect;
const viewProj = multiply(
ortho(-hw, hw, -hh, hh, 0.1, CAMERA_DISTANCE * 2),
lookAt(eye, TARGET, [0, 1, 0]),
);
const keyDir = keyDirFor(lights.keyPitch);
const innerPitch = (lights.innerPitch * Math.PI) / 180;
// 1. Opaque boxes.
gl.disable(gl.BLEND);
gl.depthMask(true);
gl.useProgram(opaqueProg.program);
gl.uniformMatrix4fv(opaqueProg.u.uViewProj, false, viewProj);
gl.uniform3fv(opaqueProg.u.uToCamera, toCamera);
gl.uniform3fv(opaqueProg.u.uKeyDir, keyDir);
gl.uniform2f(opaqueProg.u.uInnerPitch, Math.sin(innerPitch), Math.cos(innerPitch));
gl.bindVertexArray(opaqueVao);
gl.drawArraysInstanced(gl.TRIANGLES, 0, CUBE_VERTEX_COUNT, OPAQUE_BOXES.length);
// 2. Glass, back to front, front faces only, depth-tested against opaque geometry.
// Per box: fill still-empty pixels with a dark backdrop (so the page never shows through
// as a pale haze), then composite the glass with plain alpha-over.
gl.enable(gl.BLEND);
gl.depthMask(false);
gl.useProgram(glassProg.program);
gl.uniformMatrix4fv(glassProg.u.uViewProj, false, viewProj);
gl.uniform3fv(glassProg.u.uToCamera, toCamera);
gl.uniform3fv(glassProg.u.uKeyDir, keyDir);
gl.bindVertexArray(glassVao);
const sorted = GLASS_BOXES
.map((b) => ({ b, depth: dot([b[0], b[1], b[2]], toCamera) }))
.sort((p, q) => p.depth - q.depth);
for (const { b } of sorted) {
gl.vertexAttrib3f(2, b[0], b[1], b[2]);
gl.vertexAttrib3f(3, b[3], b[4], b[5]);
gl.vertexAttrib3f(4, b[6], b[7], b[8]);
const count = b[8] === KIND_GLASS_SIDES ? SIDE_VERTEX_COUNT : CUBE_VERTEX_COUNT;
gl.blendFunc(gl.ONE_MINUS_DST_ALPHA, gl.ONE);
gl.uniform1i(glassProg.u.uPass, 0);
gl.drawArrays(gl.TRIANGLES, 0, count);
gl.blendFuncSeparate(gl.SRC_ALPHA, gl.ONE_MINUS_SRC_ALPHA, gl.ZERO, gl.ONE);
gl.uniform1i(glassProg.u.uPass, 1);
gl.drawArrays(gl.TRIANGLES, 0, count);
}
gl.depthMask(true);
gl.disable(gl.BLEND);
gl.bindVertexArray(null);
if (animating) requestRender();
else lastFrame = 0;
}
function requestRender() {
if (!frameQueued) {
frameQueued = true;
requestAnimationFrame(render);
}
}
function stopMotion() {
resetAnim = null;
spin.az = spin.el = 0;
}
function rotate(dAzimuth, dElevation) {
view.azimuth += dAzimuth;
view.elevation = clamp(view.elevation + dElevation, -MAX_ELEVATION, MAX_ELEVATION);
requestRender();
}
function zoom(factor) {
view.halfExtent = clamp(view.halfExtent * factor, MIN_EXTENT, MAX_EXTENT);
requestRender();
}
function resetView() {
stopMotion();
// Take the shortest path back to the default azimuth.
const tau = Math.PI * 2;
const az = DEFAULT_VIEW.azimuth + ((((view.azimuth - DEFAULT_VIEW.azimuth) % tau) + tau + Math.PI) % tau) - Math.PI;
if (reducedMotion.matches) {
Object.assign(view, DEFAULT_VIEW);
} else {
resetAnim = {
start: performance.now(),
duration: 650,
from: { azimuth: az, elevation: view.elevation, halfExtent: view.halfExtent },
};
}
requestRender();
}
// ---- SVG export ----------------------------------------------------------
// Rebuilds a view on the CPU as plain SVG: every visible face becomes one <polygon> with a flat
// fill or a two-stop <linearGradient>, painted back to front; glass uses fill-opacity.
// shadeOpaque / shadeGlass mirror OPAQUE_FS / GLASS_FS, so keep them in sync.
const QUAD = [[-1, -1], [1, -1], [1, 1], [-1, 1]];
const SAMPLES_PER_UNIT = 128; // visibility probes per world unit along each face edge
const lerp3 = (a, b, t) => a.map((x, i) => x + (b[i] - x) * t);
const scale3 = (a, s) => a.map((x) => x * s);
const mul3 = (a, b) => a.map((x, i) => x * b[i]);
const boxMin = (b) => [b[0] - b[3] / 2, b[1] - b[4] / 2, b[2] - b[5] / 2];
const boxMax = (b) => [b[0] + b[3] / 2, b[1] + b[4] / 2, b[2] + b[5] / 2];
const faceCenterOf = (b, n) => [0, 1, 2].map((i) => b[i] + n[i] * b[i + 3] * 0.5);
const facePoint = (b, f, su, sv) =>
[0, 1, 2].map((i) => b[i] + 0.5 * (f.n[i] + su * f.u[i] + sv * f.v[i]) * b[i + 3]);
const num = (x) => String(Math.round(x * 100) / 100);
const toHex = (c) => '#' + c.map((x) => Math.round(clamp(x, 0, 1) * 255).toString(16).padStart(2, '0')).join('');
function fitRange(c) {
const pos = c.map((x) => Math.max(x, 0));
const m = Math.max(1, ...pos);
return pos.map((x) => x / m);
}
function shadeOpaque(b, n, t, S) {
const P = PALETTE;
const layer = b[6];
const fill = b[8] === KIND_FILL;
const fc = faceCenterOf(b, n);
const key = 0.6 + 0.4 * Math.max(dot(n, S.keyDir), 0);
let color, inner, lam;
if (n[1] > 0.5) {
color = scale3(lerp3(P.topLower, P.topUpper, layer), key / 0.6);
inner = P.innerTop;
lam = S.sinI;
} else if (n[1] < -0.5) {
color = scale3(lerp3(P.sideLowerLo, P.sideUpperLo, layer), 0.7 * key / 0.6);
inner = scale3(P.innerLo, 0.7);
lam = -S.sinI;
} else {
const hi = lerp3(P.sideLowerHi, P.sideUpperHi, layer);
const lo = lerp3(P.sideLowerLo, P.sideUpperLo, layer);
color = scale3(lerp3(lo, hi, t), key);
inner = lerp3(P.innerLo, P.innerHi, t);
lam = (-(n[0] * fc[0] + n[2] * fc[2]) >= 0 ? 1 : 0) * S.cosI;
}
if (layer > 0.5 && !fill) {
const back = clamp(0.5 - 0.7 * 0.70710678 * (fc[0] + fc[2]), 0, 1);
inner = scale3(inner, 0.9 + 0.1 * Math.max(dot(n, S.keyDir), 0));
color = lerp3(color, inner, back * Math.max(lam, 0));
}
if (fill) color = mul3(color, P.fillTint);
return fitRange(scale3(color, 1 + 0.06 * dot(sub(fc, TARGET), S.toCamera)));
}
function shadeGlass(b, n, t, S) {
const P = PALETTE;
const key = 0.6 + 0.4 * Math.max(dot(n, S.keyDir), 0);
let color;
if (n[1] > 0.5) color = scale3(P.glassTop, key / 0.6);
else if (n[1] < -0.5) color = scale3(P.glassLo, 0.7 * key / 0.6);
else color = scale3(lerp3(P.glassLo, P.glassHi, t), key);
const fc = faceCenterOf(b, n);
return fitRange(scale3(color, 1 + 0.06 * dot(sub(fc, TARGET), S.toCamera)));
}
// Side faces vary only with world height, so they need the colors at their bottom and top edge.
function faceShading(b, f, S, glass) {
const shade = glass ? shadeGlass : shadeOpaque;
if (Math.abs(f.n[1]) > 0.5) return { flat: shade(b, f.n, 0, S) };
const y0 = b[1] - b[4] / 2;
const y1 = b[1] + b[4] / 2;
const tOf = (y) => clamp(glass ? (y - b[7]) / b[4] : y - b[7], 0, 1);
return { y0, y1, c0: shade(b, f.n, tOf(y0), S), c1: shade(b, f.n, tOf(y1), S) };
}
// Orthographic projection matching render() on a square canvas of `size` px.
function makeProjector(v, size) {
const z = toCameraFor(v);
const x = normalize(cross([0, 1, 0], z));
const y = cross(z, x);
const k = size / 2 / v.halfExtent;
return (p) => {
const d = sub(p, TARGET);
return [size / 2 + dot(d, x) * k, size / 2 - dot(d, y) * k];
};
}
// Does the ray p + s·d (s > 0) pass through the inside of any box other than `self`?
function rayBlocked(p, d, boxes, self) {
for (const b of boxes) {
if (b === self) continue;
const lo = boxMin(b);
const hi = boxMax(b);
let t0 = 0;
let t1 = Infinity;
let hit = true;
for (let i = 0; i < 3 && hit; i++) {
if (Math.abs(d[i]) < 1e-12) {
hit = p[i] > lo[i] && p[i] < hi[i];
continue;
}
let a = (lo[i] - p[i]) / d[i];
let c = (hi[i] - p[i]) / d[i];
if (a > c) [a, c] = [c, a];
t0 = Math.max(t0, a);
t1 = Math.min(t1, c);
hit = t1 - t0 > 1e-6;
}
if (hit) return true;
}
return false;
}
function faceSamples(b, f) {
const extent = (axis) => Math.abs(dot(axis, [b[3], b[4], b[5]]));
const nu = Math.max(2, Math.ceil(extent(f.u) * SAMPLES_PER_UNIT));
const nv = Math.max(2, Math.ceil(extent(f.v) * SAMPLES_PER_UNIT));
const pts = [];
for (let i = 0; i < nu; i++) {
for (let j = 0; j < nv; j++) {
pts.push(facePoint(b, f, ((i + 0.5) / nu) * 2 - 1, ((j + 0.5) / nv) * 2 - 1));
}
}
return pts;
}
function convexHull(points) {
const p = [...points].sort((a, b) => a[0] - b[0] || a[1] - b[1]);
const turn = (o, a, b) => (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0]);
const half = (list) => {
const out = [];
for (const q of list) {
while (out.length >= 2 && turn(out[out.length - 2], out[out.length - 1], q) <= 1e-9) out.pop();
out.push(q);
}
out.pop();
return out;
};
return [...half(p), ...half([...p].reverse())];
}
// Separating-axis test; touching outlines don't count as overlap.
function hullsOverlap(A, B) {
for (const poly of [A, B]) {
for (let i = 0; i < poly.length; i++) {
const a = poly[i];
const b = poly[(i + 1) % poly.length];
const axis = [a[1] - b[1], b[0] - a[0]];
const range = (pts) => {
const d = pts.map((q) => q[0] * axis[0] + q[1] * axis[1]);
return [Math.min(...d), Math.max(...d)];
};
const [minA, maxA] = range(A);
const [minB, maxB] = range(B);
const eps = 1e-6 * Math.hypot(axis[0], axis[1]);
if (maxA <= minB + eps || maxB <= minA + eps) return false;
}
}
return true;
}
// -1 if a is behind b, 1 if b is behind a, 0 if they are not separated along a view-facing axis.
// Boxes never intersect, so any separating axis gives the same answer where they overlap on screen.
function compareDepth(a, b, toCamera) {
const aLo = boxMin(a), aHi = boxMax(a), bLo = boxMin(b), bHi = boxMax(b);
for (let k = 0; k < 3; k++) {
if (Math.abs(toCamera[k]) < 1e-9) continue;
const toward = toCamera[k] > 0 ? 1 : -1;
if (aHi[k] <= bLo[k] + 1e-9) return -toward;
if (bHi[k] <= aLo[k] + 1e-9) return toward;
}
return 0;
}
// Back-to-front box order: topological sort over pairs that overlap on screen.
function paintOrder(boxes, toCamera, project) {
const hulls = boxes.map((b) => {
const lo = boxMin(b), hi = boxMax(b);
const corners = [];
for (let i = 0; i < 8; i++) {
corners.push(project([i & 1 ? hi[0] : lo[0], i & 2 ? hi[1] : lo[1], i & 4 ? hi[2] : lo[2]]));
}
return convexHull(corners);
});
const depth = boxes.map((b) => dot(b, toCamera));
const pending = boxes.map(() => new Set());
for (let i = 0; i < boxes.length; i++) {
for (let j = i + 1; j < boxes.length; j++) {
if (!hullsOverlap(hulls[i], hulls[j])) continue;
const r = compareDepth(boxes[i], boxes[j], toCamera);
if (r < 0) pending[j].add(i);
else if (r > 0) pending[i].add(j);
}
}
const order = [];
const left = new Set(boxes.keys());
while (left.size) {
const candidates = [...left].filter((i) => [...pending[i]].every((j) => !left.has(j)));
const pool = candidates.length ? candidates : [...left]; // only on a cycle
const next = pool.reduce((best, i) => (depth[i] < depth[best] ? i : best));
order.push(next);
left.delete(next);
}
return order;
}
// World height is affine across a face's screen polygon; returns the screen points where it
// equals yA and yB, i.e. the endpoints of a userSpaceOnUse gradient.
function gradientLine(pts2, ys, yA, yB) {
const [s0, s1, s2] = pts2;
const e1 = [s1[0] - s0[0], s1[1] - s0[1]];
const e2 = [s2[0] - s0[0], s2[1] - s0[1]];
const r1 = ys[1] - ys[0];
const r2 = ys[2] - ys[0];
const det = e1[0] * e2[1] - e1[1] * e2[0];
const g = [(r1 * e2[1] - r2 * e1[1]) / det, (e1[0] * r2 - e2[0] * r1) / det];
const gg = g[0] * g[0] + g[1] * g[1];
const at = (y) => [s0[0] + (g[0] * (y - ys[0])) / gg, s0[1] + (g[1] * (y - ys[0])) / gg];
return [at(yA), at(yB)];
}
/**
* Builds an SVG string of the scene.
* options.view { azimuth, elevation, halfExtent }, defaults to the default (logo) view
* options.lights { keyPitch, innerPitch } in degrees, defaults to the current sliders
* options.size output width/height in px (default 800, same framing as the reference)
* options.seamStroke same-paint stroke width on opaque faces. Renderers anti-alias each polygon
* separately, so the page leaks through shared edges as faint lines; the
* stroke covers them and a clip to the exact silhouette keeps the outline
* unchanged. 0 disables both (default 1)
*/
function toSVG(options = {}) {
const v = { ...DEFAULT_VIEW, ...options.view };
const L = { ...lights, ...options.lights };
const size = options.size ?? 800;
const seam = options.seamStroke ?? 1;
const toCamera = toCameraFor(v);
const innerPitch = (L.innerPitch * Math.PI) / 180;
const S = { toCamera, keyDir: keyDirFor(L.keyPitch), sinI: Math.sin(innerPitch), cosI: Math.cos(innerPitch) };
const project = makeProjector(v, size);
const awayFromCamera = scale3(toCamera, -1);
const items = [
...OPAQUE_BOXES.map((b) => ({ b, glass: false })),
...GLASS_BOXES.map((b) => ({ b, glass: true })),
];
const order = paintOrder(items.map((it) => it.b), toCamera, project);
const defs = [];
const backdrops = [];
const shapes = [];
const outline = []; // every visible face as one subpath; a single path anti-aliases as a union
const paintFor = (shading, pts2, ys) => {
if (shading.flat) return toHex(shading.flat);
const h0 = toHex(shading.c0);
const h1 = toHex(shading.c1);
if (h0 === h1) return h0;
const [p0, p1] = gradientLine(pts2, ys, shading.y0, shading.y1);
const id = `g${defs.length}`;
defs.push(
`<linearGradient id="${id}" gradientUnits="userSpaceOnUse" x1="${num(p0[0])}" y1="${num(p0[1])}" x2="${num(p1[0])}" y2="${num(p1[1])}">` +
`<stop offset="0" stop-color="${h0}"/><stop offset="1" stop-color="${h1}"/></linearGradient>`,
);
return `url(#${id})`;
};
for (const index of order) {
const { b, glass } = items[index];
const faces = b[8] === KIND_GLASS_SIDES ? FACES.slice(0, 4) : FACES;
for (const f of faces) {
if (dot(f.n, toCamera) <= 1e-6) continue;
const samples = faceSamples(b, f);
if (!samples.some((p) => !rayBlocked(p, toCamera, OPAQUE_BOXES, b))) continue; // fully hidden