Visualization toolmaker. Founder @observablehq. Creator @d3. Former @nytgraphics. Pronounced BOSS-tock.
{
const context = DOM.context2d(width, height);
const iso = new Isometric(context);
iso.scale3d(30, 30, 30);
function drawCube(angle, x, y, z) {
if ((angle %= Math.PI / 2) < 0) angle += Math.PI / 2;
iso.save();
iso.translate3d(x, y, z);
iso.rotateZ(angle - Math.PI / 4);
context.beginPath();
iso.moveTo(+0.5, -0.5, +0.5);
iso.lineTo(+0.5, +0.5, +0.5);
iso.lineTo(-0.5, +0.5, +0.5);
iso.lineTo(-0.5, +0.5, -0.5);
iso.lineTo(-0.5, -0.5, -0.5);
iso.lineTo(+0.5, -0.5, -0.5);
iso.closePath();
context.fill();
context.lineWidth = 1.5;
context.stroke();
context.beginPath();
iso.moveTo(-0.5, -0.5, +0.5);
iso.lineTo(+0.5, -0.5, +0.5);
iso.moveTo(-0.5, -0.5, +0.5);
iso.lineTo(-0.5, +0.5, +0.5);
iso.moveTo(-0.5, -0.5, +0.5);
iso.lineTo(-0.5, -0.5, -0.5);
context.lineWidth = 0.75;
context.stroke();
iso.restore();
}
while (true) {
context.save();
context.clearRect(0, 0, width, height);
context.fillStyle = "#fff";
context.strokeStyle = "#000";
context.translate(width / 2, height * 0.6);
for (var x = 14, d, t = (performance.now() / 5000) % 1; x >= -14; --x) {
for (var y = 14; y >= -14; --y) {
if ((d = distanceManhattan(x, y)) > 15) continue;
var te = cubicInOut(Math.max(0, Math.min(1, t * 4.8 - distanceCartesian(x, y) / 5)));
drawCube((d & 1 ? -1 : +1) * (Math.PI / 4 - te * Math.PI / 2), x * 1.42, y * 1.42 + te * (x & 1 ? 1 : -1) * 1.42, te * 1.42 * 2);
}
}
context.restore();
yield context.canvas;
}
}
function distanceCartesian(x, y) {
return Math.sqrt(x * x + y * y);
}
function distanceManhattan(x, y) {
return Math.abs(x) + Math.abs(y);
}
function cubicInOut(t) {
return ((t *= 2) <= 1 ? t * t * t : (t -= 2) * t * t + 2) / 2;
}
height = 500
class Isometric {
constructor(context) {
this._moveTo = context.moveTo.bind(context);
this._lineTo = context.lineTo.bind(context);
this.closePath = context.closePath.bind(context);
this._matrix = [
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0
];
this._matrixes = [];
this._projection = [
Math.cos(Math.PI / 6), Math.cos(Math.PI - Math.PI / 6),
-Math.sin(Math.PI / 6), -Math.sin(Math.PI - Math.PI / 6)
];
}
_project(point, x, y, z) {
point(
x * this._projection[0] + y * this._projection[1],
x * this._projection[2] + y * this._projection[3] - z
);
}
_transform(point, x, y, z) {
this._project(
point,
x * this._matrix[0] + y * this._matrix[1] + z * this._matrix[2] + this._matrix[3],
x * this._matrix[4] + y * this._matrix[5] + z * this._matrix[6] + this._matrix[7],
x * this._matrix[8] + y * this._matrix[9] + z * this._matrix[10] + this._matrix[11]
);
}
save() {
this._matrixes.push(this._matrix.slice());
}
restore() {
if (this._matrixes.length) this._matrix = this._matrixes.pop();
}
// | a b c d | | kx 0 0 0 | | a * kx b * ky c * kz d |
// | e f g h | * | 0 ky 0 0 | = | e * kx f * ky g * kz h |
// | i j k l | | 0 0 kz 0 | | i * kx j * ky k * kz l |
// | 0 0 0 1 | | 0 0 0 1 | | 0 0 0 1 |
scale3d(kx, ky, kz) {
this._matrix[0] *= kx;
this._matrix[1] *= ky;
this._matrix[2] *= kz;
this._matrix[4] *= kx;
this._matrix[5] *= ky;
this._matrix[6] *= kz;
this._matrix[8] *= kx;
this._matrix[9] *= ky;
this._matrix[10] *= kz;
}
// | a b c d | | cos -sin 0 0 | | a * cos + b * sin a * -sin + b * cos c d |
// | e f g h | * | sin cos 0 0 | = | e * cos + f * sin e * -sin + f * cos g h |
// | i j k l | | 0 0 1 0 | | i * cos + j * sin i * -sin + j * cos k l |
// | 0 0 0 1 | | 0 0 0 1 | | 0 0 0 1 |
rotateZ(angle) {
const cos = Math.cos(angle);
const sin = Math.sin(angle);
const a = this._matrix[0];
const b = this._matrix[1];
const e = this._matrix[4];
const f = this._matrix[5];
const i = this._matrix[8];
const j = this._matrix[9];
this._matrix[0] = a * cos + b * sin;
this._matrix[1] = a * -sin + b * cos;
this._matrix[4] = e * cos + f * sin;
this._matrix[5] = e * -sin + f * cos;
this._matrix[8] = i * cos + j * sin;
this._matrix[9] = i * -sin + j * cos;
}
// | a b c d | | 1 0 0 tx | | a b c a * tx + b * ty + c * tz + d |
// | e f g h | * | 0 1 0 ty | = | e f g e * tx + f * ty + g * tz + h |
// | i j k l | | 0 0 1 tz | | i j k i * tx + j * ty + k * tz + l |
// | 0 0 0 1 | | 0 0 0 1 | | 0 0 0 1 |
translate3d(tx, ty, tz) {
this._matrix[3] += this._matrix[0] * tx + this._matrix[1] * ty + this._matrix[2] * tz;
this._matrix[7] += this._matrix[4] * tx + this._matrix[5] * ty + this._matrix[6] * tz;
this._matrix[11] += this._matrix[8] * tx + this._matrix[9] * ty + this._matrix[10] * tz;
}
moveTo(x, y, z) {
this._transform(this._moveTo, x, y, z);
}
lineTo(x, y, z) {
this._transform(this._lineTo, x, y, z);
}
}
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