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closed-surface.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<title>MathBox - Closed Surface</title>
<script
type="text/javascript"
src="https://cdn.jsdelivr.net/npm/three@0.137.0/build/three.min.js"
></script>
<script
type="text/javascript"
src="https://cdn.jsdelivr.net/npm/three@0.137.0/examples/js/controls/OrbitControls.js"
></script>
<!--
- a minified version mathbox.min.js is also available;
- recommend using a specific version (not @latest) in public sites
-->
<script
type="text/javascript"
src="https://cdn.jsdelivr.net/npm/mathbox@latest/build/bundle/mathbox.js"
></script>
<link rel="stylesheet" href="../../build/mathbox.css" />
<meta name="viewport" content="initial-scale=1, maximum-scale=1" />
</head>
<body>
<script>
mathbox = MathBox.mathBox({
plugins: ["core", "controls", "cursor", "stats"],
controls: {
klass: THREE.OrbitControls,
},
});
three = mathbox.three;
three.camera.position.set(-3.5, 2.2, -3.3);
three.renderer.setClearColor(new THREE.Color(0xffffff), 1.0);
view = mathbox.cartesian({
range: [
[-1, 1],
[-1, 1],
[-1, 1],
],
scale: [1, 1, 1],
});
view.axis({
axis: 1,
});
view.axis({
axis: 3,
});
view.grid({
width: 5,
opacity: 0.5,
axes: [1, 3],
});
// Horizontally closed, explicit normals
var sphere = view
.matrix({
id: "sphere",
bufferWidth: 128,
bufferHeight: 64,
width: 64,
height: 32,
live: false,
expr: (emit, i, j, time) => {
let φ = (i / 64) * MathBox.τ;
let θ = (j / 31 - 0.5) * MathBox.π;
emit(
Math.cos(φ) * Math.cos(θ),
Math.sin(θ),
Math.sin(φ) * Math.cos(θ)
);
},
channels: 3,
})
.transform({
scale: [0.5, 0.5, 0.5],
})
.surface({
points: "<",
normals: "<",
color: 0x3090ff,
shaded: true,
closedX: true,
});
// Completely closed, implicit normals
var torus = view
.matrix({
id: "torus",
bufferWidth: 128,
bufferHeight: 64,
width: 64,
height: 32,
live: false,
expr: (emit, i, j, time) => {
let φ = (i / 64) * MathBox.τ;
let θ = (j / 32) * MathBox.τ;
let x = Math.cos(φ) * 0.5 + 2;
let y = Math.sin(φ) * 0.5;
emit(x * Math.cos(θ), y, x * Math.sin(θ));
},
channels: 3,
})
.transform({
scale: [0.5, 0.5, 0.5],
})
.surface({
points: "<",
color: 0x3090ff,
shaded: true,
closedX: true,
closedY: true,
});
</script>
</body>
</html>