mathbox/examples/math/helitorus.html at master · unconed/mathbox · GitHub

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<!DOCTYPE html>
<html>
  <head>
    <meta charset="utf-8" />
    <title>MathBox - Helitoroidal 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/TrackballControls.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>
    <script src="https://cdn.jsdelivr.net/npm/dat.gui@latest/build/dat.gui.min.js"></script>
    <link rel="stylesheet" href="../../build/mathbox.css" />
    <meta name="viewport" content="initial-scale=1, maximum-scale=1" />
  </head>
  <body>
    <script>
      var mathbox = MathBox.mathBox({
        plugins: ["core", "controls", "cursor", "mathbox"],
        controls: {
          // Trackball controls, i.e. Free quaternion rotation
          klass: THREE.TrackballControls,
        },
      });
      if (mathbox.fallback) throw "WebGL not supported";

      var three = mathbox.three;
      three.renderer.setClearColor(new THREE.Color(0xffffff), 1.0);

      // Dat GUI
      var gui = new dat.GUI();
      var props = {
        n: 16,
        r1: 1,
        r2: 0.3,
        r3: 0.1,
      };
      gui.add(props, "n").min(0).max(32).step(1);
      gui.add(props, "r1").min(0).max(3).step(0.01);
      gui.add(props, "r2").min(0.01).max(0.5).step(0.01);
      gui.add(props, "r3").min(0.01).max(0.2).step(0.01);

      // DOM
      mathbox.set("focus", 3);

      var camera = mathbox.camera({
        proxy: true,
        position: [1, 1, 3],
      });

      var view = mathbox.clock({ speed: 1 / 16 }).cartesian({
        range: [
          [-1, 1],
          [-1, 1],
          [-1, 1],
        ],
        scale: [1, 1, 1],
        quaternion: [0.7, 0, 0, 0.7],
      });

      var vs = new THREE.Vector3();
      var spine = function (θ) {
        var s, c, x, y, z, x2, y2, z2, r;

        var a = θ * props.n;
        var b = θ;

        s = Math.sin(a);
        c = Math.cos(a);

        r = props.r2 + props.r3;
        x = 1 + c * r;
        y = 0;
        z = s * r;

        s = Math.sin(b);
        c = Math.cos(b);

        r = props.r1;
        x2 = x * c * r;
        y2 = x * s * r;
        z2 = z * r;

        return vs.set(x2, y2, z2);
      };

      var circle = function (θ) {
        var s, c, x, y, z;

        var b = θ;

        s = Math.sin(b);
        c = Math.cos(b);

        x = c * props.r1;
        y = s * props.r1;
        z = 0;

        return vs.set(x, y, z);
      };

      // Compute TBN matrix
      var vo = new THREE.Vector3();
      var vt = new THREE.Vector3();
      var vb = new THREE.Vector3();
      var vn = new THREE.Vector3();
      var mtbn = new THREE.Matrix4();
      var e = 0.001;
      var tbn = function (θ) {
        var f;

        vt.copy(vo.copy(spine(θ)));
        vt.sub(spine(θ + e));
        vt.multiplyScalar(1 / e);
        vt.normalize();

        if (props.n) {
          vb.copy(circle(θ));
          vb.sub(circle(θ + e));
          vb.multiplyScalar(1 / e);
        } else {
          vb.copy(vo);
        }
        vb.normalize();

        vn.crossVectors(vt, vb);
        vn.normalize();

        vb.crossVectors(vt, vn);
        vb.normalize();

        mtbn.set(
          vt.x,
          vb.x,
          vn.x,
          vo.x,
          vt.y,
          vb.y,
          vn.y,
          vo.y,
          vt.z,
          vb.z,
          vn.z,
          vo.z,
          0,
          0,
          0,
          1
        );

        return mtbn;
      };

      // Compute helitoroidal surface
      var data = view.area({
        rangeX: [-MathBox.π, MathBox.π],
        rangeY: [-MathBox.π, MathBox.π],
        expr: function (emit, θ, φ, i, j, t) {
          var f = spine(θ);
          var m = tbn(θ);

          var c = Math.cos(φ);
          var s = Math.sin(φ);

          vs.set(0, c * props.r3, s * props.r3);
          vs.applyMatrix4(m);

          emit(vs.x, vs.y, vs.z);
        },
        width: 512,
        height: 16,
        channels: 3,
      });

      // Draw spine curve
      var helitoroidalSurface = view.surface({
        shaded: true,
        color: 0xcc0040,
        lineY: true,
        width: 1,
      });

      var curves1 = view
        .resample({
          height: 5,
        })
        .line({
          color: 0xffffff,
          width: 2,
        });
    </script>
  </body>
</html>