ParametricGeometries.js

/*
 * @author zz85
 *
 * Experimenting of primitive geometry creation using Surface Parametric equations
 *
 */


THREE.ParametricGeometries = {

    klein: function (v, u) {
        u *= Math.PI;
        v *= 2 * Math.PI;

        u = u * 2;
        var x, y, z;
        if (u < Math.PI) {
            x = 3 * Math.cos(u) * (1 + Math.sin(u)) + (2 * (1 - Math.cos(u) / 2)) * Math.cos(u) * Math.cos(v);
            z = -8 * Math.sin(u) - 2 * (1 - Math.cos(u) / 2) * Math.sin(u) * Math.cos(v);
        } else {
            x = 3 * Math.cos(u) * (1 + Math.sin(u)) + (2 * (1 - Math.cos(u) / 2)) * Math.cos(v + Math.PI);
            z = -8 * Math.sin(u);
        }

        y = -2 * (1 - Math.cos(u) / 2) * Math.sin(v);

        return new THREE.Vector3(x, y, z);
    },

    plane: function (width, height) {

        return function(u, v) {
            var x = u * width;
            var y = 0;
            var z = v * height;

            return new THREE.Vector3(x, y, z);
        };
    },

    mobius: function(u, t) {

        // flat mobius strip
        // http://www.wolframalpha.com/input/?i=M%C3%B6bius+strip+parametric+equations&lk=1&a=ClashPrefs_*Surface.MoebiusStrip.SurfaceProperty.ParametricEquations-
        u = u - 0.5;
        var v = 2 * Math.PI * t;

        var x, y, z;

        var a = 2;
        x = Math.cos(v) * (a + u * Math.cos(v/2));
        y = Math.sin(v) * (a + u * Math.cos(v/2));
        z = u * Math.sin(v/2);
        return new THREE.Vector3(x, y, z);

    },

    mobius3d: function(u, t) {

        // volumetric mobius strip
        u *= Math.PI;
        t *= 2 * Math.PI;

        u = u * 2;
        var phi = u / 2;
        var major = 2.25, a = 0.125, b = 0.65;
        var x, y, z;
        x = a * Math.cos(t) * Math.cos(phi) - b * Math.sin(t) * Math.sin(phi);
        z = a * Math.cos(t) * Math.sin(phi) + b * Math.sin(t) * Math.cos(phi);
        y = (major + x) * Math.sin(u);
        x = (major + x) * Math.cos(u);
        return new THREE.Vector3(x, y, z);
    }

};


/*********************************************
 *
 * Parametric Replacement for TubeGeometry
 *
 *********************************************/

THREE.ParametricGeometries.TubeGeometry = function(path, segments, radius, segmentsRadius, closed, debug) {

    this.path = path;
    this.segments = segments || 64;
    this.radius = radius || 1;
    this.segmentsRadius = segmentsRadius || 8;
    this.closed = closed || false;
    if (debug) this.debug = new THREE.Object3D();


    var scope = this,

        tangent, normal, binormal,

        numpoints = this.segments + 1,

        x, y, z, tx, ty, tz, u, v,

        cx, cy, pos, pos2 = new THREE.Vector3(),
        i, j, ip, jp, a, b, c, d, uva, uvb, uvc, uvd;

    var frames = new THREE.TubeGeometry.FrenetFrames(path, segments, closed),
        tangents = frames.tangents,
        normals = frames.normals,
        binormals = frames.binormals;

    // proxy internals
    this.tangents = tangents;
    this.normals = normals;
    this.binormals = binormals;



    var ParametricTube = function(u, v) {
        v *= 2 * Math.PI;

        i = u * (numpoints - 1);
        i = Math.floor(i);

        pos = path.getPointAt(u);

        tangent = tangents[i];
        normal = normals[i];
        binormal = binormals[i];

        if (scope.debug) {

            scope.debug.add(new THREE.ArrowHelper(tangent, pos, radius, 0x0000ff));
            scope.debug.add(new THREE.ArrowHelper(normal, pos, radius, 0xff0000));
            scope.debug.add(new THREE.ArrowHelper(binormal, pos, radius, 0x00ff00));

        }

        cx = -scope.radius * Math.cos(v); // TODO: Hack: Negating it so it faces outside.
        cy = scope.radius * Math.sin(v);

        pos2.copy(pos);
        pos2.x += cx * normal.x + cy * binormal.x;
        pos2.y += cx * normal.y + cy * binormal.y;
        pos2.z += cx * normal.z + cy * binormal.z;

        return pos2.clone();
    };

    THREE.ParametricGeometry.call(this, ParametricTube, segments, segmentsRadius);

};

THREE.ParametricGeometries.TubeGeometry.prototype = Object.create( THREE.Geometry.prototype );


/*********************************************
 *
 * Parametric Replacement for TorusKnotGeometry
 *
 *********************************************/
THREE.ParametricGeometries.TorusKnotGeometry = function ( radius, tube, segmentsR, segmentsT, p, q, heightScale ) {

    var scope = this;

    this.radius = radius || 200;
    this.tube = tube || 40;
    this.segmentsR = segmentsR || 64;
    this.segmentsT = segmentsT || 8;
    this.p = p || 2;
    this.q = q || 3;
    this.heightScale = heightScale || 1;


    var TorusKnotCurve = THREE.Curve.create(

        function() {
        },

        function(t) {

            t *= Math.PI * 2;

            var r = 0.5;

            var tx = (1 + r * Math.cos(q * t)) * Math.cos(p * t),
                ty = (1 + r * Math.cos(q * t)) * Math.sin(p * t),
                tz = r * Math.sin(q * t);

            return new THREE.Vector3(tx, ty * heightScale, tz).multiplyScalar(radius);

        }

    );
    var segments = segmentsR;
    var radiusSegments = segmentsT;
    var extrudePath = new TorusKnotCurve();

    THREE.ParametricGeometries.TubeGeometry.call( this, extrudePath, segments, tube, radiusSegments, true, false );


};

THREE.ParametricGeometries.TorusKnotGeometry.prototype = Object.create( THREE.Geometry.prototype );


/*********************************************
 *
 * Parametric Replacement for SphereGeometry
 *
 *********************************************/
THREE.ParametricGeometries.SphereGeometry = function(size, u, v) {

    function sphere(u, v) {
        u *= Math.PI;
        v *= 2 * Math.PI;

        var x = size * Math.sin(u) * Math.cos(v);
        var y = size * Math.sin(u) * Math.sin(v);
        var z = size * Math.cos(u);


        return new THREE.Vector3(x, y, z);
    }

    THREE.ParametricGeometry.call(this, sphere, u, v, !true);

};

THREE.ParametricGeometries.SphereGeometry.prototype = Object.create( THREE.Geometry.prototype );


/*********************************************
 *
 * Parametric Replacement for PlaneGeometry
 *
 *********************************************/

THREE.ParametricGeometries.PlaneGeometry = function(width, depth, segmentsWidth, segmentsDepth) {

    function plane(u, v) {

        var x = u * width;
        var y = 0;
        var z = v * depth;

        return new THREE.Vector3(x, y, z);
    }

    THREE.ParametricGeometry.call(this, plane, segmentsWidth, segmentsDepth);

};

THREE.ParametricGeometries.PlaneGeometry.prototype = Object.create( THREE.Geometry.prototype );