polyhedrons for three.js

PolyhedronGeometry.js

/**
 * Polyhedrons which support subdivision.
 * 
 * Vertices have 'smooth' normals, 
 * to make a sharp edge choose a material that uses face normals instead.
 *
 * @author [email protected]
 * @author [email protected]
 * @param radius
 * @param detail Final number of triangles = 4^detail * X
 */

THREE.TetrahedronGeometry = function (radius, detail) {
    var vs = [[+1, +1, +1],
            [-1, -1, +1],
            [-1, +1, -1],
            [+1, -1, -1]],
        fs = [[2, 1, 0],
            [0, 3, 2],
            [1, 3, 0],
            [2, 3, 1]];

    THREE.PolyhedronGeometry.call(this, vs, fs, radius, detail);
};
THREE.TetrahedronGeometry.prototype = new THREE.Geometry();
THREE.TetrahedronGeometry.prototype.constructor = THREE.TetrahedronGeometry;

THREE.OctahedronGeometry = function (radius, detail) {
    var vs = [[+1, 0, 0],
	        [-1, 0, 0], // left
	        [0, +1, 0], // up
	        [0, -1, 0], // down
	        [0, 0, +1], // front
	        [0, 0, -1]], // back
        fs = [[0, 2, 4],
            [0, 4, 3],
            [0, 3, 5],
            [0, 5, 2],
            [1, 2, 5],
            [1, 5, 3],
            [1, 3, 4],
            [1, 4, 2]];

    THREE.PolyhedronGeometry.call(this, vs, fs, radius, detail);
};
THREE.OctahedronGeometry.prototype = new THREE.Geometry();
THREE.OctahedronGeometry.prototype.constructor = THREE.OctahedronGeometry;

THREE.IcosahedronGeometry = function (radius, detail) {
    var t = (1 + Math.sqrt(5)) / 2,
    // create 12 vertices of a Icosahedron
        vs = [[-1, t, 0],
            [1, t, 0],
            [-1, -t, 0],
            [1, -t, 0],

            [0, -1, t],
            [0, 1, t],
            [0, -1, -t],
            [0, 1, -t],

            [t, 0, -1],
            [t, 0, 1],
            [-t, 0, -1],
            [-t, 0, 1]],
        fs = [
    // 5 faces around point 0
            [0, 11, 5],
            [0, 5, 1],
            [0, 1, 7],
            [0, 7, 10],
            [0, 10, 11],

    // 5 adjacent faces
            [1, 5, 9],
            [5, 11, 4],
            [11, 10, 2],
            [10, 7, 6],
            [7, 1, 8],

    // 5 faces around point 3
            [3, 9, 4],
            [3, 4, 2],
            [3, 2, 6],
            [3, 6, 8],
            [3, 8, 9],

    // 5 adjacent faces
            [4, 9, 5],
            [2, 4, 11],
            [6, 2, 10],
            [8, 6, 7],
            [9, 8, 1]];

    THREE.PolyhedronGeometry.call(this, vs, fs, radius, detail);
};
THREE.IcosahedronGeometry.prototype = new THREE.Geometry();
THREE.IcosahedronGeometry.prototype.constructor = THREE.IcosahedronGeometry;


THREE.PolyhedronGeometry = function (vs, fs, radius, detail) {

    THREE.Geometry.call(this);

    radius = radius || 1;
    detail = detail || 0;

    var that = this,
        ii;

    for (ii = 0; ii < vs.length; ii++) {
        prepare(new THREE.Vector3(vs[ii][0], vs[ii][1], vs[ii][2]));
    }
    var midpoints = [], p = this.vertices;

    // careful to output faces counter-clockwise, that is required for meshes
    for (ii = 0; ii < fs.length; ii++) {
        make(p[fs[ii][0]], p[fs[ii][1]], p[fs[ii][2]], detail);
    }

    this.mergeVertices();

    /**
    * Project vector onto sphere's surface
    */
    function prepare(vector) {

        var vertex = new THREE.Vertex(vector.clone().normalize().multiplyScalar(radius));
        vertex.index = that.vertices.push(vertex) - 1;

        // Texture coords are equivalent to map coords, calculate angle and convert to fraction of a circle.
        var u = azimuth(vector) / 2 / Math.PI + 0.5;
        var v = inclination(vector) / Math.PI + 0.5;
        vertex.uv = new THREE.UV(u, v);

        return vertex;

    }

    /**
    * Approximate a curved face with recursively sub-divided triangles.
    */
    function make(v1, v2, v3, detail) {

        if (detail < 1) {

            var face = new THREE.Face3(v1.index, v2.index, v3.index, [v1.position, v2.position, v3.position]);
            face.centroid.addSelf(v1.position).addSelf(v2.position).addSelf(v3.position).divideScalar(3);
            face.normal = face.centroid.clone().normalize();
            that.faces.push(face);

            var azi = azimuth(face.centroid);
            that.faceVertexUvs[0].push([
				correctUV(v1.uv, v1.position, azi),
				correctUV(v2.uv, v2.position, azi),
				correctUV(v3.uv, v3.position, azi)
			]);

        }
        else {

            detail -= 1;
            // split triangle into 4 smaller triangles
            make(v1, midpoint(v1, v2), midpoint(v1, v3), detail); // top quadrant
            make(midpoint(v1, v2), v2, midpoint(v2, v3), detail); // left quadrant
            make(midpoint(v1, v3), midpoint(v2, v3), v3, detail); // right quadrant
            make(midpoint(v1, v2), midpoint(v2, v3), midpoint(v1, v3), detail); // center quadrant

        }

    }

    function midpoint(v1, v2) {

        if (!midpoints[v1.index]) midpoints[v1.index] = [];
        if (!midpoints[v2.index]) midpoints[v2.index] = [];
        var mid = midpoints[v1.index][v2.index];
        if (mid === undefined) {
            // generate mean point and project to surface with prepare()
            midpoints[v1.index][v2.index] = midpoints[v2.index][v1.index] = mid = prepare(
				new THREE.Vector3().add(v1.position, v2.position).divideScalar(2)
			);
        }
        return mid;

    }

    /**
    * Angle around the Y axis, counter-clockwise when looking from above.
    */
    function azimuth(vector) {

        return Math.atan2(vector.z, -vector.x);

    }

    /**
    * Angle above the XZ plane.
    */
    function inclination(vector) {

        return Math.atan2(-vector.y, Math.sqrt((vector.x * vector.x) + (vector.z * vector.z)));

    }

    /**
    * Texture fixing helper. Spheres have some odd behaviours.
    */
    function correctUV(uv, vector, azimuth) {

        if ((azimuth < 0) && (uv.u === 1)) uv = new THREE.UV(uv.u - 1, uv.v);
        if ((vector.x === 0) && (vector.z === 0)) uv = new THREE.UV(azimuth / 2 / Math.PI + 0.5, uv.v);
        return uv;

    }

    this.boundingSphere = { radius: radius };

};

THREE.PolyhedronGeometry.prototype = new THREE.Geometry();
THREE.PolyhedronGeometry.prototype.constructor = THREE.PolyhedronGeometry;

testPolyhedron.js

testGeometry = function (world) {
    var green = new THREE.MeshLambertMaterial({ color: 0x00FF00 }),
        tetrahedron = new THREE.Mesh(new THREE.TetrahedronGeometry(50), green),
        tetrahedron2 = new THREE.Mesh(new THREE.TetrahedronGeometry(50, 2), green),
        grey = new THREE.MeshLambertMaterial({ color: 0x444444 }),
        octahedron = new THREE.Mesh(new THREE.OctahedronGeometry(50), grey),
        octahedron2 = new THREE.Mesh(new THREE.OctahedronGeometry(50, 2), grey),
        blue = new THREE.MeshLambertMaterial({ color: 0x0000FF }),
        icosahedron = new THREE.Mesh(new THREE.IcosahedronGeometry(50), blue),
        icosahedron2 = new THREE.Mesh(new THREE.IcosahedronGeometry(50, 2), blue);

    tetrahedron.position.set(100, 0, 0);
    world.add(tetrahedron);
    octahedron.position.set(0, 100, 0);
    world.add(octahedron);
    icosahedron.position.set(100, 100, 0);
    world.add(icosahedron);

    tetrahedron2.position.set(-100, 0, 0);
    world.add(tetrahedron2);
    octahedron2.position.set(0, -100, 0);
    world.add(octahedron2);
    icosahedron2.position.set(-100, -100, 0);
    world.add(icosahedron2);
};