Babylon.js/src/Meshes/Builders/polyhedronBuilder.ts

import { Scene } from "../../scene";
import { Color4, Vector4 } from "../../Maths/math";
import { Mesh, _CreationDataStorage } from "../mesh";
import { VertexData } from "../mesh.vertexData";
import { Nullable } from '../../types';

VertexData.CreatePolyhedron = function(options: { type?: number, size?: number, sizeX?: number, sizeY?: number, sizeZ?: number, custom?: any, faceUV?: Vector4[], faceColors?: Color4[], flat?: boolean, sideOrientation?: number, frontUVs?: Vector4, backUVs?: Vector4 }): VertexData {
    // provided polyhedron types :
    // 0 : Tetrahedron, 1 : Octahedron, 2 : Dodecahedron, 3 : Icosahedron, 4 : Rhombicuboctahedron, 5 : Triangular Prism, 6 : Pentagonal Prism, 7 : Hexagonal Prism, 8 : Square Pyramid (J1)
    // 9 : Pentagonal Pyramid (J2), 10 : Triangular Dipyramid (J12), 11 : Pentagonal Dipyramid (J13), 12 : Elongated Square Dipyramid (J15), 13 : Elongated Pentagonal Dipyramid (J16), 14 : Elongated Pentagonal Cupola (J20)
    var polyhedra: { vertex: number[][], face: number[][] }[] = [];
    polyhedra[0] = { vertex: [[0, 0, 1.732051], [1.632993, 0, -0.5773503], [-0.8164966, 1.414214, -0.5773503], [-0.8164966, -1.414214, -0.5773503]], face: [[0, 1, 2], [0, 2, 3], [0, 3, 1], [1, 3, 2]] };
    polyhedra[1] = { vertex: [[0, 0, 1.414214], [1.414214, 0, 0], [0, 1.414214, 0], [-1.414214, 0, 0], [0, -1.414214, 0], [0, 0, -1.414214]], face: [[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 1], [1, 4, 5], [1, 5, 2], [2, 5, 3], [3, 5, 4]] };
    polyhedra[2] = {
        vertex: [[0, 0, 1.070466], [0.7136442, 0, 0.7978784], [-0.3568221, 0.618034, 0.7978784], [-0.3568221, -0.618034, 0.7978784], [0.7978784, 0.618034, 0.3568221], [0.7978784, -0.618034, 0.3568221], [-0.9341724, 0.381966, 0.3568221], [0.1362939, 1, 0.3568221], [0.1362939, -1, 0.3568221], [-0.9341724, -0.381966, 0.3568221], [0.9341724, 0.381966, -0.3568221], [0.9341724, -0.381966, -0.3568221], [-0.7978784, 0.618034, -0.3568221], [-0.1362939, 1, -0.3568221], [-0.1362939, -1, -0.3568221], [-0.7978784, -0.618034, -0.3568221], [0.3568221, 0.618034, -0.7978784], [0.3568221, -0.618034, -0.7978784], [-0.7136442, 0, -0.7978784], [0, 0, -1.070466]],
        face: [[0, 1, 4, 7, 2], [0, 2, 6, 9, 3], [0, 3, 8, 5, 1], [1, 5, 11, 10, 4], [2, 7, 13, 12, 6], [3, 9, 15, 14, 8], [4, 10, 16, 13, 7], [5, 8, 14, 17, 11], [6, 12, 18, 15, 9], [10, 11, 17, 19, 16], [12, 13, 16, 19, 18], [14, 15, 18, 19, 17]]
    };
    polyhedra[3] = {
        vertex: [[0, 0, 1.175571], [1.051462, 0, 0.5257311], [0.3249197, 1, 0.5257311], [-0.8506508, 0.618034, 0.5257311], [-0.8506508, -0.618034, 0.5257311], [0.3249197, -1, 0.5257311], [0.8506508, 0.618034, -0.5257311], [0.8506508, -0.618034, -0.5257311], [-0.3249197, 1, -0.5257311], [-1.051462, 0, -0.5257311], [-0.3249197, -1, -0.5257311], [0, 0, -1.175571]],
        face: [[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1], [1, 5, 7], [1, 7, 6], [1, 6, 2], [2, 6, 8], [2, 8, 3], [3, 8, 9], [3, 9, 4], [4, 9, 10], [4, 10, 5], [5, 10, 7], [6, 7, 11], [6, 11, 8], [7, 10, 11], [8, 11, 9], [9, 11, 10]]
    };
    polyhedra[4] = {
        vertex: [[0, 0, 1.070722], [0.7148135, 0, 0.7971752], [-0.104682, 0.7071068, 0.7971752], [-0.6841528, 0.2071068, 0.7971752], [-0.104682, -0.7071068, 0.7971752], [0.6101315, 0.7071068, 0.5236279], [1.04156, 0.2071068, 0.1367736], [0.6101315, -0.7071068, 0.5236279], [-0.3574067, 1, 0.1367736], [-0.7888348, -0.5, 0.5236279], [-0.9368776, 0.5, 0.1367736], [-0.3574067, -1, 0.1367736], [0.3574067, 1, -0.1367736], [0.9368776, -0.5, -0.1367736], [0.7888348, 0.5, -0.5236279], [0.3574067, -1, -0.1367736], [-0.6101315, 0.7071068, -0.5236279], [-1.04156, -0.2071068, -0.1367736], [-0.6101315, -0.7071068, -0.5236279], [0.104682, 0.7071068, -0.7971752], [0.6841528, -0.2071068, -0.7971752], [0.104682, -0.7071068, -0.7971752], [-0.7148135, 0, -0.7971752], [0, 0, -1.070722]],
        face: [[0, 2, 3], [1, 6, 5], [4, 9, 11], [7, 15, 13], [8, 16, 10], [12, 14, 19], [17, 22, 18], [20, 21, 23], [0, 1, 5, 2], [0, 3, 9, 4], [0, 4, 7, 1], [1, 7, 13, 6], [2, 5, 12, 8], [2, 8, 10, 3], [3, 10, 17, 9], [4, 11, 15, 7], [5, 6, 14, 12], [6, 13, 20, 14], [8, 12, 19, 16], [9, 17, 18, 11], [10, 16, 22, 17], [11, 18, 21, 15], [13, 15, 21, 20], [14, 20, 23, 19], [16, 19, 23, 22], [18, 22, 23, 21]]
    };
    polyhedra[5] = { vertex: [[0, 0, 1.322876], [1.309307, 0, 0.1889822], [-0.9819805, 0.8660254, 0.1889822], [0.1636634, -1.299038, 0.1889822], [0.3273268, 0.8660254, -0.9449112], [-0.8183171, -0.4330127, -0.9449112]], face: [[0, 3, 1], [2, 4, 5], [0, 1, 4, 2], [0, 2, 5, 3], [1, 3, 5, 4]] };
    polyhedra[6] = { vertex: [[0, 0, 1.159953], [1.013464, 0, 0.5642542], [-0.3501431, 0.9510565, 0.5642542], [-0.7715208, -0.6571639, 0.5642542], [0.6633206, 0.9510565, -0.03144481], [0.8682979, -0.6571639, -0.3996071], [-1.121664, 0.2938926, -0.03144481], [-0.2348831, -1.063314, -0.3996071], [0.5181548, 0.2938926, -0.9953061], [-0.5850262, -0.112257, -0.9953061]], face: [[0, 1, 4, 2], [0, 2, 6, 3], [1, 5, 8, 4], [3, 6, 9, 7], [5, 7, 9, 8], [0, 3, 7, 5, 1], [2, 4, 8, 9, 6]] };
    polyhedra[7] = { vertex: [[0, 0, 1.118034], [0.8944272, 0, 0.6708204], [-0.2236068, 0.8660254, 0.6708204], [-0.7826238, -0.4330127, 0.6708204], [0.6708204, 0.8660254, 0.2236068], [1.006231, -0.4330127, -0.2236068], [-1.006231, 0.4330127, 0.2236068], [-0.6708204, -0.8660254, -0.2236068], [0.7826238, 0.4330127, -0.6708204], [0.2236068, -0.8660254, -0.6708204], [-0.8944272, 0, -0.6708204], [0, 0, -1.118034]], face: [[0, 1, 4, 2], [0, 2, 6, 3], [1, 5, 8, 4], [3, 6, 10, 7], [5, 9, 11, 8], [7, 10, 11, 9], [0, 3, 7, 9, 5, 1], [2, 4, 8, 11, 10, 6]] };
    polyhedra[8] = { vertex: [[-0.729665, 0.670121, 0.319155], [-0.655235, -0.29213, -0.754096], [-0.093922, -0.607123, 0.537818], [0.702196, 0.595691, 0.485187], [0.776626, -0.36656, -0.588064]], face: [[1, 4, 2], [0, 1, 2], [3, 0, 2], [4, 3, 2], [4, 1, 0, 3]] };
    polyhedra[9] = { vertex: [[-0.868849, -0.100041, 0.61257], [-0.329458, 0.976099, 0.28078], [-0.26629, -0.013796, -0.477654], [-0.13392, -1.034115, 0.229829], [0.738834, 0.707117, -0.307018], [0.859683, -0.535264, -0.338508]], face: [[3, 0, 2], [5, 3, 2], [4, 5, 2], [1, 4, 2], [0, 1, 2], [0, 3, 5, 4, 1]] };
    polyhedra[10] = { vertex: [[-0.610389, 0.243975, 0.531213], [-0.187812, -0.48795, -0.664016], [-0.187812, 0.9759, -0.664016], [0.187812, -0.9759, 0.664016], [0.798201, 0.243975, 0.132803]], face: [[1, 3, 0], [3, 4, 0], [3, 1, 4], [0, 2, 1], [0, 4, 2], [2, 4, 1]] };
    polyhedra[11] = { vertex: [[-1.028778, 0.392027, -0.048786], [-0.640503, -0.646161, 0.621837], [-0.125162, -0.395663, -0.540059], [0.004683, 0.888447, -0.651988], [0.125161, 0.395663, 0.540059], [0.632925, -0.791376, 0.433102], [1.031672, 0.157063, -0.354165]], face: [[3, 2, 0], [2, 1, 0], [2, 5, 1], [0, 4, 3], [0, 1, 4], [4, 1, 5], [2, 3, 6], [3, 4, 6], [5, 2, 6], [4, 5, 6]] };
    polyhedra[12] = { vertex: [[-0.669867, 0.334933, -0.529576], [-0.669867, 0.334933, 0.529577], [-0.4043, 1.212901, 0], [-0.334933, -0.669867, -0.529576], [-0.334933, -0.669867, 0.529577], [0.334933, 0.669867, -0.529576], [0.334933, 0.669867, 0.529577], [0.4043, -1.212901, 0], [0.669867, -0.334933, -0.529576], [0.669867, -0.334933, 0.529577]], face: [[8, 9, 7], [6, 5, 2], [3, 8, 7], [5, 0, 2], [4, 3, 7], [0, 1, 2], [9, 4, 7], [1, 6, 2], [9, 8, 5, 6], [8, 3, 0, 5], [3, 4, 1, 0], [4, 9, 6, 1]] };
    polyhedra[13] = { vertex: [[-0.931836, 0.219976, -0.264632], [-0.636706, 0.318353, 0.692816], [-0.613483, -0.735083, -0.264632], [-0.326545, 0.979634, 0], [-0.318353, -0.636706, 0.692816], [-0.159176, 0.477529, -0.856368], [0.159176, -0.477529, -0.856368], [0.318353, 0.636706, 0.692816], [0.326545, -0.979634, 0], [0.613482, 0.735082, -0.264632], [0.636706, -0.318353, 0.692816], [0.931835, -0.219977, -0.264632]], face: [[11, 10, 8], [7, 9, 3], [6, 11, 8], [9, 5, 3], [2, 6, 8], [5, 0, 3], [4, 2, 8], [0, 1, 3], [10, 4, 8], [1, 7, 3], [10, 11, 9, 7], [11, 6, 5, 9], [6, 2, 0, 5], [2, 4, 1, 0], [4, 10, 7, 1]] };
    polyhedra[14] = {
        vertex: [[-0.93465, 0.300459, -0.271185], [-0.838689, -0.260219, -0.516017], [-0.711319, 0.717591, 0.128359], [-0.710334, -0.156922, 0.080946], [-0.599799, 0.556003, -0.725148], [-0.503838, -0.004675, -0.969981], [-0.487004, 0.26021, 0.48049], [-0.460089, -0.750282, -0.512622], [-0.376468, 0.973135, -0.325605], [-0.331735, -0.646985, 0.084342], [-0.254001, 0.831847, 0.530001], [-0.125239, -0.494738, -0.966586], [0.029622, 0.027949, 0.730817], [0.056536, -0.982543, -0.262295], [0.08085, 1.087391, 0.076037], [0.125583, -0.532729, 0.485984], [0.262625, 0.599586, 0.780328], [0.391387, -0.726999, -0.716259], [0.513854, -0.868287, 0.139347], [0.597475, 0.85513, 0.326364], [0.641224, 0.109523, 0.783723], [0.737185, -0.451155, 0.538891], [0.848705, -0.612742, -0.314616], [0.976075, 0.365067, 0.32976], [1.072036, -0.19561, 0.084927]],
        face: [[15, 18, 21], [12, 20, 16], [6, 10, 2], [3, 0, 1], [9, 7, 13], [2, 8, 4, 0], [0, 4, 5, 1], [1, 5, 11, 7], [7, 11, 17, 13], [13, 17, 22, 18], [18, 22, 24, 21], [21, 24, 23, 20], [20, 23, 19, 16], [16, 19, 14, 10], [10, 14, 8, 2], [15, 9, 13, 18], [12, 15, 21, 20], [6, 12, 16, 10], [3, 6, 2, 0], [9, 3, 1, 7], [9, 15, 12, 6, 3], [22, 17, 11, 5, 4, 8, 14, 19, 23, 24]]
    };

    var type: number = options.type && (options.type < 0 || options.type >= polyhedra.length) ? 0 : options.type || 0;
    var size = options.size;
    var sizeX: number = options.sizeX || size || 1;
    var sizeY: number = options.sizeY || size || 1;
    var sizeZ: number = options.sizeZ || size || 1;
    var data: { vertex: number[][], face: number[][], name?: string, category?: string } = options.custom || polyhedra[type];
    var nbfaces = data.face.length;
    var faceUV = options.faceUV || new Array(nbfaces);
    var faceColors = options.faceColors;
    var flat = (options.flat === undefined) ? true : options.flat;
    var sideOrientation = (options.sideOrientation === 0) ? 0 : options.sideOrientation || VertexData.DEFAULTSIDE;

    var positions = new Array<number>();
    var indices = new Array<number>();
    var normals = new Array<number>();
    var uvs = new Array<number>();
    var colors = new Array<number>();
    var index = 0;
    var faceIdx = 0;  // face cursor in the array "indexes"
    var indexes = new Array<number>();
    var i = 0;
    var f = 0;
    var u: number, v: number, ang: number, x: number, y: number, tmp: number;

    // default face colors and UV if undefined
    if (flat) {
        for (f = 0; f < nbfaces; f++) {
            if (faceColors && faceColors[f] === undefined) {
                faceColors[f] = new Color4(1, 1, 1, 1);
            }
            if (faceUV && faceUV[f] === undefined) {
                faceUV[f] = new Vector4(0, 0, 1, 1);
            }
        }
    }

    if (!flat) {

        for (i = 0; i < data.vertex.length; i++) {
            positions.push(data.vertex[i][0] * sizeX, data.vertex[i][1] * sizeY, data.vertex[i][2] * sizeZ);
            uvs.push(0, 0);
        }
        for (f = 0; f < nbfaces; f++) {
            for (i = 0; i < data.face[f].length - 2; i++) {
                indices.push(data.face[f][0], data.face[f][i + 2], data.face[f][i + 1]);
            }
        }

    } else {

        for (f = 0; f < nbfaces; f++) {
            var fl = data.face[f].length;  // number of vertices of the current face
            ang = 2 * Math.PI / fl;
            x = 0.5 * Math.tan(ang / 2);
            y = 0.5;

            // positions, uvs, colors
            for (i = 0; i < fl; i++) {
                // positions
                positions.push(data.vertex[data.face[f][i]][0] * sizeX, data.vertex[data.face[f][i]][1] * sizeY, data.vertex[data.face[f][i]][2] * sizeZ);
                indexes.push(index);
                index++;
                // uvs
                u = faceUV[f].x + (faceUV[f].z - faceUV[f].x) * (0.5 + x);
                v = faceUV[f].y + (faceUV[f].w - faceUV[f].y) * (y - 0.5);
                uvs.push(u, v);
                tmp = x * Math.cos(ang) - y * Math.sin(ang);
                y = x * Math.sin(ang) + y * Math.cos(ang);
                x = tmp;
                // colors
                if (faceColors) {
                    colors.push(faceColors[f].r, faceColors[f].g, faceColors[f].b, faceColors[f].a);
                }
            }

            // indices from indexes
            for (i = 0; i < fl - 2; i++) {
                indices.push(indexes[0 + faceIdx], indexes[i + 2 + faceIdx], indexes[i + 1 + faceIdx]);
            }
            faceIdx += fl;
        }
    }

    VertexData.ComputeNormals(positions, indices, normals);
    VertexData._ComputeSides(sideOrientation, positions, indices, normals, uvs, options.frontUVs, options.backUVs);

    var vertexData = new VertexData();
    vertexData.positions = positions;
    vertexData.indices = indices;
    vertexData.normals = normals;
    vertexData.uvs = uvs;
    if (faceColors && flat) {
        vertexData.colors = colors;
    }
    return vertexData;
};

Mesh.CreatePolyhedron = (name: string, options: { type?: number, size?: number, sizeX?: number, sizeY?: number, sizeZ?: number, custom?: any, faceUV?: Vector4[], faceColors?: Color4[], updatable?: boolean, sideOrientation?: number }, scene: Scene): Mesh => {
    return PolyhedronBuilder.CreatePolyhedron(name, options, scene);
};

/**
 * Class containing static functions to help procedurally build meshes
 */
export class PolyhedronBuilder {
    /**
     * Creates a polyhedron mesh
     * * The parameter `type` (positive integer, max 14, default 0) sets the polyhedron type to build among the 15 embbeded types. Please refer to the type sheet in the tutorial to choose the wanted type
     * * The parameter `size` (positive float, default 1) sets the polygon size
     * * You can overwrite the `size` on each dimension bu using the parameters `sizeX`, `sizeY` or `sizeZ` (positive floats, default to `size` value)
     * * You can build other polyhedron types than the 15 embbeded ones by setting the parameter `custom` (`polyhedronObject`, default null). If you set the parameter `custom`, this overwrittes the parameter `type`
     * * A `polyhedronObject` is a formatted javascript object. You'll find a full file with pre-set polyhedra here : https://github.com/BabylonJS/Extensions/tree/master/Polyhedron
     * * You can set the color and the UV of each side of the polyhedron with the parameters `faceColors` (Color4, default `(1, 1, 1, 1)`) and faceUV (Vector4, default `(0, 0, 1, 1)`)
     * * To understand how to set `faceUV` or `faceColors`, please read this by considering the right number of faces of your polyhedron, instead of only 6 for the box : https://doc.babylonjs.com/how_to/createbox_per_face_textures_and_colors
     * * The parameter `flat` (boolean, default true). If set to false, it gives the polyhedron a single global face, so less vertices and shared normals. In this case, `faceColors` and `faceUV` are ignored
     * * You can also set the mesh side orientation with the values : BABYLON.Mesh.FRONTSIDE (default), BABYLON.Mesh.BACKSIDE or BABYLON.Mesh.DOUBLESIDE
     * * If you create a double-sided mesh, you can choose what parts of the texture image to crop and stick respectively on the front and the back sides with the parameters `frontUVs` and `backUVs` (Vector4). Detail here : https://doc.babylonjs.com/babylon101/discover_basic_elements#side-orientation
     * * The mesh can be set to updatable with the boolean parameter `updatable` (default false) if its internal geometry is supposed to change once created
     * @param name defines the name of the mesh
     * @param options defines the options used to create the mesh
     * @param scene defines the hosting scene
     * @returns the polyhedron mesh
     * @see https://doc.babylonjs.com/how_to/polyhedra_shapes
     */
    public static CreatePolyhedron(name: string, options: { type?: number, size?: number, sizeX?: number, sizeY?: number, sizeZ?: number, custom?: any, faceUV?: Vector4[], faceColors?: Color4[], flat?: boolean, updatable?: boolean, sideOrientation?: number, frontUVs?: Vector4, backUVs?: Vector4 }, scene: Nullable<Scene> = null): Mesh {
        var polyhedron = new Mesh(name, scene);

        options.sideOrientation = Mesh._GetDefaultSideOrientation(options.sideOrientation);
        polyhedron._originalBuilderSideOrientation = options.sideOrientation;

        var vertexData = VertexData.CreatePolyhedron(options);

        vertexData.applyToMesh(polyhedron, options.updatable);

        return polyhedron;
    }
}