/** * @author Eric Haines / http://erichaines.com/ * * Tessellates the famous Utah teapot database by Martin Newell into triangles. * * THREE.TeapotBufferGeometry = function ( size, segments, bottom, lid, body, fitLid, blinn ) * * defaults: size = 50, segments = 10, bottom = true, lid = true, body = true, * fitLid = false, blinn = true * * size is a relative scale: I've scaled the teapot to fit vertically between -1 and 1. * Think of it as a "radius". * segments - number of line segments to subdivide each patch edge; * 1 is possible but gives degenerates, so two is the real minimum. * bottom - boolean, if true (default) then the bottom patches are added. Some consider * adding the bottom heresy, so set this to "false" to adhere to the One True Way. * lid - to remove the lid and look inside, set to true. * body - to remove the body and leave the lid, set this and "bottom" to false. * fitLid - the lid is a tad small in the original. This stretches it a bit so you can't * see the teapot's insides through the gap. * blinn - Jim Blinn scaled the original data vertically by dividing by about 1.3 to look * nicer. If you want to see the original teapot, similar to the real-world model, set * this to false. True by default. * See http://en.wikipedia.org/wiki/File:Original_Utah_Teapot.jpg for the original * real-world teapot (from http://en.wikipedia.org/wiki/Utah_teapot). * * Note that the bottom (the last four patches) is not flat - blame Frank Crow, not me. * * The teapot should normally be rendered as a double sided object, since for some * patches both sides can be seen, e.g., the gap around the lid and inside the spout. * * Segments 'n' determines the number of triangles output. * Total triangles = 32*2*n*n - 8*n [degenerates at the top and bottom cusps are deleted] * * size_factor # triangles * 1 56 * 2 240 * 3 552 * 4 992 * * 10 6320 * 20 25440 * 30 57360 * * Code converted from my ancient SPD software, http://tog.acm.org/resources/SPD/ * Created for the Udacity course "Interactive Rendering", http://bit.ly/ericity * Lesson: https://www.udacity.com/course/viewer#!/c-cs291/l-68866048/m-106482448 * YouTube video on teapot history: https://www.youtube.com/watch?v=DxMfblPzFNc * * See https://en.wikipedia.org/wiki/Utah_teapot for the history of the teapot * */ /*global THREE */ THREE.TeapotBufferGeometry = function ( size, segments, bottom, lid, body, fitLid, blinn ) { // 32 * 4 * 4 Bezier spline patches var teapotPatches = [ /*rim*/ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 3, 16, 17, 18, 7, 19, 20, 21, 11, 22, 23, 24, 15, 25, 26, 27, 18, 28, 29, 30, 21, 31, 32, 33, 24, 34, 35, 36, 27, 37, 38, 39, 30, 40, 41, 0, 33, 42, 43, 4, 36, 44, 45, 8, 39, 46, 47, 12, /*body*/ 12, 13, 14, 15, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 15, 25, 26, 27, 51, 60, 61, 62, 55, 63, 64, 65, 59, 66, 67, 68, 27, 37, 38, 39, 62, 69, 70, 71, 65, 72, 73, 74, 68, 75, 76, 77, 39, 46, 47, 12, 71, 78, 79, 48, 74, 80, 81, 52, 77, 82, 83, 56, 56, 57, 58, 59, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 59, 66, 67, 68, 87, 96, 97, 98, 91, 99, 100, 101, 95, 102, 103, 104, 68, 75, 76, 77, 98, 105, 106, 107, 101, 108, 109, 110, 104, 111, 112, 113, 77, 82, 83, 56, 107, 114, 115, 84, 110, 116, 117, 88, 113, 118, 119, 92, /*handle*/ 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 123, 136, 137, 120, 127, 138, 139, 124, 131, 140, 141, 128, 135, 142, 143, 132, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151, 68, 152, 153, 154, 135, 142, 143, 132, 147, 155, 156, 144, 151, 157, 158, 148, 154, 159, 160, 68, /*spout*/ 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 164, 177, 178, 161, 168, 179, 180, 165, 172, 181, 182, 169, 176, 183, 184, 173, 173, 174, 175, 176, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 176, 183, 184, 173, 188, 197, 198, 185, 192, 199, 200, 189, 196, 201, 202, 193, /*lid*/ 203, 203, 203, 203, 204, 205, 206, 207, 208, 208, 208, 208, 209, 210, 211, 212, 203, 203, 203, 203, 207, 213, 214, 215, 208, 208, 208, 208, 212, 216, 217, 218, 203, 203, 203, 203, 215, 219, 220, 221, 208, 208, 208, 208, 218, 222, 223, 224, 203, 203, 203, 203, 221, 225, 226, 204, 208, 208, 208, 208, 224, 227, 228, 209, 209, 210, 211, 212, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 212, 216, 217, 218, 232, 241, 242, 243, 236, 244, 245, 246, 240, 247, 248, 249, 218, 222, 223, 224, 243, 250, 251, 252, 246, 253, 254, 255, 249, 256, 257, 258, 224, 227, 228, 209, 252, 259, 260, 229, 255, 261, 262, 233, 258, 263, 264, 237, /*bottom*/ 265, 265, 265, 265, 266, 267, 268, 269, 270, 271, 272, 273, 92, 119, 118, 113, 265, 265, 265, 265, 269, 274, 275, 276, 273, 277, 278, 279, 113, 112, 111, 104, 265, 265, 265, 265, 276, 280, 281, 282, 279, 283, 284, 285, 104, 103, 102, 95, 265, 265, 265, 265, 282, 286, 287, 266, 285, 288, 289, 270, 95, 94, 93, 92 ]; var teapotVertices = [ 1.4, 0, 2.4, 1.4, - 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0.798, 0, 0.84, - 1.5, 0.075, 1.5, - 0.84, 0.075 ]; THREE.BufferGeometry.call( this ); size = size || 50; // number of segments per patch segments = segments !== undefined ? Math.max( 2, Math.floor( segments ) || 10 ) : 10; // which parts should be visible bottom = bottom === undefined ? true : bottom; lid = lid === undefined ? true : lid; body = body === undefined ? true : body; // Should the lid be snug? It's not traditional, but we make it snug by default fitLid = fitLid === undefined ? true : fitLid; // Jim Blinn scaled the teapot down in size by about 1.3 for // some rendering tests. He liked the new proportions that he kept // the data in this form. The model was distributed with these new // proportions and became the norm. Trivia: comparing images of the // real teapot and the computer model, the ratio for the bowl of the // real teapot is more like 1.25, but since 1.3 is the traditional // value given, we use it here. var blinnScale = 1.3; blinn = blinn === undefined ? true : blinn; // scale the size to be the real scaling factor var maxHeight = 3.15 * ( blinn ? 1 : blinnScale ); var maxHeight2 = maxHeight / 2; var trueSize = size / maxHeight2; // Number of elements depends on what is needed. Subtract degenerate // triangles at tip of bottom and lid out in advance. var numTriangles = bottom ? ( 8 * segments - 4 ) * segments : 0; numTriangles += lid ? ( 16 * segments - 4 ) * segments : 0; numTriangles += body ? 40 * segments * segments : 0; var indices = new Uint32Array( numTriangles * 3 ); var numVertices = bottom ? 4 : 0; numVertices += lid ? 8 : 0; numVertices += body ? 20 : 0; numVertices *= ( segments + 1 ) * ( segments + 1 ); var vertices = new Float32Array( numVertices * 3 ); var normals = new Float32Array( numVertices * 3 ); var uvs = new Float32Array( numVertices * 2 ); // Bezier form var ms = new THREE.Matrix4(); ms.set( - 1.0, 3.0, - 3.0, 1.0, 3.0, - 6.0, 3.0, 0.0, - 3.0, 3.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0 ); var g = []; var i, r, c; var sp = []; var tp = []; var dsp = []; var dtp = []; // M * G * M matrix, sort of see // http://www.cs.helsinki.fi/group/goa/mallinnus/curves/surfaces.html var mgm = []; var vert = []; var sdir = []; var tdir = []; var norm = new THREE.Vector3(); var tcoord; var sstep, tstep; var vertPerRow; var s, t, sval, tval, p; var dsval = 0; var dtval = 0; var normOut = new THREE.Vector3(); var v1, v2, v3, v4; var gmx = new THREE.Matrix4(); var tmtx = new THREE.Matrix4(); var vsp = new THREE.Vector4(); var vtp = new THREE.Vector4(); var vdsp = new THREE.Vector4(); var vdtp = new THREE.Vector4(); var vsdir = new THREE.Vector3(); var vtdir = new THREE.Vector3(); var mst = ms.clone(); mst.transpose(); // internal function: test if triangle has any matching vertices; // if so, don't save triangle, since it won't display anything. var notDegenerate = function ( vtx1, vtx2, vtx3 ) { // if any vertex matches, return false return ! ( ( ( vertices[ vtx1 * 3 ] === vertices[ vtx2 * 3 ] ) && ( vertices[ vtx1 * 3 + 1 ] === vertices[ vtx2 * 3 + 1 ] ) && ( vertices[ vtx1 * 3 + 2 ] === vertices[ vtx2 * 3 + 2 ] ) ) || ( ( vertices[ vtx1 * 3 ] === vertices[ vtx3 * 3 ] ) && ( vertices[ vtx1 * 3 + 1 ] === vertices[ vtx3 * 3 + 1 ] ) && ( vertices[ vtx1 * 3 + 2 ] === vertices[ vtx3 * 3 + 2 ] ) ) || ( ( vertices[ vtx2 * 3 ] === vertices[ vtx3 * 3 ] ) && ( vertices[ vtx2 * 3 + 1 ] === vertices[ vtx3 * 3 + 1 ] ) && ( vertices[ vtx2 * 3 + 2 ] === vertices[ vtx3 * 3 + 2 ] ) ) ); }; for ( i = 0; i < 3; i ++ ) { mgm[ i ] = new THREE.Matrix4(); } var minPatches = body ? 0 : 20; var maxPatches = bottom ? 32 : 28; vertPerRow = segments + 1; var surfCount = 0; var vertCount = 0; var normCount = 0; var uvCount = 0; var indexCount = 0; for ( var surf = minPatches; surf < maxPatches; surf ++ ) { // lid is in the middle of the data, patches 20-27, // so ignore it for this part of the loop if the lid is not desired if ( lid || ( surf < 20 || surf >= 28 ) ) { // get M * G * M matrix for x,y,z for ( i = 0; i < 3; i ++ ) { // get control patches for ( r = 0; r < 4; r ++ ) { for ( c = 0; c < 4; c ++ ) { // transposed g[ c * 4 + r ] = teapotVertices[ teapotPatches[ surf * 16 + r * 4 + c ] * 3 + i ]; // is the lid to be made larger, and is this a point on the lid // that is X or Y? if ( fitLid && ( surf >= 20 && surf < 28 ) && ( i !== 2 ) ) { // increase XY size by 7.7%, found empirically. I don't // increase Z so that the teapot will continue to fit in the // space -1 to 1 for Y (Y is up for the final model). g[ c * 4 + r ] *= 1.077; } // Blinn "fixed" the teapot by dividing Z by blinnScale, and that's the // data we now use. The original teapot is taller. Fix it: if ( ! blinn && ( i === 2 ) ) { g[ c * 4 + r ] *= blinnScale; } } } gmx.set( g[ 0 ], g[ 1 ], g[ 2 ], g[ 3 ], g[ 4 ], g[ 5 ], g[ 6 ], g[ 7 ], g[ 8 ], g[ 9 ], g[ 10 ], g[ 11 ], g[ 12 ], g[ 13 ], g[ 14 ], g[ 15 ] ); tmtx.multiplyMatrices( gmx, ms ); mgm[ i ].multiplyMatrices( mst, tmtx ); } // step along, get points, and output for ( sstep = 0; sstep <= segments; sstep ++ ) { s = sstep / segments; for ( tstep = 0; tstep <= segments; tstep ++ ) { t = tstep / segments; // point from basis // get power vectors and their derivatives for ( p = 4, sval = tval = 1.0; p --; ) { sp[ p ] = sval; tp[ p ] = tval; sval *= s; tval *= t; if ( p === 3 ) { dsp[ p ] = dtp[ p ] = 0.0; dsval = dtval = 1.0; } else { dsp[ p ] = dsval * ( 3 - p ); dtp[ p ] = dtval * ( 3 - p ); dsval *= s; dtval *= t; } } vsp.fromArray( sp ); vtp.fromArray( tp ); vdsp.fromArray( dsp ); vdtp.fromArray( dtp ); // do for x,y,z for ( i = 0; i < 3; i ++ ) { // multiply power vectors times matrix to get value tcoord = vsp.clone(); tcoord.applyMatrix4( mgm[ i ] ); vert[ i ] = tcoord.dot( vtp ); // get s and t tangent vectors tcoord = vdsp.clone(); tcoord.applyMatrix4( mgm[ i ] ); sdir[ i ] = tcoord.dot( vtp ); tcoord = vsp.clone(); tcoord.applyMatrix4( mgm[ i ] ); tdir[ i ] = tcoord.dot( vdtp ); } // find normal vsdir.fromArray( sdir ); vtdir.fromArray( tdir ); norm.crossVectors( vtdir, vsdir ); norm.normalize(); // if X and Z length is 0, at the cusp, so point the normal up or down, depending on patch number if ( vert[ 0 ] === 0 && vert[ 1 ] === 0 ) { // if above the middle of the teapot, normal points up, else down normOut.set( 0, vert[ 2 ] > maxHeight2 ? 1 : - 1, 0 ); } else { // standard output: rotate on X axis normOut.set( norm.x, norm.z, - norm.y ); } // store it all vertices[ vertCount ++ ] = trueSize * vert[ 0 ]; vertices[ vertCount ++ ] = trueSize * ( vert[ 2 ] - maxHeight2 ); vertices[ vertCount ++ ] = - trueSize * vert[ 1 ]; normals[ normCount ++ ] = normOut.x; normals[ normCount ++ ] = normOut.y; normals[ normCount ++ ] = normOut.z; uvs[ uvCount ++ ] = 1 - t; uvs[ uvCount ++ ] = 1 - s; } } // save the faces for ( sstep = 0; sstep < segments; sstep ++ ) { for ( tstep = 0; tstep < segments; tstep ++ ) { v1 = surfCount * vertPerRow * vertPerRow + sstep * vertPerRow + tstep; v2 = v1 + 1; v3 = v2 + vertPerRow; v4 = v1 + vertPerRow; // Normals and UVs cannot be shared. Without clone(), you can see the consequences // of sharing if you call geometry.applyMatrix( matrix ). if ( notDegenerate( v1, v2, v3 ) ) { indices[ indexCount ++ ] = v1; indices[ indexCount ++ ] = v2; indices[ indexCount ++ ] = v3; } if ( notDegenerate( v1, v3, v4 ) ) { indices[ indexCount ++ ] = v1; indices[ indexCount ++ ] = v3; indices[ indexCount ++ ] = v4; } } } // increment only if a surface was used surfCount ++; } } this.setIndex( new THREE.BufferAttribute( indices, 1 ) ); this.addAttribute( 'position', new THREE.BufferAttribute( vertices, 3 ) ); this.addAttribute( 'normal', new THREE.BufferAttribute( normals, 3 ) ); this.addAttribute( 'uv', new THREE.BufferAttribute( uvs, 2 ) ); this.computeBoundingSphere(); }; THREE.TeapotBufferGeometry.prototype = Object.create( THREE.BufferGeometry.prototype ); THREE.TeapotBufferGeometry.prototype.constructor = THREE.TeapotBufferGeometry;