/** * @author Eric Haines / http://erichaines.com/ * * Tessellates the famous Utah teapot database by Martin Newell into triangles. * * THREE.TeapotGeometry = 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.TeapotGeometry = function ( size, segments, bottom, lid, body, fitLid, blinn ) { "use strict"; // 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,-0.784,2.4, 0.784,-1.4,2.4, 0,-1.4,2.4, 1.3375,0,2.53125, 1.3375,-0.749,2.53125, 0.749,-1.3375,2.53125, 0,-1.3375,2.53125, 1.4375,0,2.53125, 1.4375,-0.805,2.53125, 0.805,-1.4375,2.53125, 0,-1.4375,2.53125, 1.5,0,2.4, 1.5,-0.84,2.4, 0.84,-1.5,2.4, 0,-1.5,2.4, -0.784,-1.4,2.4, -1.4,-0.784,2.4, -1.4,0,2.4, -0.749,-1.3375,2.53125, -1.3375,-0.749,2.53125, -1.3375,0,2.53125, -0.805,-1.4375,2.53125, -1.4375,-0.805,2.53125, -1.4375,0,2.53125, -0.84,-1.5,2.4, -1.5,-0.84,2.4, -1.5,0,2.4, -1.4,0.784,2.4, -0.784,1.4,2.4, 0,1.4,2.4, -1.3375,0.749,2.53125, -0.749,1.3375,2.53125, 0,1.3375,2.53125, -1.4375,0.805,2.53125, -0.805,1.4375,2.53125, 0,1.4375,2.53125, -1.5,0.84,2.4, -0.84,1.5,2.4, 0,1.5,2.4, 0.784,1.4,2.4, 1.4,0.784,2.4, 0.749,1.3375,2.53125, 1.3375,0.749,2.53125, 0.805,1.4375,2.53125, 1.4375,0.805,2.53125, 0.84,1.5,2.4, 1.5,0.84,2.4, 1.75,0,1.875, 1.75,-0.98,1.875, 0.98,-1.75,1.875, 0,-1.75,1.875, 2,0,1.35, 2,-1.12,1.35, 1.12,-2,1.35, 0,-2,1.35, 2,0,0.9, 2,-1.12,0.9, 1.12,-2,0.9, 0,-2,0.9, -0.98,-1.75,1.875, -1.75,-0.98,1.875, -1.75,0,1.875, -1.12,-2,1.35, -2,-1.12,1.35, -2,0,1.35, -1.12,-2,0.9, -2,-1.12,0.9, -2,0,0.9, -1.75,0.98,1.875, -0.98,1.75,1.875, 0,1.75,1.875, -2,1.12,1.35, -1.12,2,1.35, 0,2,1.35, -2,1.12,0.9, -1.12,2,0.9, 0,2,0.9, 0.98,1.75,1.875, 1.75,0.98,1.875, 1.12,2,1.35, 2,1.12,1.35, 1.12,2,0.9, 2,1.12,0.9, 2,0,0.45, 2,-1.12,0.45, 1.12,-2,0.45, 0,-2,0.45, 1.5,0,0.225, 1.5,-0.84,0.225, 0.84,-1.5,0.225, 0,-1.5,0.225, 1.5,0,0.15, 1.5,-0.84,0.15, 0.84,-1.5,0.15, 0,-1.5,0.15, -1.12,-2,0.45, -2,-1.12,0.45, -2,0,0.45, -0.84,-1.5,0.225, -1.5,-0.84,0.225, -1.5,0,0.225, -0.84,-1.5,0.15, -1.5,-0.84,0.15, -1.5,0,0.15, -2,1.12,0.45, -1.12,2,0.45, 0,2,0.45, -1.5,0.84,0.225, -0.84,1.5,0.225, 0,1.5,0.225, -1.5,0.84,0.15, -0.84,1.5,0.15, 0,1.5,0.15, 1.12,2,0.45, 2,1.12,0.45, 0.84,1.5,0.225, 1.5,0.84,0.225, 0.84,1.5,0.15, 1.5,0.84,0.15, -1.6,0,2.025, -1.6,-0.3,2.025, -1.5,-0.3,2.25, -1.5,0,2.25, -2.3,0,2.025, -2.3,-0.3,2.025, -2.5,-0.3,2.25, -2.5,0,2.25, -2.7,0,2.025, -2.7,-0.3,2.025, -3,-0.3,2.25, -3,0,2.25, -2.7,0,1.8, -2.7,-0.3,1.8, -3,-0.3,1.8, -3,0,1.8, -1.5,0.3,2.25, -1.6,0.3,2.025, -2.5,0.3,2.25, -2.3,0.3,2.025, -3,0.3,2.25, -2.7,0.3,2.025, -3,0.3,1.8, -2.7,0.3,1.8, -2.7,0,1.575, -2.7,-0.3,1.575, -3,-0.3,1.35, -3,0,1.35, -2.5,0,1.125, -2.5,-0.3,1.125, -2.65,-0.3,0.9375, -2.65,0,0.9375, -2,-0.3,0.9, -1.9,-0.3,0.6, -1.9,0,0.6, -3,0.3,1.35, -2.7,0.3,1.575, -2.65,0.3,0.9375, -2.5,0.3,1.125, -1.9,0.3,0.6, -2,0.3,0.9, 1.7,0,1.425, 1.7,-0.66,1.425, 1.7,-0.66,0.6, 1.7,0,0.6, 2.6,0,1.425, 2.6,-0.66,1.425, 3.1,-0.66,0.825, 3.1,0,0.825, 2.3,0,2.1, 2.3,-0.25,2.1, 2.4,-0.25,2.025, 2.4,0,2.025, 2.7,0,2.4, 2.7,-0.25,2.4, 3.3,-0.25,2.4, 3.3,0,2.4, 1.7,0.66,0.6, 1.7,0.66,1.425, 3.1,0.66,0.825, 2.6,0.66,1.425, 2.4,0.25,2.025, 2.3,0.25,2.1, 3.3,0.25,2.4, 2.7,0.25,2.4, 2.8,0,2.475, 2.8,-0.25,2.475, 3.525,-0.25,2.49375, 3.525,0,2.49375, 2.9,0,2.475, 2.9,-0.15,2.475, 3.45,-0.15,2.5125, 3.45,0,2.5125, 2.8,0,2.4, 2.8,-0.15,2.4, 3.2,-0.15,2.4, 3.2,0,2.4, 3.525,0.25,2.49375, 2.8,0.25,2.475, 3.45,0.15,2.5125, 2.9,0.15,2.475, 3.2,0.15,2.4, 2.8,0.15,2.4, 0,0,3.15, 0.8,0,3.15, 0.8,-0.45,3.15, 0.45,-0.8,3.15, 0,-0.8,3.15, 0,0,2.85, 0.2,0,2.7, 0.2,-0.112,2.7, 0.112,-0.2,2.7, 0,-0.2,2.7, -0.45,-0.8,3.15, -0.8,-0.45,3.15, -0.8,0,3.15, -0.112,-0.2,2.7, -0.2,-0.112,2.7, -0.2,0,2.7, -0.8,0.45,3.15, -0.45,0.8,3.15, 0,0.8,3.15, -0.2,0.112,2.7, -0.112,0.2,2.7, 0,0.2,2.7, 0.45,0.8,3.15, 0.8,0.45,3.15, 0.112,0.2,2.7, 0.2,0.112,2.7, 0.4,0,2.55, 0.4,-0.224,2.55, 0.224,-0.4,2.55, 0,-0.4,2.55, 1.3,0,2.55, 1.3,-0.728,2.55, 0.728,-1.3,2.55, 0,-1.3,2.55, 1.3,0,2.4, 1.3,-0.728,2.4, 0.728,-1.3,2.4, 0,-1.3,2.4, -0.224,-0.4,2.55, -0.4,-0.224,2.55, -0.4,0,2.55, -0.728,-1.3,2.55, -1.3,-0.728,2.55, -1.3,0,2.55, -0.728,-1.3,2.4, -1.3,-0.728,2.4, -1.3,0,2.4, -0.4,0.224,2.55, -0.224,0.4,2.55, 0,0.4,2.55, -1.3,0.728,2.55, -0.728,1.3,2.55, 0,1.3,2.55, -1.3,0.728,2.4, -0.728,1.3,2.4, 0,1.3,2.4, 0.224,0.4,2.55, 0.4,0.224,2.55, 0.728,1.3,2.55, 1.3,0.728,2.55, 0.728,1.3,2.4, 1.3,0.728,2.4, 0,0,0, 1.425,0,0, 1.425,0.798,0, 0.798,1.425,0, 0,1.425,0, 1.5,0,0.075, 1.5,0.84,0.075, 0.84,1.5,0.075, 0,1.5,0.075, -0.798,1.425,0, -1.425,0.798,0, -1.425,0,0, -0.84,1.5,0.075, -1.5,0.84,0.075, -1.5,0,0.075, -1.425,-0.798,0, -0.798,-1.425,0, 0,-1.425,0, -1.5,-0.84,0.075, -0.84,-1.5,0.075, 0,-1.5,0.075, 0.798,-1.425,0, 1.425,-0.798,0, 0.84,-1.5,0.075, 1.5,-0.84,0.075 ] ; THREE.Geometry.call( this ); this.type = 'TeapotGeometry'; this.size = size || 50; // number of segments per patch this.segments = Math.max( 2, Math.floor( segments ) || 10 ); // which parts should be visible this.bottom = bottom === undefined ? true : bottom; this.lid = lid === undefined ? true : lid; this.body = body === undefined ? true : body; // Should the lid be snug? It's not traditional, so off by default this.fitLid = fitLid === undefined ? false : 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; this.blinn = blinn === undefined ? true : blinn; // scale the size to be the real scaling factor var maxHeight = 3.15 * (this.blinn ? 1 : blinnScale); var maxHeight2 = maxHeight / 2; var trueSize = this.size / maxHeight2; var normals = [], uvs = []; // 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 gmx, tmtx; var vertPerRow, eps; var s, t, sval, tval, p, dsval, dtval; var vsp, vtp, vdsp, vdtp; var vsdir, vtdir, normOut, vertOut; var v1, v2, v3, v4; 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 ( vtx1.equals( vtx2 ) ) { return false; } if ( vtx1.equals( vtx3 ) ) { return false; } if ( vtx2.equals( vtx3 ) ) { return false; } return true; }; for ( i = 0; i < 3; i++ ) { mgm[i] = new THREE.Matrix4(); } var minPatches = this.body ? 0 : 20; var maxPatches = this.bottom ? 32 : 28; vertPerRow = (this.segments+1); eps = 0.0000001; var surfCount = 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 ( this.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 ( this.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 ( !this.blinn && (i === 2) ) { g[c*4+r] *= blinnScale; } } } gmx = new THREE.Matrix4(); 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 = new THREE.Matrix4(); tmtx.multiplyMatrices( gmx, ms ); mgm[i].multiplyMatrices( mst, tmtx ); } // step along, get points, and output for ( sstep = 0 ; sstep <= this.segments ; sstep++ ) { s = sstep / this.segments; for ( tstep = 0 ; tstep <= this.segments ; tstep++ ) { t = tstep / this.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 = new THREE.Vector4( sp[0], sp[1], sp[2], sp[3] ); vtp = new THREE.Vector4( tp[0], tp[1], tp[2], tp[3] ); vdsp = new THREE.Vector4( dsp[0], dsp[1], dsp[2], dsp[3] ); vdtp = new THREE.Vector4( dtp[0], dtp[1], dtp[2], dtp[3] ); // 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 = new THREE.Vector3( sdir[0], sdir[1], sdir[2] ); vtdir = new THREE.Vector3( tdir[0], tdir[1], tdir[2] ); norm.crossVectors( vtdir, vsdir ); norm.normalize(); // rotate on X axis normOut = new THREE.Vector3( norm.x, norm.z, -norm.y ); // 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 ); } normals.push( normOut ); uvs.push( new THREE.Vector2( 1-t, 1-s ) ); // three.js uses Y up, the code makes Z up, so time for a trick: // rotate on X axis, and offset down on Y axis so object ranges from -1 to 1 in Y vertOut = new THREE.Vector3( trueSize*vert[0], trueSize*(vert[2] - maxHeight2), -trueSize*vert[1] ); this.vertices.push( vertOut ); } } // save the faces for ( sstep = 0 ; sstep < this.segments ; sstep++ ) { for ( tstep = 0 ; tstep < this.segments ; tstep++ ) { v1 = surfCount * vertPerRow * vertPerRow + sstep * vertPerRow + tstep; v2 = v1 + 1; v3 = v2 + vertPerRow; v4 = v1 + vertPerRow; if ( notDegenerate ( this.vertices[v1], this.vertices[v2], this.vertices[v3] ) ) { this.faces.push( new THREE.Face3( v1, v2, v3, [ normals[v1], normals[v2], normals[v3] ] ) ); this.faceVertexUvs[ 0 ].push( [ uvs[v1], uvs[v2], uvs[v3] ] ); } if ( notDegenerate ( this.vertices[v1], this.vertices[v3], this.vertices[v4] ) ) { this.faces.push( new THREE.Face3( v1, v3, v4, [ normals[v1], normals[v3], normals[v4] ] ) ); this.faceVertexUvs[ 0 ].push( [ uvs[v1], uvs[v3], uvs[v4] ] ); } } } // increment only if a surface was used surfCount++; } } this.computeFaceNormals(); }; THREE.TeapotGeometry.prototype = Object.create( THREE.Geometry.prototype ); THREE.TeapotGeometry.prototype.constructor = THREE.TeapotGeometry;