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// import {
// BufferAttribute,
// BufferGeometry,
// Matrix4,
// Vector3,
// Vector4
// } from '../../../build/three.module.js';
/**
* Tessellates the famous Utah teapot database by Martin Newell into triangles.
*
* Parameters: 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
*
*/
var TeapotGeometry = 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, - 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
];
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;
<