/**
* @file
*
* Summary.
* <p>Utah teapot.</p>
*
* In the early years of 3D modeling and rendering, {@link https://en.wikipedia.org/wiki/Martin_Newell_(computer_scientist) Martin Newel}
* created a computer-generated three dimensional teapot.
* The original {@link https://www.computerhistory.org/revolution/computer-graphics-music-and-art/15/206/556 "Utah teapot"}
* was actually taller than the famed teapot we see in so many places today.
* Legend has it that during a demo, using a system with non-square pixels, {@link https://en.wikipedia.org/wiki/Jim_Blinn Jim Blinn}
* scaled the teapot rather than scaling the image.
* As this dataset became more widely distributed than the original, his edit changed the aspect of teapots in 3D software for years to come.
*
* @author Martin Newell
* @since 07/01/2023
*
* @see <a href="/cwdc/13-webgl/lib/TeapotGeometry.js">source</a>
* @see https://en.wikipedia.org/wiki/Utah_teapot
* @see http://www.holmes3d.net/graphics/teapot/
* @see <img src="https://upload.wikimedia.org/wikipedia/commons/a/af/Original_Utah_Teapot_-_Computer_History_Museums.jpg" width="512">
*/
import {
BufferAttribute,
BufferGeometry,
Matrix4,
Vector3,
Vector4,
} from "/cwdc/13-webgl/lib/three.module.js";
/**
* <p>Tessellates the famous Utah teapot database, by Martin Newell, into triangles.</p>
* <pre>
* Parameters:
* size = 50,
* segments = 10,
* bottom = true,
* lid = true,
* body = true,
* fitLid = false,
* blinn = true
* </pre>
*
* Go to {@link https://en.wikipedia.org/wiki/Utah_teapot Wikipedia} for the original real-world teapot.
*
* <p>Note that the bottom (the last four patches) is not flat - blame Frank Crow, not me.</p>
*
* <p>The teapot should normally be rendered as a double sided object, since for some
* patches both sides can be seen, <br>
* e.g., the gap around the lid and inside the spout.</p>
*
* <p>Segments 'n' determines the number of triangles output.</p>
* [degenerates at the top and bottom cusps are deleted]
* <pre>
* Total triangles = 32*2*n*n - 8*n
*
* size_factor # triangles
* 1 56
* 2 240
* 3 552
* 4 992
*
* 10 6320
* 20 25440
* 30 57360
* </pre>
*
* Code converted from my ancient {@link https://tog.acm.org/resources/SPD/ SPD software}.<br>
* Created for the Udacity course {@link https://bit.ly/ericity "Interactive Rendering"}.<br>
* YouTube video on teapot history: {@link https://www.youtube.com/watch?v=DxMfblPzFNc}
*
* @param {Number} size is a relative scale: I've scaled the teapot to fit vertically between -1 and 1. <br>
* Think of it as a "radius".
* @param {Number} segments - number of line segments to subdivide each patch edge; <br>
* 1 is possible but gives degenerates, so two is the real minimum.
* @param {Boolean} bottom - boolean, if true (default) then the bottom patches are added. <br>
* Some consider adding the bottom heresy, so set this to "false" to adhere to the One True Way.
* @param {Boolean} lid - to remove the lid and look inside, set to true.
* @param {Boolean} body - to remove the body and leave the lid, set this and "bottom" to false.
* @param {Boolean} fitLid - the lid is a tad small in the original. <br>
* This stretches it a bit, so you can't see the teapot's insides through the gap.
* @param {Boolean} blinn - Jim Blinn scaled the original data vertically by dividing by about 1.3 to look nicer. <br>
* If you want to see the original teapot, similar to the real-world model, set
* this to false. <br>
* True by default.
*/
class TeapotGeometry extends BufferGeometry {
constructor(
size = 50,
segments = 10,
bottom = true,
lid = true,
body = true,
fitLid = true,
blinn = true,
) {
// 32 * 4 * 4 Bezier spline patches
// prettier-ignore
const 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
];
// prettier-ignore
const 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
];
super();
// number of segments per patch
segments = Math.max(2, Math.floor(segments));
// 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.
const blinnScale = 1.3;
// scale the size to be the real scaling factor
const maxHeight = 3.15 * (blinn ? 1 : blinnScale);
const maxHeight2 = maxHeight / 2;
const trueSize = size / maxHeight2;
// Number of elements depends on what is needed. Subtract degenerate
// triangles at tip of bottom and lid out in advance.
let numTriangles = bottom ? (8 * segments - 4) * segments : 0;
numTriangles += lid ? (16 * segments - 4) * segments : 0;
numTriangles += body ? 40 * segments * segments : 0;
const indices = new Uint32Array(numTriangles * 3);
let numVertices = bottom ? 4 : 0;
numVertices += lid ? 8 : 0;
numVertices += body ? 20 : 0;
numVertices *= (segments + 1) * (segments + 1);
const vertices = new Float32Array(numVertices * 3);
const normals = new Float32Array(numVertices * 3);
const uvs = new Float32Array(numVertices * 2);
// Bezier form
const ms = new Matrix4();
// prettier-ignore
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
);
const g = [];
const sp = [];
const tp = [];
const dsp = [];
const dtp = [];
// M * G * M matrix, sort of see
// http://www.cs.helsinki.fi/group/goa/mallinnus/curves/surfaces.html
const mgm = [];
const vert = [];
const sdir = [];
const tdir = [];
const norm = new Vector3();
let tcoord;
let sval;
let tval;
let p;
let dsval = 0;
let dtval = 0;
const normOut = new Vector3();
const gmx = new Matrix4();
const tmtx = new Matrix4();
const vsp = new Vector4();
const vtp = new Vector4();
const vdsp = new Vector4();
const vdtp = new Vector4();
const vsdir = new Vector3();
const vtdir = new Vector3();
const 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.
const notDegenerate = (
vtx1,
vtx2,
vtx3, // if any vertex matches, return false
) =>
!(
(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 (let i = 0; i < 3; i++) {
mgm[i] = new Matrix4();
}
const minPatches = body ? 0 : 20;
const maxPatches = bottom ? 32 : 28;
const vertPerRow = segments + 1;
let surfCount = 0;
let vertCount = 0;
let normCount = 0;
let uvCount = 0;
let indexCount = 0;
for (let 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 (let i = 0; i < 3; i++) {
// get control patches
for (let r = 0; r < 4; r++) {
for (let 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;
}
}
}
// prettier-ignore
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 (let sstep = 0; sstep <= segments; sstep++) {
const s = sstep / segments;
for (let tstep = 0; tstep <= segments; tstep++) {
const 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 (let 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 (let sstep = 0; sstep < segments; sstep++) {
for (let tstep = 0; tstep < segments; tstep++) {
const v1 =
surfCount * vertPerRow * vertPerRow + sstep * vertPerRow + tstep;
const v2 = v1 + 1;
const v3 = v2 + vertPerRow;
const v4 = v1 + vertPerRow;
// Normals and UVs cannot be shared. Without clone(), you can see the consequences
// of sharing if you call geometry.applyMatrix4( 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++;
}
}
/**
* @name TeapotGeometry.BufferAttribute
* @property {Object} attributes TeaPot vertex attributes.
* @property {Float32Array} attributes.position vertex coordinates.
* @property {Float32Array} attributes.normal vertex normals.
* @property {Float32Array} attributes.uv texture coordinates.
* @property {Float32Array} index face index array.
* @see {@link https://threejs.org/docs/#api/en/core/BufferAttribute BufferAttribute}
*/
this.setIndex(new BufferAttribute(indices, 1));
this.setAttribute("position", new BufferAttribute(vertices, 3));
this.setAttribute("normal", new BufferAttribute(normals, 3));
this.setAttribute("uv", new BufferAttribute(uvs, 2));
this.computeBoundingSphere();
}
}
export { TeapotGeometry };