three.js/examples/jsm/geometries/TeapotGeometry.js

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
	];

	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 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 Vector3();

	var tcoord;

	var sstep, tstep;
	var vertPerRow;

	var s, t, sval, tval, p;
	var dsval = 0;
	var dtval = 0;

	var normOut = new Vector3();
	var v1, v2, v3, v4;

	var gmx = new Matrix4();
	var tmtx = new Matrix4();

	var vsp = new Vector4();
	var vtp = new Vector4();
	var vdsp = new Vector4();
	var vdtp = new Vector4();

	var vsdir = new Vector3();
	var vtdir = new 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 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.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 ++;

		}

	}

	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();

};


TeapotGeometry.prototype = Object.create( BufferGeometry.prototype );
TeapotGeometry.prototype.constructor = TeapotGeometry;

export { TeapotGeometry };