TeapotGeometry.js 18 KB

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