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UtahTeapot
README.md
Utah Teapot
We faithfully polygonize the original model by cubic Bezier surfaces (Normal, Tangent and Bi-normal vectors are computed accurately by automatic differentiation).
The data posted on "The History of The Teapot - Wikiid" are 9+1 Bezier surfaces omitting mirror symmetric patches and control points (The true original model has no bottom). The History of The Teapot - Wikiid
Complementing the omitted Bezier surfaces will result in 32 patches (It's 28 patches as an original model), and the number of net control points avoiding duplication on shared edges is 290 points.
##▼ Cubic Bézier Surface
▼ Lid
{ ( 0, 0, 0, 0 ) ( 1, 2, 3, 4 ) ( 5, 5, 5, 5 ) ( 6, 7, 8, 9 ) }
{ ( 0, 0, 0, 0 ) ( 10, 11, 12, 1 ) ( 5, 5, 5, 5 ) ( 13, 14, 15, 6 ) }
{ ( 0, 0, 0, 0 ) ( 4, 16, 17, 18 ) ( 5, 5, 5, 5 ) ( 9, 19, 20, 21 ) }
{ ( 0, 0, 0, 0 ) ( 18, 22, 23, 10 ) ( 5, 5, 5, 5 ) ( 21, 24, 25, 13 ) }
{ ( 6, 7, 8, 9 ) ( 26, 27, 28, 29 ) ( 30, 31, 32, 33 ) ( 34, 35, 36, 37 ) }
{ ( 13, 14, 15, 6 ) ( 38, 39, 40, 26 ) ( 41, 42, 43, 30 ) ( 44, 45, 46, 34 ) }
{ ( 9, 19, 20, 21 ) ( 29, 47, 48, 49 ) ( 33, 50, 51, 52 ) ( 37, 53, 54, 55 ) }
{ ( 21, 24, 25, 13 ) ( 49, 56, 57, 38 ) ( 52, 58, 59, 41 ) ( 55, 60, 61, 44 ) }
▼ Rim
{ ( 62, 63, 64, 65 ) ( 66, 67, 68, 69 ) ( 70, 71, 72, 73 ) ( 74, 75, 76, 77 ) }
{ ( 78, 79, 80, 62 ) ( 81, 82, 83, 66 ) ( 84, 85, 86, 70 ) ( 87, 88, 89, 74 ) }
{ ( 65, 90, 91, 92 ) ( 69, 93, 94, 95 ) ( 73, 96, 97, 98 ) ( 77, 99, 100, 101 ) }
{ ( 92, 102, 103, 78 ) ( 95, 104, 105, 81 ) ( 98, 106, 107, 84 ) ( 101, 108, 109, 87 ) }
▼ Body
{ ( 74, 75, 76, 77 ) ( 110, 111, 112, 113 ) ( 114, 115, 116, 117 ) ( 118, 119, 120, 121 ) }
{ ( 87, 88, 89, 74 ) ( 122, 123, 124, 110 ) ( 125, 126, 127, 114 ) ( 128, 129, 130, 118 ) }
{ ( 77, 99, 100, 101 ) ( 113, 131, 132, 133 ) ( 117, 134, 135, 136 ) ( 121, 137, 138, 139 ) }
{ ( 101, 108, 109, 87 ) ( 133, 140, 141, 122 ) ( 136, 142, 143, 125 ) ( 139, 144, 145, 128 ) }
{ ( 118, 119, 120, 121 ) ( 146, 147, 148, 149 ) ( 150, 151, 152, 153 ) ( 154, 155, 156, 157 ) }
{ ( 128, 129, 130, 118 ) ( 158, 159, 160, 146 ) ( 161, 162, 163, 150 ) ( 164, 165, 166, 154 ) }
{ ( 121, 137, 138, 139 ) ( 149, 167, 168, 169 ) ( 153, 170, 171, 172 ) ( 157, 173, 174, 175 ) }
{ ( 139, 144, 145, 128 ) ( 169, 176, 177, 158 ) ( 172, 178, 179, 161 ) ( 175, 180, 181, 164 ) }
▼ Bottom
{ ( 154, 155, 156, 157 ) ( 182, 183, 184, 185 ) ( 186, 187, 188, 189 ) ( 190, 190, 190, 190 ) }
{ ( 164, 165, 166, 154 ) ( 191, 192, 193, 182 ) ( 194, 195, 196, 186 ) ( 190, 190, 190, 190 ) }
{ ( 157, 173, 174, 175 ) ( 185, 197, 198, 199 ) ( 189, 200, 201, 202 ) ( 190, 190, 190, 190 ) }
{ ( 175, 180, 181, 164 ) ( 199, 203, 204, 191 ) ( 202, 205, 206, 194 ) ( 190, 190, 190, 190 ) }
▼ Spout
{ ( 207, 208, 209, 210 ) ( 211, 212, 213, 214 ) ( 215, 216, 217, 218 ) ( 219, 220, 221, 222 ) }
{ ( 210, 223, 224, 207 ) ( 214, 225, 226, 211 ) ( 218, 227, 228, 215 ) ( 222, 229, 230, 219 ) }
{ ( 219, 220, 221, 222 ) ( 231, 232, 233, 234 ) ( 235, 236, 237, 238 ) ( 239, 240, 241, 242 ) }
{ ( 222, 229, 230, 219 ) ( 234, 243, 244, 231 ) ( 238, 245, 246, 235 ) ( 242, 247, 248, 239 ) }
▼ Handle
{ ( 249, 250, 251, 252 ) ( 253, 254, 255, 256 ) ( 257, 258, 259, 260 ) ( 261, 262, 263, 264 ) }
{ ( 252, 265, 266, 249 ) ( 256, 267, 268, 253 ) ( 260, 269, 270, 257 ) ( 264, 271, 272, 261 ) }
{ ( 261, 262, 263, 264 ) ( 273, 274, 275, 276 ) ( 277, 278, 279, 280 ) ( 281, 282, 283, 128 ) }
{ ( 264, 271, 272, 261 ) ( 276, 284, 285, 273 ) ( 280, 286, 287, 277 ) ( 128, 288, 289, 281 ) }
##▼ Control Point × 290
( 0 , 0 , +3.15 ) ( 0 , -0.8 , +3.15 ) ( +0.45 , -0.8 , +3.15 ) ( +0.8 , -0.45 , +3.15 ) ( +0.8 , 0 , +3.15 )
( 0 , 0 , +2.85 ) ( 0 , -0.2 , +2.7 ) ( +0.112 , -0.2 , +2.7 ) ( +0.2 , -0.112 , +2.7 ) ( +0.2 , 0 , +2.7 )
( -0.8 , 0 , +3.15 ) ( -0.8 , -0.45 , +3.15 ) ( -0.45 , -0.8 , +3.15 ) ( -0.2 , 0 , +2.7 ) ( -0.2 , -0.112 , +2.7 )
( -0.112 , -0.2 , +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 , -0.4 , +2.55 ) ( +0.224 , -0.4 , +2.55 ) ( +0.4 , -0.224 , +2.55 ) ( +0.4 , 0 , +2.55 )
( 0 , -1.3 , +2.55 ) ( +0.728 , -1.3 , +2.55 ) ( +1.3 , -0.728 , +2.55 ) ( +1.3 , 0 , +2.55 ) ( 0 , -1.3 , +2.4 )
( +0.728 , -1.3 , +2.4 ) ( +1.3 , -0.728 , +2.4 ) ( +1.3 , 0 , +2.4 ) ( -0.4 , 0 , +2.55 ) ( -0.4 , -0.224 , +2.55 )
( -0.224 , -0.4 , +2.55 ) ( -1.3 , 0 , +2.55 ) ( -1.3 , -0.728 , +2.55 ) ( -0.728 , -1.3 , +2.55 ) ( -1.3 , 0 , +2.4 )
( -1.3 , -0.728 , +2.4 ) ( -0.728 , -1.3 , +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 , -1.4 , +2.4 ) ( +0.784 , -1.4 , +2.4 ) ( +1.4 , -0.784 , +2.4 )
( +1.4 , 0 , +2.4 ) ( 0 , -1.3375 , +2.53125 ) ( +0.749 , -1.3375 , +2.53125 ) ( +1.3375 , -0.749 , +2.53125 ) ( +1.3375 , 0 , +2.53125 )
( 0 , -1.4375 , +2.53125 ) ( +0.805 , -1.4375 , +2.53125 ) ( +1.4375 , -0.805 , +2.53125 ) ( +1.4375 , 0 , +2.53125 ) ( 0 , -1.5 , +2.4 )
( +0.84 , -1.5 , +2.4 ) ( +1.5 , -0.84 , +2.4 ) ( +1.5 , 0 , +2.4 ) ( -1.4 , 0 , +2.4 ) ( -1.4 , -0.784 , +2.4 )
( -0.784 , -1.4 , +2.4 ) ( -1.3375 , 0 , +2.53125 ) ( -1.3375 , -0.749 , +2.53125 ) ( -0.749 , -1.3375 , +2.53125 ) ( -1.4375 , 0 , +2.53125 )
( -1.4375 , -0.805 , +2.53125 ) ( -0.805 , -1.4375 , +2.53125 ) ( -1.5 , 0 , +2.4 ) ( -1.5 , -0.84 , +2.4 ) ( -0.84 , -1.5 , +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 )
( 0 , -1.75 , +1.875 ) ( +0.98 , -1.75 , +1.875 ) ( +1.75 , -0.98 , +1.875 ) ( +1.75 , 0 , +1.875 ) ( 0 , -2 , +1.35 )
( +1.12 , -2 , +1.35 ) ( +2 , -1.12 , +1.35 ) ( +2 , 0 , +1.35 ) ( 0 , -2 , +0.9 ) ( +1.12 , -2 , +0.9 )
( +2 , -1.12 , +0.9 ) ( +2 , 0 , +0.9 ) ( -1.75 , 0 , +1.875 ) ( -1.75 , -0.98 , +1.875 ) ( -0.98 , -1.75 , +1.875 )
( -2 , 0 , +1.35 ) ( -2 , -1.12 , +1.35 ) ( -1.12 , -2 , +1.35 ) ( -2 , 0 , +0.9 ) ( -2 , -1.12 , +0.9 )
( -1.12 , -2 , +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 ) ( 0 , -2 , +0.45 ) ( +1.12 , -2 , +0.45 ) ( +2 , -1.12 , +0.45 ) ( +2 , 0 , +0.45 )
( 0 , -1.5 , +0.225 ) ( +0.84 , -1.5 , +0.225 ) ( +1.5 , -0.84 , +0.225 ) ( +1.5 , 0 , +0.225 ) ( 0 , -1.5 , +0.15 )
( +0.84 , -1.5 , +0.15 ) ( +1.5 , -0.84 , +0.15 ) ( +1.5 , 0 , +0.15 ) ( -2 , 0 , +0.45 ) ( -2 , -1.12 , +0.45 )
( -1.12 , -2 , +0.45 ) ( -1.5 , 0 , +0.225 ) ( -1.5 , -0.84 , +0.225 ) ( -0.84 , -1.5 , +0.225 ) ( -1.5 , 0 , +0.15 )
( -1.5 , -0.84 , +0.15 ) ( -0.84 , -1.5 , +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 ) ( 0 , -1.5 , +0.075 ) ( +0.84 , -1.5 , +0.075 ) ( +1.5 , -0.84 , +0.075 )
( +1.5 , 0 , +0.075 ) ( 0 , -1.425 , +0 ) ( +0.798 , -1.425 , +0 ) ( +1.425 , -0.798 , +0 ) ( +1.425 , 0 , +0 )
( 0 , 0 , +0 ) ( -1.5 , 0 , +0.075 ) ( -1.5 , -0.84 , +0.075 ) ( -0.84 , -1.5 , +0.075 ) ( -1.425 , 0 , +0 )
( -1.425 , -0.798 , +0 ) ( -0.798 , -1.425 , +0 ) ( +1.5 , +0.84 , +0.075 ) ( +0.84 , +1.5 , +0.075 ) ( 0 , +1.5 , +0.075 )
( +1.425 , +0.798 , +0 ) ( +0.798 , +1.425 , +0 ) ( 0 , +1.425 , +0 ) ( -0.84 , +1.5 , +0.075 ) ( -1.5 , +0.84 , +0.075 )
( -0.798 , +1.425 , +0 ) ( -1.425 , +0.798 , +0 ) ( +2.8 , 0 , +2.4 ) ( +2.8 , -0.15 , +2.4 ) ( +3.2 , -0.15 , +2.4 )
( +3.2 , 0 , +2.4 ) ( +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 , +2.475 ) ( +2.8 , -0.25 , +2.475 ) ( +3.525 , -0.25 , +2.49375 ) ( +3.525 , 0 , +2.49375 ) ( +2.7 , 0 , +2.4 )
( +2.7 , -0.25 , +2.4 ) ( +3.3 , -0.25 , +2.4 ) ( +3.3 , 0 , +2.4 ) ( +3.2 , +0.15 , +2.4 ) ( +2.8 , +0.15 , +2.4 )
( +3.45 , +0.15 , +2.5125 ) ( +2.9 , +0.15 , +2.475 ) ( +3.525 , +0.25 , +2.49375 ) ( +2.8 , +0.25 , +2.475 ) ( +3.3 , +0.25 , +2.4 )
( +2.7 , +0.25 , +2.4 ) ( +2.3 , 0 , +2.1 ) ( +2.3 , -0.25 , +2.1 ) ( +2.4 , -0.25 , +2.025 ) ( +2.4 , 0 , +2.025 )
( +2.6 , 0 , +1.425 ) ( +2.6 , -0.66 , +1.425 ) ( +3.1 , -0.66 , +0.825 ) ( +3.1 , 0 , +0.825 ) ( +1.7 , 0 , +1.425 )
( +1.7 , -0.66 , +1.425 ) ( +1.7 , -0.66 , +0.6 ) ( +1.7 , 0 , +0.6 ) ( +2.4 , +0.25 , +2.025 ) ( +2.3 , +0.25 , +2.1 )
( +3.1 , +0.66 , +0.825 ) ( +2.6 , +0.66 , +1.425 ) ( +1.7 , +0.66 , +0.6 ) ( +1.7 , +0.66 , +1.425 ) ( -1.5 , 0 , +2.25 )
( -1.5 , -0.3 , +2.25 ) ( -1.6 , -0.3 , +2.025 ) ( -1.6 , 0 , +2.025 ) ( -2.5 , 0 , +2.25 ) ( -2.5 , -0.3 , +2.25 )
( -2.3 , -0.3 , +2.025 ) ( -2.3 , 0 , +2.025 ) ( -3 , 0 , +2.25 ) ( -3 , -0.3 , +2.25 ) ( -2.7 , -0.3 , +2.025 )
( -2.7 , 0 , +2.025 ) ( -3 , 0 , +1.8 ) ( -3 , -0.3 , +1.8 ) ( -2.7 , -0.3 , +1.8 ) ( -2.7 , 0 , +1.8 )
( -1.6 , +0.3 , +2.025 ) ( -1.5 , +0.3 , +2.25 ) ( -2.3 , +0.3 , +2.025 ) ( -2.5 , +0.3 , +2.25 ) ( -2.7 , +0.3 , +2.025 )
( -3 , +0.3 , +2.25 ) ( -2.7 , +0.3 , +1.8 ) ( -3 , +0.3 , +1.8 ) ( -3 , 0 , +1.35 ) ( -3 , -0.3 , +1.35 )
( -2.7 , -0.3 , +1.575 ) ( -2.7 , 0 , +1.575 ) ( -2.65 , 0 , +0.9375 ) ( -2.65 , -0.3 , +0.9375 ) ( -2.5 , -0.3 , +1.125 )
( -2.5 , 0 , +1.125 ) ( -1.9 , 0 , +0.6 ) ( -1.9 , -0.3 , +0.6 ) ( -2 , -0.3 , +0.9 ) ( -2.7 , +0.3 , +1.575 )
( -3 , +0.3 , +1.35 ) ( -2.5 , +0.3 , +1.125 ) ( -2.65 , +0.3 , +0.9375 ) ( -2 , +0.3 , +0.9 ) ( -1.9 , +0.3 , +0.6 )
