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teapot.c
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1991-01-13
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/*
* teapot.c - Tessellate the famous teapot into triangular patches, and sit the
* object on top of a checkerboard which is meshed to the same degree. In
* other words, the number of squares on the checkerboard is the same as
* the amount of meshing for each of the 32 patches on the teapot, with
* each mesh quadrilateral on the teapot further split into two triangles.
* Two light sources.
*
* Note that the teapot should always be rendered as a double sided object
* (since for some patches both sides can be seen). (See IEEE CG&A
* January 1987 for a history of the teapot. Note that their vertex list
* has duplicates, e.g. 93 and 271, as well as unused vertices, e.g.
* 205,206,216,223). Also, note that the bottom (the last four patches)
* is not flat - blame Frank Crow, not me.
*
* Author: Eric Haines, 3D/Eye, Inc.
*
* SizeFactor determines the number of objects output.
* Total patches = 32*2*n*n - 8*n [degenerates are deleted]
* Total squares = n*n
*
* SizeFactor # patches # squares
* 1 56 1 [has more degenerates!]
* 2 240 4
* 3 552 9
*
* 12 9120 144
*/
#include <stdio.h>
#include <math.h>
#include "def.h"
#include "lib.h"
static int SizeFactor = 12 ;
/* comment out the next line to generate all patches except the bottom,
* i.e. the original Newell teapot
*/
#define BOTTOM
#ifdef BOTTOM
#define NUM_PATCHES 32
#else
#define NUM_PATCHES 28
#endif
int check_for_cusp() ;
main(argc,argv)
int argc ;
char *argv[] ;
{
COORD3 back_color ;
COORD3 light ;
COORD3 from, at, up ;
if ( !lib_get_size( argc, argv, &SizeFactor ) ) {
fprintf( stderr, "usage: %s [size]\n", *argv ) ;
exit(EXIT_FAIL) ;
}
if ( SizeFactor == 1 ) {
fprintf( stderr,
"warning: a size of 1 is not supported - use at your own risk\n" ) ;
}
/* output viewpoint */
SET_COORD3( from, 4.86, 7.2, 5.4 ) ;
SET_COORD3( at, 0.0, 0.0, 0.0 ) ;
SET_COORD3( up, 0.0, 0.0, 1.0 ) ;
lib_output_viewpoint( from, at, up, 45.0, 1.0, 512, 512 ) ;
/* output background color - UNC sky blue */
SET_COORD3( back_color, 0.078, 0.361, 0.753 ) ;
lib_output_background_color( back_color ) ;
/* output light sources */
SET_COORD3( light, -3.1, 9.8, 12.1 ) ;
lib_output_light( light ) ;
SET_COORD3( light, 11.3, 5.1, 8.8 ) ;
lib_output_light( light ) ;
output_checkerboard() ;
output_teapot() ;
exit(EXIT_SUCCESS) ;
}
output_checkerboard()
{
int sstep, tstep ;
COORD3 vert[4] ;
COORD3 obj_color ;
SET_COORD3( obj_color, 1.0, 1.0, 1.0 ) ;
lib_output_color( obj_color, 0.5, 0.5, 3.0, 0.0, 0.0 ) ;
for ( sstep = 0 ; sstep < SizeFactor ; sstep++ ) {
for ( tstep = 0 ; tstep < SizeFactor ; tstep++ ) {
if ( ( sstep + tstep ) % 2 ) {
loc_to_square( sstep, tstep, vert ) ;
lib_output_polygon( 4, vert ) ;
}
}
}
SET_COORD3( obj_color, 0.5, 0.5, 0.5 ) ;
lib_output_color( obj_color, 0.5, 0.5, 3.0, 0.0, 0.0 ) ;
for ( sstep = 0 ; sstep < SizeFactor ; sstep++ ) {
for ( tstep = 0 ; tstep < SizeFactor ; tstep++ ) {
if ( !(( sstep + tstep ) % 2) ) {
loc_to_square( sstep, tstep, vert ) ;
lib_output_polygon( 4, vert ) ;
}
}
}
}
loc_to_square( sstep, tstep, vert )
int sstep ;
int tstep ;
COORD3 vert[4] ;
{
int i ;
for ( i = 0 ; i < 4 ; i++ ) {
/* vertex 0 & 3 are x.low, 1 & 2 are x.high */
vert[i][X] = 4.0 * ( 2.0 * (double)(sstep + (i%3 ? 1 : 0) ) /
(double)SizeFactor - 1.0 ) ;
/* vertex 0 & 1 are y.low, 2 & 3 are y.high */
vert[i][Y] = 4.0 * ( 2.0 * (double)(tstep + (i/2 ? 1 : 0) ) /
(double)SizeFactor - 1.0 ) ;
vert[i][Z] = 0.0 ;
}
}
static int Patches[32][4][4] = {
/* 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
} ;
static COORD3 Verts[290] = {
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
} ;
/* Compute points on each spline surface of teapot by brute force.
* Forward differencing would be faster, but this is compact & simple.
*/
output_teapot()
{
/* bezier form */
static MATRIX ms = { -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 } ;
int surf, i, r, c, sstep, tstep, num_tri, num_vert, num_tri_vert ;
double s[3], t[3] ;
COORD3 vert[4], norm[4] ;
COORD3 obj_color ;
MATRIX mst, g, mgm[3], tmtx ;
SET_COORD3( obj_color, 1.0, 0.5, 0.1 ) ;
lib_output_color( obj_color, 0.75, 0.25, 20.0, 0.0, 0.0 ) ;
lib_transpose_matrix( mst, ms ) ;
for ( surf = 0 ; surf < NUM_PATCHES ; surf++ ) {
/* 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++ ) {
g[r][c] = Verts[Patches[surf][r][c]][i] ;
}
}
lib_matrix_multiply( tmtx, ms, g ) ;
lib_matrix_multiply( mgm[i], tmtx, mst ) ;
}
/* step along, get points, and output */
for ( sstep = 0 ; sstep < SizeFactor ; sstep++ ) {
for ( tstep = 0 ; tstep < SizeFactor ; tstep++ ) {
for ( num_tri = 0 ; num_tri < 2 ; num_tri++ ) {
for ( num_vert = 0 ; num_vert < 3 ; num_vert++ ) {
num_tri_vert = ( num_vert + num_tri * 2 ) % 4 ;
/* trickiness: add 1 to sstep if 1 or 2 */
s[num_vert] = (double)(sstep + (num_tri_vert/2 ? 1:0) )
/ (double)SizeFactor ;
/* trickiness: add 1 to tstep if 2 or 3 */
t[num_vert] = (double)(tstep + (num_tri_vert%3 ? 1:0) )
/ (double)SizeFactor ;
}
points_from_basis( 3, s, t, mgm,
vert, norm ) ;
/* don't output degenerate polygons */
if ( check_for_cusp( 3, vert, norm ) ) {
lib_output_polypatch( 3, vert, norm ) ;
}
}
}
}
}
}
points_from_basis( tot_vert, s, t, mgm, vert, norm )
int tot_vert ;
double s[] ;
double t[] ;
MATRIX mgm[3] ;
COORD3 vert[] ;
COORD3 norm[] ;
{
int i, num_vert, p ;
double sval, tval, dsval, dtval, sxyz, txyz ;
COORD3 sdir, tdir ;
COORD4 sp, tp, dsp, dtp, tcoord ;
for ( num_vert = 0 ; num_vert < tot_vert ; num_vert++ ) {
sxyz = s[num_vert] ;
txyz = t[num_vert] ;
/* get power vectors and their derivatives */
for ( p = 4, sval = tval = 1.0 ; p-- ; ) {
sp[p] = sval ;
tp[p] = tval ;
sval *= sxyz ;
tval *= txyz ;
if ( p == 3 ) {
dsp[p] = dtp[p] = 0.0 ;
dsval = dtval = 1.0 ;
} else {
dsp[p] = dsval * (double)(3-p) ;
dtp[p] = dtval * (double)(3-p) ;
dsval *= sxyz ;
dtval *= txyz ;
}
}
/* do for x,y,z */
for ( i = 0 ; i < 3 ; i++ ) {
/* multiply power vectors times matrix to get value */
lib_transform_coord( tcoord, sp, mgm[i] ) ;
vert[num_vert][i] = DOT4( tcoord, tp ) ;
/* get s and t tangent vectors */
lib_transform_coord( tcoord, dsp, mgm[i] ) ;
sdir[i] = DOT4( tcoord, tp ) ;
lib_transform_coord( tcoord, sp, mgm[i] ) ;
tdir[i] = DOT4( tcoord, dtp ) ;
}
/* find normal */
CROSS( norm[num_vert], tdir, sdir ) ;
(void)lib_normalize_vector( norm[num_vert] ) ;
}
}
/* at the center of the lid's handle and at bottom are cusp points -
* check if normal is (0 0 0), if so, check that polygon is not degenerate.
* If degenerate, return FALSE, else set normal.
*/
int check_for_cusp( tot_vert, vert, norm )
int tot_vert ;
COORD3 vert[] ;
COORD3 norm[] ;
{
int count, i, nv ;
for ( count = 0, i = tot_vert ; i-- ; ) {
/* check if vertex is at cusp */
if ( IS_VAL_ALMOST_ZERO( vert[i][X], 0.0001 ) &&
IS_VAL_ALMOST_ZERO( vert[i][Y], 0.0001 ) ) {
count++ ;
nv = i ;
}
}
if ( count > 1 ) {
/* degenerate */
return( FALSE ) ;
}
if ( count == 1 ) {
/* check if point is somewhere above the middle of the teapot */
if ( vert[nv][Z] > 1.5 ) {
/* cusp at lid */
SET_COORD3( norm[nv], 0.0, 0.0, 1.0 ) ;
} else {
/* cusp at bottom */
SET_COORD3( norm[nv], 0.0, 0.0, -1.0 ) ;
}
}
return( TRUE ) ;
}