1 /* klein --- Shows a Klein bottle that rotates in 4d or on which you
5 static const char sccsid[] = "@(#)klein.c 1.1 08/10/04 xlockmore";
8 /* Copyright (c) 2005-2009 Carsten Steger <carsten@mirsanmir.org>. */
11 * Permission to use, copy, modify, and distribute this software and its
12 * documentation for any purpose and without fee is hereby granted,
13 * provided that the above copyright notice appear in all copies and that
14 * both that copyright notice and this permission notice appear in
15 * supporting documentation.
17 * This file is provided AS IS with no warranties of any kind. The author
18 * shall have no liability with respect to the infringement of copyrights,
19 * trade secrets or any patents by this file or any part thereof. In no
20 * event will the author be liable for any lost revenue or profits or
21 * other special, indirect and consequential damages.
24 * C. Steger - 08/10/04: Initial version
25 * C. Steger - 09/08/03: Changes to the parameter handling
29 * This program shows two different Klein bottles in 4d: the figure-8 Klein
30 * bottle or the Lawson Klein bottle. You can walk on the Klein bottle, see
31 * it turn in 4d, or walk on it while it turns in 4d. The figure-8 Klein
32 * bottle is well known in its 3d form. The 4d form used in this program is
33 * an extension of the 3d form to 4d that does not intersect itself in 4d
34 * (which can be seen in the depth colors mode). The Lawson Klein bottle,
35 * on the other hand, does intersect itself in 4d. Its primary use is that
36 * it has a nice appearance for walking and for turning in 3d. The Klein
37 * bottle is a non-orientable surface. To make this apparent, the two-sided
38 * color mode can be used. Alternatively, orientation markers (curling
39 * arrows) can be drawn as a texture map on the surface of the Klein bottle.
40 * While walking on the Klein bottle, you will notice that the orientation
41 * of the curling arrows changes (which it must because the Klein bottle is
42 * non-orientable). The program projects the 4d Klein bottle to 3d using
43 * either a perspective or an orthographic projection. Which of the two
44 * alternatives looks more appealing depends on the viewing mode and the
45 * Klein bottle. For example, the Lawson Klein bottle looks nicest when
46 * projected perspectively. The figure-8 Klein bottle, on the other
47 * hand, looks nicer while walking when projected orthographically from 4d.
48 * The projected Klein bottle can then be projected to the screen either
49 * perspectively or orthographically. When using the walking modes,
50 * perspective projection to the screen should be used. There are three
51 * display modes for the Klein bottle: mesh (wireframe), solid, or
52 * transparent. Furthermore, the appearance of the Klein bottle can be as
53 * a solid object or as a set of see-through bands. Finally, the colors
54 * with with the Klein bottle is drawn can be set to two-sided, rainbow, or
55 * depth. In the first case, the Klein bottle is drawn with red on one
56 * "side" and green on the "other side". Of course, the Klein bottle only
57 * has one side, so the color jumps from red to green along a curve on the
58 * surface of the Klein bottle. This mode enables you to see that the Klein
59 * bottle is non-orientable. The second mode draws the Klein bottle with
60 * fully saturated rainbow colors. This gives a very nice effect when
61 * combined with the see-through bands mode or with the orientation markers
62 * drawn. The third mode draws the Klein bottle with colors that are chosen
63 * according to the 4d "depth" of the points. This mode enables you to see
64 * that the figure-8 Klein bottle does not intersect itself in 4d, while the
65 * Lawson Klein bottle does intersect itself. The rotation speed for each
66 * of the six planes around which the Klein bottle rotates can be chosen.
67 * For the walk-and-turn more, only the rotation speeds around the true 4d
68 * planes are used (the xy, xz, and yz planes). Furthermore, in the walking
69 * modes the walking direction in the 2d base square of the Klein bottle and
70 * the walking speed can be chosen. This program is somewhat inspired by
71 * Thomas Banchoff's book "Beyond the Third Dimension: Geometry, Computer
72 * Graphics, and Higher Dimensions", Scientific American Library, 1990.
76 #define M_PI 3.14159265358979323846
79 #define KLEIN_BOTTLE_FIGURE_8 0
80 #define KLEIN_BOTTLE_LAWSON 1
81 #define NUM_KLEIN_BOTTLES 2
83 #define DISP_WIREFRAME 0
84 #define DISP_SURFACE 1
85 #define DISP_TRANSPARENT 2
86 #define NUM_DISPLAY_MODES 3
88 #define APPEARANCE_SOLID 0
89 #define APPEARANCE_BANDS 1
90 #define NUM_APPEARANCES 2
92 #define COLORS_TWOSIDED 0
93 #define COLORS_RAINBOW 1
94 #define COLORS_DEPTH 2
99 #define VIEW_WALKTURN 2
100 #define NUM_VIEW_MODES 3
102 #define DISP_3D_PERSPECTIVE 0
103 #define DISP_3D_ORTHOGRAPHIC 1
104 #define NUM_DISP_3D_MODES 2
106 #define DISP_4D_PERSPECTIVE 0
107 #define DISP_4D_ORTHOGRAPHIC 1
108 #define NUM_DISP_4D_MODES 2
110 #define DEF_KLEIN_BOTTLE "random"
111 #define DEF_DISPLAY_MODE "random"
112 #define DEF_APPEARANCE "random"
113 #define DEF_COLORS "random"
114 #define DEF_VIEW_MODE "random"
115 #define DEF_MARKS "False"
116 #define DEF_PROJECTION_3D "random"
117 #define DEF_PROJECTION_4D "random"
118 #define DEF_SPEEDWX "1.1"
119 #define DEF_SPEEDWY "1.3"
120 #define DEF_SPEEDWZ "1.5"
121 #define DEF_SPEEDXY "1.7"
122 #define DEF_SPEEDXZ "1.9"
123 #define DEF_SPEEDYZ "2.1"
124 #define DEF_WALK_DIRECTION "7.0"
125 #define DEF_WALK_SPEED "20.0"
128 # define DEFAULTS "*delay: 10000 \n" \
129 "*showFPS: False \n" \
131 # define refresh_klein 0
132 # include "xlockmore.h" /* from the xscreensaver distribution */
133 #else /* !STANDALONE */
134 # include "xlock.h" /* from the xlockmore distribution */
135 #endif /* !STANDALONE */
139 #include <X11/keysym.h>
141 #include "gltrackball.h"
145 ModStruct klein_description =
146 {"klein", "init_klein", "draw_klein", "release_klein",
147 "draw_klein", "change_klein", NULL, &klein_opts,
148 25000, 1, 1, 1, 1.0, 4, "",
149 "Rotate a Klein bottle in 4d or walk on it", 0, NULL};
154 static char *klein_bottle;
155 static int bottle_type;
157 static int display_mode;
159 static int appearance;
160 static char *color_mode;
162 static char *view_mode;
165 static char *proj_3d;
166 static int projection_3d;
167 static char *proj_4d;
168 static int projection_4d;
169 static float speed_wx;
170 static float speed_wy;
171 static float speed_wz;
172 static float speed_xy;
173 static float speed_xz;
174 static float speed_yz;
175 static float walk_direction;
176 static float walk_speed;
179 static XrmOptionDescRec opts[] =
181 {"-klein-bottle", ".kleinBottle", XrmoptionSepArg, 0 },
182 {"-figure-8", ".kleinBottle", XrmoptionNoArg, "figure-8" },
183 {"-lawson", ".kleinBottle", XrmoptionNoArg, "lawson" },
184 {"-mode", ".displayMode", XrmoptionSepArg, 0 },
185 {"-wireframe", ".displayMode", XrmoptionNoArg, "wireframe" },
186 {"-surface", ".displayMode", XrmoptionNoArg, "surface" },
187 {"-transparent", ".displayMode", XrmoptionNoArg, "transparent" },
188 {"-appearance", ".appearance", XrmoptionSepArg, 0 },
189 {"-solid", ".appearance", XrmoptionNoArg, "solid" },
190 {"-bands", ".appearance", XrmoptionNoArg, "bands" },
191 {"-colors", ".colors", XrmoptionSepArg, 0 },
192 {"-twosided", ".colors", XrmoptionNoArg, "two-sided" },
193 {"-rainbow", ".colors", XrmoptionNoArg, "rainbow" },
194 {"-depth", ".colors", XrmoptionNoArg, "depth" },
195 {"-view-mode", ".viewMode", XrmoptionSepArg, 0 },
196 {"-walk", ".viewMode", XrmoptionNoArg, "walk" },
197 {"-turn", ".viewMode", XrmoptionNoArg, "turn" },
198 {"-walk-turn", ".viewMode", XrmoptionNoArg, "walk-turn" },
199 {"-orientation-marks", ".marks", XrmoptionNoArg, "on"},
200 {"+orientation-marks", ".marks", XrmoptionNoArg, "off"},
201 {"-projection-3d", ".projection3d", XrmoptionSepArg, 0 },
202 {"-perspective-3d", ".projection3d", XrmoptionNoArg, "perspective" },
203 {"-orthographic-3d", ".projection3d", XrmoptionNoArg, "orthographic" },
204 {"-projection-4d", ".projection4d", XrmoptionSepArg, 0 },
205 {"-perspective-4d", ".projection4d", XrmoptionNoArg, "perspective" },
206 {"-orthographic-4d", ".projection4d", XrmoptionNoArg, "orthographic" },
207 {"-speed-wx", ".speedwx", XrmoptionSepArg, 0 },
208 {"-speed-wy", ".speedwy", XrmoptionSepArg, 0 },
209 {"-speed-wz", ".speedwz", XrmoptionSepArg, 0 },
210 {"-speed-xy", ".speedxy", XrmoptionSepArg, 0 },
211 {"-speed-xz", ".speedxz", XrmoptionSepArg, 0 },
212 {"-speed-yz", ".speedyz", XrmoptionSepArg, 0 },
213 {"-walk-direction", ".walkDirection", XrmoptionSepArg, 0 },
214 {"-walk-speed", ".walkSpeed", XrmoptionSepArg, 0 }
217 static argtype vars[] =
219 { &klein_bottle, "kleinBottle", "KleinBottle", DEF_KLEIN_BOTTLE, t_String },
220 { &mode, "displayMode", "DisplayMode", DEF_DISPLAY_MODE, t_String },
221 { &appear, "appearance", "Appearance", DEF_APPEARANCE, t_String },
222 { &color_mode, "colors", "Colors", DEF_COLORS, t_String },
223 { &view_mode, "viewMode", "ViewMode", DEF_VIEW_MODE, t_String },
224 { &marks, "marks", "Marks", DEF_MARKS, t_Bool },
225 { &proj_3d, "projection3d", "Projection3d", DEF_PROJECTION_3D, t_String },
226 { &proj_4d, "projection4d", "Projection4d", DEF_PROJECTION_4D, t_String },
227 { &speed_wx, "speedwx", "Speedwx", DEF_SPEEDWX, t_Float},
228 { &speed_wy, "speedwy", "Speedwy", DEF_SPEEDWY, t_Float},
229 { &speed_wz, "speedwz", "Speedwz", DEF_SPEEDWZ, t_Float},
230 { &speed_xy, "speedxy", "Speedxy", DEF_SPEEDXY, t_Float},
231 { &speed_xz, "speedxz", "Speedxz", DEF_SPEEDXZ, t_Float},
232 { &speed_yz, "speedyz", "Speedyz", DEF_SPEEDYZ, t_Float},
233 { &walk_direction, "walkDirection", "WalkDirection", DEF_WALK_DIRECTION, t_Float},
234 { &walk_speed, "walkSpeed", "WalkSpeed", DEF_WALK_SPEED, t_Float}
237 ENTRYPOINT ModeSpecOpt klein_opts =
238 {sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, NULL};
241 /* Radius of the Figure 8 Klein bottle */
242 #define FIGURE_8_RADIUS 2.0
244 /* Offset by which we walk above the Klein bottle */
247 /* Number of subdivisions of the Klein bottle */
251 /* Number of subdivisions per band */
257 GLXContext *glx_context;
258 /* 4D rotation angles */
259 float alpha, beta, delta, zeta, eta, theta;
260 /* Movement parameters */
261 float umove, vmove, dumove, dvmove;
263 /* The viewing offset in 4d */
265 /* The viewing offset in 3d */
267 /* The 4d coordinates of the Klein bottle and their derivatives */
268 float x[(NUMU+1)*(NUMV+1)][4];
269 float xu[(NUMU+1)*(NUMV+1)][4];
270 float xv[(NUMU+1)*(NUMV+1)][4];
271 float pp[(NUMU+1)*(NUMV+1)][3];
272 float pn[(NUMU+1)*(NUMV+1)][3];
273 /* The precomputed colors of the Klein bottle */
274 float col[(NUMU+1)*(NUMV+1)][4];
275 /* The precomputed texture coordinates of the Klein bottle */
276 float tex[(NUMU+1)*(NUMV+1)][2];
277 /* The "curlicue" texture */
279 /* Aspect ratio of the current window */
281 /* Trackball states */
282 trackball_state *trackballs[2];
283 int current_trackball;
285 /* A random factor to modify the rotation speeds */
289 static kleinstruct *klein = (kleinstruct *) NULL;
292 /* A texture map containing a "curlicue" */
293 #define TEX_DIMENSION 64
294 static const unsigned char texture[TEX_DIMENSION*TEX_DIMENSION] = {
295 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
296 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
297 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
298 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
299 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
300 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
301 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
302 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
303 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
304 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
305 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
306 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
307 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
308 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
309 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
310 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
311 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
312 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
313 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
314 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
315 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
316 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
317 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
318 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
319 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
320 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
321 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
322 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
323 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
324 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
325 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
326 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
327 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
328 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
329 255,255,255,255,255,255,255, 58, 43, 43, 43, 43, 45, 70, 70, 70,
330 70, 70, 70, 70, 74, 98, 98, 98,100,194,255,255,255,255,255,255,
331 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
332 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
333 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
334 0, 0, 0, 0, 0, 0, 0, 30,186,255,255,255,255,255,255,255,
335 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
336 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
337 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
338 0, 0, 0, 0, 0, 1,111,244,255,255,255,255,255,255,255,255,
339 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
340 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
341 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
342 0, 0, 0, 0, 43,198,255,255,255,255,255,255,255,255,255,255,
343 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
344 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
345 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
346 0, 0, 5,123,248,255,255,255,255,255,255,255,255,255,255,255,
347 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
348 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
349 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
350 0, 50,209,255,255,255,255,255,255,255,255,255,255,255,255,255,
351 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,246,
352 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
353 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
354 74,252,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
355 255,255,255,255,255,255,255,255,255,255,255,255,255,255,138, 4,
356 66,229,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
357 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
358 1,170,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
359 255,255,255,255,255,255,255,255,255,255,255,255,255,153, 0, 0,
360 0, 53,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
361 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
362 0, 6,188,255,255,255,255,255,255,255,255,255,255,255,255,255,
363 255,255,255,255,255,255,255,255,255,255,255,255,213, 7, 0, 0,
364 0, 0,226,255,255,255,255,255,255,255,255,255,255,255,255,255,
365 255,255,255,255,255,255,255, 45, 0, 0, 0, 0, 0, 47, 0, 0,
366 0, 0, 22,225,255,255,255,255,255,255,255,255,255,255,255,255,
367 255,255,255,255,255,255,255,255,255,255,255,254, 54, 0, 0, 0,
368 0, 81,254,255,255,255,255,255,255,255,255,255,255,255,255,255,
369 255,255,255,255,255,255,255, 45, 0, 0, 0, 0, 56,247, 82, 0,
370 0, 0, 0, 59,253,255,255,255,255,255,255,255,255,255,255,255,
371 255,255,255,255,255,255,255,255,255,255,255,152, 0, 0, 0, 0,
372 52,243,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
373 255,255,255,255,255,255,255, 45, 0, 0, 0, 8,215,255,250, 56,
374 0, 0, 0, 0,142,255,255,255,255,255,255,255,255,255,255,255,
375 255,255,255,255,255,255,255,255,255,255,241, 19, 0, 0, 0, 15,
376 220,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
377 255,255,255,255,255,255,255, 45, 0, 0, 0,129,255,255,255,230,
378 23, 0, 0, 0, 12,230,255,255,255,255,255,255,255,255,255,255,
379 255,255,255,255,255,255,255,255,255,255,131, 0, 0, 0, 0,157,
380 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
381 255,255,255,255,255,255,255, 45, 0, 0, 49,250,255,255,255,255,
382 171, 0, 0, 0, 0,112,255,255,255,255,255,255,255,255,255,255,
383 255,255,255,255,255,255,255,255,255,246, 19, 0, 0, 0, 54,253,
384 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
385 255,255,255,255,255,255,255, 45, 0, 5,208,255,255,255,255,255,
386 255, 77, 0, 0, 0, 9,231,255,255,255,255,255,255,255,255,255,
387 255,255,255,255,255,255,255,255,255,163, 0, 0, 0, 0,186,255,
388 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
389 255,255,255,255,255,255,255, 45, 0,121,255,255,255,255,255,255,
390 255,211, 2, 0, 0, 0,134,255,255,255,255,255,255,255,255,255,
391 255,255,255,255,255,255,255,255,255, 69, 0, 0, 0, 50,255,255,
392 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
393 255,255,255,255,255,255,255, 45, 41,247,255,255,255,255,255,255,
394 255,255, 73, 0, 0, 0, 38,254,255,255,255,255,255,255,255,255,
395 255,255,255,255,255,255,255,255,237, 4, 0, 0, 0,145,255,255,
396 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
397 255,255,255,255,255,255,255, 52,201,255,255,255,255,255,255,255,
398 255,255,169, 0, 0, 0, 0,216,255,255,255,255,255,255,255,255,
399 255,255,255,255,255,255,255,255,181, 0, 0, 0, 0,229,255,255,
400 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
401 255,255,255,255,255,255,255,186,255,255,255,255,255,255,255,255,
402 255,255,247, 7, 0, 0, 0,150,255,255,255,255,255,255,255,255,
403 255,255,255,255,255,255,255,255,130, 0, 0, 0, 42,255,255,255,
404 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
405 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
406 255,255,255, 67, 0, 0, 0, 91,255,255,255,255,255,255,255,255,
407 255,255,255,255,255,255,255,255, 79, 0, 0, 0, 95,255,255,255,
408 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
409 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
410 255,255,255,120, 0, 0, 0, 56,255,255,255,255,255,255,255,255,
411 255,255,255,255,255,255,255,255, 55, 0, 0, 0,130,255,255,255,
412 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
413 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
414 255,255,255,157, 0, 0, 0, 21,255,255,255,255,255,255,255,255,
415 255,255,255,255,255,255,255,255, 34, 0, 0, 0,161,255,255,255,
416 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
417 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
418 255,255,255,179, 0, 0, 0, 2,250,255,255,255,255,255,255,255,
419 255,255,255,255,255,255,255,255, 27, 0, 0, 0,168,255,255,255,
420 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
421 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
422 255,255,255,200, 0, 0, 0, 0,249,255,255,255,255,255,255,255,
423 255,255,255,255,255,255,255,255, 27, 0, 0, 0,168,255,255,255,
424 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
425 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
426 255,255,255,200, 0, 0, 0, 0,249,255,255,255,255,255,255,255,
427 255,255,255,255,255,255,255,255, 27, 0, 0, 0,163,255,255,255,
428 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
429 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
430 255,255,255,183, 0, 0, 0, 0,249,255,255,255,255,255,255,255,
431 255,255,255,255,255,255,255,255, 42, 0, 0, 0,135,255,255,255,
432 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
433 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
434 255,255,255,161, 0, 0, 0, 17,254,255,255,255,255,255,255,255,
435 255,255,255,255,255,255,255,255, 76, 0, 0, 0,100,255,255,255,
436 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
437 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
438 255,255,255,126, 0, 0, 0, 48,255,255,255,255,255,255,255,255,
439 255,255,255,255,255,255,255,255,114, 0, 0, 0, 53,255,255,255,
440 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
441 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
442 255,255,255, 78, 0, 0, 0, 84,255,255,255,255,255,255,255,255,
443 255,255,255,255,255,255,255,255,165, 0, 0, 0, 3,241,255,255,
444 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
445 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
446 255,255,252, 16, 0, 0, 0,139,255,255,255,255,255,255,255,255,
447 255,255,255,255,255,255,255,255,228, 0, 0, 0, 0,161,255,255,
448 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
449 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
450 255,255,192, 0, 0, 0, 0,198,255,255,255,255,255,255,255,255,
451 255,255,255,255,255,255,255,255,255, 46, 0, 0, 0, 67,255,255,
452 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
453 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
454 255,255, 93, 0, 0, 0, 21,250,255,255,255,255,255,255,255,255,
455 255,255,255,255,255,255,255,255,255,139, 0, 0, 0, 1,211,255,
456 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
457 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
458 255,226, 7, 0, 0, 0,108,255,255,255,255,255,255,255,255,255,
459 255,255,255,255,255,255,255,255,255,230, 6, 0, 0, 0, 79,255,
460 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
461 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
462 255,106, 0, 0, 0, 1,206,255,255,255,255,255,255,255,255,255,
463 255,255,255,255,255,255,255,255,255,255, 97, 0, 0, 0, 0,183,
464 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
465 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
466 202, 3, 0, 0, 0, 67,255,255,255,255,255,255,255,255,255,255,
467 255,255,255,255,255,255,255,255,255,255,221, 8, 0, 0, 0, 27,
468 235,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
469 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,243,
470 40, 0, 0, 0, 0,198,255,255,255,255,255,255,255,255,255,255,
471 255,255,255,255,255,255,255,255,255,255,255,126, 0, 0, 0, 0,
472 71,252,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
473 255,255,255,255,255,255,255,255,255,255,255,255,255,255,253, 85,
474 0, 0, 0, 0, 96,255,255,255,255,255,255,255,255,255,255,255,
475 255,255,255,255,255,255,255,255,255,255,255,247, 44, 0, 0, 0,
476 0, 91,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
477 255,255,255,255,255,255,255,255,255,255,255,255,255,255,116, 0,
478 0, 0, 0, 25,233,255,255,255,255,255,255,255,255,255,255,255,
479 255,255,255,255,255,255,255,255,255,255,255,255,216, 11, 0, 0,
480 0, 0, 90,251,255,255,255,255,255,255,255,255,255,255,255,255,
481 255,255,255,255,255,255,255,255,255,255,255,255,252,112, 0, 0,
482 0, 0, 4,191,255,255,255,255,255,255,255,255,255,255,255,255,
483 255,255,255,255,255,255,255,255,255,255,255,255,255,174, 4, 0,
484 0, 0, 0, 72,235,255,255,255,255,255,255,255,255,255,255,255,
485 255,255,255,255,255,255,255,255,255,255,255,242, 84, 0, 0, 0,
486 0, 0,146,255,255,255,255,255,255,255,255,255,255,255,255,255,
487 255,255,255,255,255,255,255,255,255,255,255,255,255,255,150, 1,
488 0, 0, 0, 0, 27,181,255,255,255,255,255,255,255,255,255,255,
489 255,255,255,255,255,255,255,255,255,255,194, 39, 0, 0, 0, 0,
490 0,120,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
491 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,151,
492 4, 0, 0, 0, 0, 0, 77,209,255,255,255,255,255,255,255,255,
493 255,255,255,255,255,255,255,255,216, 92, 1, 0, 0, 0, 0, 0,
494 125,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
495 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
496 175, 12, 0, 0, 0, 0, 0, 1, 70,164,241,255,255,255,255,255,
497 255,255,255,255,255,242,171, 77, 2, 0, 0, 0, 0, 0, 4,150,
498 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
499 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
500 255,214, 41, 0, 0, 0, 0, 0, 0, 0, 4, 48, 98,138,163,163,
501 163,163,140,103, 55, 5, 0, 0, 0, 0, 0, 0, 0, 30,199,255,
502 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
503 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
504 255,255,245,125, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
505 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3,105,240,255,255,
506 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
507 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
508 255,255,255,255,222,100, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0,
509 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 83,210,255,255,255,255,
510 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
511 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
512 255,255,255,255,255,255,228,136, 45, 0, 0, 0, 0, 0, 0, 0,
513 0, 0, 0, 0, 0, 0, 0, 37,125,220,255,255,255,255,255,255,
514 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
515 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
516 255,255,255,255,255,255,255,255,255,225,166,112, 74, 43, 32, 12,
517 8, 32, 40, 71,105,162,218,255,255,255,255,255,255,255,255,255,
518 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
519 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
520 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
521 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
522 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
523 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
524 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
525 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
526 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
527 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
528 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
529 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
530 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
531 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
532 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
533 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
534 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
535 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
536 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
537 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
538 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
539 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
540 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
541 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
542 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
543 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
544 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
545 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
546 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
547 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
548 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
549 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
550 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
554 /* Add a rotation around the wx-plane to the matrix m. */
555 static void rotatewx(float m[4][4], float phi)
573 /* Add a rotation around the wy-plane to the matrix m. */
574 static void rotatewy(float m[4][4], float phi)
592 /* Add a rotation around the wz-plane to the matrix m. */
593 static void rotatewz(float m[4][4], float phi)
611 /* Add a rotation around the xy-plane to the matrix m. */
612 static void rotatexy(float m[4][4], float phi)
630 /* Add a rotation around the xz-plane to the matrix m. */
631 static void rotatexz(float m[4][4], float phi)
649 /* Add a rotation around the yz-plane to the matrix m. */
650 static void rotateyz(float m[4][4], float phi)
668 /* Compute the rotation matrix m from the rotation angles. */
669 static void rotateall(float al, float be, float de, float ze, float et,
670 float th, float m[4][4])
686 /* Compute the rotation matrix m from the 4d rotation angles. */
687 static void rotateall4d(float ze, float et, float th, float m[4][4])
700 /* Multiply two rotation matrices: o=m*n. */
701 static void mult_rotmat(float m[4][4], float n[4][4], float o[4][4])
711 o[i][j] += m[i][k]*n[k][j];
717 /* Compute a 4D rotation matrix from two unit quaternions. */
718 static void quats_to_rotmat(float p[4], float q[4], float m[4][4])
720 double al, be, de, ze, et, th;
721 double r00, r01, r02, r12, r22;
723 r00 = 1.0-2.0*(p[1]*p[1]+p[2]*p[2]);
724 r01 = 2.0*(p[0]*p[1]+p[2]*p[3]);
725 r02 = 2.0*(p[2]*p[0]-p[1]*p[3]);
726 r12 = 2.0*(p[1]*p[2]+p[0]*p[3]);
727 r22 = 1.0-2.0*(p[1]*p[1]+p[0]*p[0]);
729 al = atan2(-r12,r22)*180.0/M_PI;
730 be = atan2(r02,sqrt(r00*r00+r01*r01))*180.0/M_PI;
731 de = atan2(-r01,r00)*180.0/M_PI;
733 r00 = 1.0-2.0*(q[1]*q[1]+q[2]*q[2]);
734 r01 = 2.0*(q[0]*q[1]+q[2]*q[3]);
735 r02 = 2.0*(q[2]*q[0]-q[1]*q[3]);
736 r12 = 2.0*(q[1]*q[2]+q[0]*q[3]);
737 r22 = 1.0-2.0*(q[1]*q[1]+q[0]*q[0]);
739 et = atan2(-r12,r22)*180.0/M_PI;
740 th = atan2(r02,sqrt(r00*r00+r01*r01))*180.0/M_PI;
741 ze = atan2(-r01,r00)*180.0/M_PI;
743 rotateall(al,be,de,ze,et,-th,m);
747 /* Compute a fully saturated and bright color based on an angle. */
748 static void color(double angle, float col[4])
753 if (colors == COLORS_TWOSIDED)
757 angle = fmod(angle,2.0*M_PI);
759 angle = fmod(angle,-2.0*M_PI);
760 s = floor(angle/(M_PI/3));
761 t = angle/(M_PI/3)-s;
797 if (display_mode == DISP_TRANSPARENT)
804 /* Set up the figure-8 Klein bottle coordinates, colors, and texture. */
805 static void setup_figure8(ModeInfo *mi, double umin, double umax, double vmin,
810 double cu, su, cv, sv, cv2, sv2, c2u, s2u;
811 kleinstruct *kb = &klein[MI_SCREEN(mi)];
815 for (i=0; i<=NUMU; i++)
817 for (j=0; j<=NUMV; j++)
822 if (colors == COLORS_DEPTH)
823 color((cos(u)+1.0)*M_PI*2.0/3.0,kb->col[k]);
826 kb->tex[k][0] = -32*u/(2.0*M_PI);
827 kb->tex[k][1] = 32*v/(2.0*M_PI);
836 kb->x[k][0] = (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*cv;
837 kb->x[k][1] = (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*sv;
838 kb->x[k][2] = su*sv2+s2u*cv2;
840 kb->xu[k][0] = (cu*cv2-2.0*c2u*sv2)*cv;
841 kb->xu[k][1] = (cu*cv2-2.0*c2u*sv2)*sv;
842 kb->xu[k][2] = cu*sv2+2.0*c2u*cv2;
844 kb->xv[k][0] = ((-0.5*su*sv2-0.5*s2u*cv2)*cv-
845 (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*sv);
846 kb->xv[k][1] = ((-0.5*su*sv2-0.5*s2u*cv2)*sv+
847 (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*cv);
848 kb->xv[k][2] = 0.5*su*cv2-0.5*s2u*sv2;
852 kb->x[k][l] /= FIGURE_8_RADIUS+1.25;
853 kb->xu[k][l] /= FIGURE_8_RADIUS+1.25;
854 kb->xv[k][l] /= FIGURE_8_RADIUS+1.25;
861 /* Set up the Lawson Klein bottle coordinates, colors, and texture. */
862 static void setup_lawson(ModeInfo *mi, double umin, double umax, double vmin,
867 double cu, su, cv, sv, cv2, sv2;
868 kleinstruct *kb = &klein[MI_SCREEN(mi)];
872 for (i=0; i<=NUMV; i++)
874 for (j=0; j<=NUMU; j++)
879 if (colors == COLORS_DEPTH)
880 color((sin(u)*cos(0.5*v)+1.0)*M_PI*2.0/3.0,kb->col[k]);
883 kb->tex[k][0] = -32*u/(2.0*M_PI);
884 kb->tex[k][1] = 32*v/(2.0*M_PI);
893 kb->x[k][2] = su*sv2;
894 kb->x[k][3] = su*cv2;
895 kb->xu[k][0] = -su*cv;
896 kb->xu[k][1] = -su*sv;
897 kb->xu[k][2] = cu*sv2;
898 kb->xu[k][3] = cu*cv2;
899 kb->xv[k][0] = -cu*sv;
900 kb->xv[k][1] = cu*cv;
901 kb->xv[k][2] = su*cv2*0.5;
902 kb->xv[k][3] = -su*sv2*0.5;
908 /* Draw a figure-8 Klein bottle projected into 3D. */
909 static int figure8(ModeInfo *mi, double umin, double umax, double vmin,
913 static const GLfloat mat_diff_red[] = { 1.0, 0.0, 0.0, 1.0 };
914 static const GLfloat mat_diff_green[] = { 0.0, 1.0, 0.0, 1.0 };
915 static const GLfloat mat_diff_trans_red[] = { 1.0, 0.0, 0.0, 0.7 };
916 static const GLfloat mat_diff_trans_green[] = { 0.0, 1.0, 0.0, 0.7 };
917 float p[3], pu[3], pv[3], pm[3], n[3], b[3], mat[4][4];
918 int i, j, k, l, m, o;
920 double xx[4], xxu[4], xxv[4], y[4], yu[4], yv[4];
922 double cu, su, cv, sv, cv2, sv2, c2u, s2u;
923 float q1[4], q2[4], r1[4][4], r2[4][4];
924 kleinstruct *kb = &klein[MI_SCREEN(mi)];
926 if (view == VIEW_WALK || view == VIEW_WALKTURN)
928 /* Compute the rotation that rotates the Klein bottle in 4D without the
929 trackball rotations. */
930 rotateall4d(kb->zeta,kb->eta,kb->theta,mat);
942 xx[0] = (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*cv;
943 xx[1] = (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*sv;
944 xx[2] = su*sv2+s2u*cv2;
946 xxu[0] = (cu*cv2-2.0*c2u*sv2)*cv;
947 xxu[1] = (cu*cv2-2.0*c2u*sv2)*sv;
948 xxu[2] = cu*sv2+2.0*c2u*cv2;
950 xxv[0] = ((-0.5*su*sv2-0.5*s2u*cv2)*cv-
951 (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*sv);
952 xxv[1] = ((-0.5*su*sv2-0.5*s2u*cv2)*sv+
953 (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*cv);
954 xxv[2] = 0.5*su*cv2-0.5*s2u*sv2;
958 xx[l] /= FIGURE_8_RADIUS+1.25;
959 xxu[l] /= FIGURE_8_RADIUS+1.25;
960 xxv[l] /= FIGURE_8_RADIUS+1.25;
964 y[l] = (mat[l][0]*xx[0]+mat[l][1]*xx[1]+
965 mat[l][2]*xx[2]+mat[l][3]*xx[3]);
966 yu[l] = (mat[l][0]*xxu[0]+mat[l][1]*xxu[1]+
967 mat[l][2]*xxu[2]+mat[l][3]*xxu[3]);
968 yv[l] = (mat[l][0]*xxv[0]+mat[l][1]*xxv[1]+
969 mat[l][2]*xxv[2]+mat[l][3]*xxv[3]);
971 if (projection_4d == DISP_4D_ORTHOGRAPHIC)
975 p[l] = y[l]+kb->offset4d[l];
982 s = y[3]+kb->offset4d[3];
987 r = y[l]+kb->offset4d[l];
989 pu[l] = (yu[l]*s-r*yu[3])*t;
990 pv[l] = (yv[l]*s-r*yv[3])*t;
993 n[0] = pu[1]*pv[2]-pu[2]*pv[1];
994 n[1] = pu[2]*pv[0]-pu[0]*pv[2];
995 n[2] = pu[0]*pv[1]-pu[1]*pv[0];
996 t = 1.0/(kb->side*4.0*sqrt(n[0]*n[0]+n[1]*n[1]+n[2]*n[2]));
1000 pm[0] = pu[0]*kb->dumove+pv[0]*kb->dvmove;
1001 pm[1] = pu[1]*kb->dumove+pv[1]*kb->dvmove;
1002 pm[2] = pu[2]*kb->dumove+pv[2]*kb->dvmove;
1003 t = 1.0/(4.0*sqrt(pm[0]*pm[0]+pm[1]*pm[1]+pm[2]*pm[2]));
1007 b[0] = n[1]*pm[2]-n[2]*pm[1];
1008 b[1] = n[2]*pm[0]-n[0]*pm[2];
1009 b[2] = n[0]*pm[1]-n[1]*pm[0];
1010 t = 1.0/(4.0*sqrt(b[0]*b[0]+b[1]*b[1]+b[2]*b[2]));
1015 /* Compute alpha, beta, delta from the three basis vectors.
1016 | -b[0] -b[1] -b[2] |
1017 m = | n[0] n[1] n[2] |
1018 | -pm[0] -pm[1] -pm[2] |
1020 kb->alpha = atan2(-n[2],-pm[2])*180/M_PI;
1021 kb->beta = atan2( -b[2],sqrt(b[0]*b[0]+b[1]*b[1]))*180/M_PI;
1022 kb->delta = atan2(b[1],-b[0])*180/M_PI;
1024 /* Compute the rotation that rotates the Klein bottle in 4D. */
1025 rotateall(kb->alpha,kb->beta,kb->delta,kb->zeta,kb->eta,kb->theta,mat);
1037 xx[0] = (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*cv;
1038 xx[1] = (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*sv;
1039 xx[2] = su*sv2+s2u*cv2;
1042 xx[l] /= FIGURE_8_RADIUS+1.25;
1047 r += mat[l][m]*xx[m];
1050 if (projection_4d == DISP_4D_ORTHOGRAPHIC)
1053 p[l] = y[l]+kb->offset4d[l];
1057 s = y[3]+kb->offset4d[3];
1059 p[l] = (y[l]+kb->offset4d[l])/s;
1062 kb->offset3d[0] = -p[0];
1063 kb->offset3d[1] = -p[1]-DELTAY;
1064 kb->offset3d[2] = -p[2];
1068 /* Compute the rotation that rotates the Klein bottle in 4D, including
1069 the trackball rotations. */
1070 rotateall(kb->alpha,kb->beta,kb->delta,kb->zeta,kb->eta,kb->theta,r1);
1072 gltrackball_get_quaternion(kb->trackballs[0],q1);
1073 gltrackball_get_quaternion(kb->trackballs[1],q2);
1074 quats_to_rotmat(q1,q2,r2);
1076 mult_rotmat(r2,r1,mat);
1079 /* Project the points from 4D to 3D. */
1080 for (i=0; i<=NUMU; i++)
1082 for (j=0; j<=NUMV; j++)
1087 y[l] = (mat[l][0]*kb->x[o][0]+mat[l][1]*kb->x[o][1]+
1088 mat[l][2]*kb->x[o][2]+mat[l][3]*kb->x[o][3]);
1089 yu[l] = (mat[l][0]*kb->xu[o][0]+mat[l][1]*kb->xu[o][1]+
1090 mat[l][2]*kb->xu[o][2]+mat[l][3]*kb->xu[o][3]);
1091 yv[l] = (mat[l][0]*kb->xv[o][0]+mat[l][1]*kb->xv[o][1]+
1092 mat[l][2]*kb->xv[o][2]+mat[l][3]*kb->xv[o][3]);
1094 if (projection_4d == DISP_4D_ORTHOGRAPHIC)
1098 kb->pp[o][l] = (y[l]+kb->offset4d[l])+kb->offset3d[l];
1105 s = y[3]+kb->offset4d[3];
1110 r = y[l]+kb->offset4d[l];
1111 kb->pp[o][l] = r*q+kb->offset3d[l];
1112 pu[l] = (yu[l]*s-r*yu[3])*t;
1113 pv[l] = (yv[l]*s-r*yv[3])*t;
1116 kb->pn[o][0] = pu[1]*pv[2]-pu[2]*pv[1];
1117 kb->pn[o][1] = pu[2]*pv[0]-pu[0]*pv[2];
1118 kb->pn[o][2] = pu[0]*pv[1]-pu[1]*pv[0];
1119 t = 1.0/sqrt(kb->pn[o][0]*kb->pn[o][0]+kb->pn[o][1]*kb->pn[o][1]+
1120 kb->pn[o][2]*kb->pn[o][2]);
1127 if (colors == COLORS_TWOSIDED)
1129 glColor3fv(mat_diff_red);
1130 if (display_mode == DISP_TRANSPARENT)
1132 glMaterialfv(GL_FRONT,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_red);
1133 glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_green);
1137 glMaterialfv(GL_FRONT,GL_AMBIENT_AND_DIFFUSE,mat_diff_red);
1138 glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,mat_diff_green);
1141 glBindTexture(GL_TEXTURE_2D,kb->tex_name);
1143 for (i=0; i<NUMU; i++)
1145 if (appearance == APPEARANCE_BANDS && ((i & (NUMB-1)) >= NUMB/2))
1147 if (display_mode == DISP_WIREFRAME)
1148 glBegin(GL_QUAD_STRIP);
1150 glBegin(GL_TRIANGLE_STRIP);
1151 for (j=0; j<=NUMV; j++)
1153 for (k=0; k<=1; k++)
1158 glNormal3fv(kb->pn[o]);
1159 glTexCoord2fv(kb->tex[o]);
1160 if (colors != COLORS_TWOSIDED)
1162 glColor3fv(kb->col[o]);
1163 glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,kb->col[o]);
1165 glVertex3fv(kb->pp[o]);
1176 /* Draw a Lawson Klein bottle projected into 3D. */
1177 static int lawson(ModeInfo *mi, double umin, double umax, double vmin,
1181 static const GLfloat mat_diff_red[] = { 1.0, 0.0, 0.0, 1.0 };
1182 static const GLfloat mat_diff_green[] = { 0.0, 1.0, 0.0, 1.0 };
1183 static const GLfloat mat_diff_trans_red[] = { 1.0, 0.0, 0.0, 0.7 };
1184 static const GLfloat mat_diff_trans_green[] = { 0.0, 1.0, 0.0, 0.7 };
1185 float p[3], pu[3], pv[3], pm[3], n[3], b[3], mat[4][4];
1186 int i, j, k, l, m, o;
1188 double cu, su, cv, sv, cv2, sv2;
1189 double xx[4], xxu[4], xxv[4], y[4], yu[4], yv[4];
1191 float q1[4], q2[4], r1[4][4], r2[4][4];
1192 kleinstruct *kb = &klein[MI_SCREEN(mi)];
1194 if (view == VIEW_WALK || view == VIEW_WALKTURN)
1196 /* Compute the rotation that rotates the Klein bottle in 4D without the
1197 trackball rotations. */
1198 rotateall4d(kb->zeta,kb->eta,kb->theta,mat);
1218 xxv[2] = su*cv2*0.5;
1219 xxv[3] = -su*sv2*0.5;
1222 y[l] = (mat[l][0]*xx[0]+mat[l][1]*xx[1]+
1223 mat[l][2]*xx[2]+mat[l][3]*xx[3]);
1224 yu[l] = (mat[l][0]*xxu[0]+mat[l][1]*xxu[1]+
1225 mat[l][2]*xxu[2]+mat[l][3]*xxu[3]);
1226 yv[l] = (mat[l][0]*xxv[0]+mat[l][1]*xxv[1]+
1227 mat[l][2]*xxv[2]+mat[l][3]*xxv[3]);
1229 if (projection_4d == DISP_4D_ORTHOGRAPHIC)
1233 p[l] = y[l]+kb->offset4d[l];
1240 s = y[3]+kb->offset4d[3];
1245 r = y[l]+kb->offset4d[l];
1247 pu[l] = (yu[l]*s-r*yu[3])*t;
1248 pv[l] = (yv[l]*s-r*yv[3])*t;
1251 n[0] = pu[1]*pv[2]-pu[2]*pv[1];
1252 n[1] = pu[2]*pv[0]-pu[0]*pv[2];
1253 n[2] = pu[0]*pv[1]-pu[1]*pv[0];
1254 t = 1.0/(kb->side*4.0*sqrt(n[0]*n[0]+n[1]*n[1]+n[2]*n[2]));
1258 pm[0] = pu[0]*kb->dumove+pv[0]*kb->dvmove;
1259 pm[1] = pu[1]*kb->dumove+pv[1]*kb->dvmove;
1260 pm[2] = pu[2]*kb->dumove+pv[2]*kb->dvmove;
1261 t = 1.0/(4.0*sqrt(pm[0]*pm[0]+pm[1]*pm[1]+pm[2]*pm[2]));
1265 b[0] = n[1]*pm[2]-n[2]*pm[1];
1266 b[1] = n[2]*pm[0]-n[0]*pm[2];
1267 b[2] = n[0]*pm[1]-n[1]*pm[0];
1268 t = 1.0/(4.0*sqrt(b[0]*b[0]+b[1]*b[1]+b[2]*b[2]));
1273 /* Compute alpha, beta, delta from the three basis vectors.
1274 | -b[0] -b[1] -b[2] |
1275 m = | n[0] n[1] n[2] |
1276 | -pm[0] -pm[1] -pm[2] |
1278 kb->alpha = atan2(-n[2],-pm[2])*180/M_PI;
1279 kb->beta = atan2( -b[2],sqrt(b[0]*b[0]+b[1]*b[1]))*180/M_PI;
1280 kb->delta = atan2(b[1],-b[0])*180/M_PI;
1282 /* Compute the rotation that rotates the Klein bottle in 4D. */
1283 rotateall(kb->alpha,kb->beta,kb->delta,kb->zeta,kb->eta,kb->theta,mat);
1301 r += mat[l][m]*xx[m];
1304 if (projection_4d == DISP_4D_ORTHOGRAPHIC)
1307 p[l] = y[l]+kb->offset4d[l];
1311 s = y[3]+kb->offset4d[3];
1313 p[l] = (y[l]+kb->offset4d[l])/s;
1316 kb->offset3d[0] = -p[0];
1317 kb->offset3d[1] = -p[1]-DELTAY;
1318 kb->offset3d[2] = -p[2];
1322 /* Compute the rotation that rotates the Klein bottle in 4D, including
1323 the trackball rotations. */
1324 rotateall(kb->alpha,kb->beta,kb->delta,kb->zeta,kb->eta,kb->theta,r1);
1326 gltrackball_get_quaternion(kb->trackballs[0],q1);
1327 gltrackball_get_quaternion(kb->trackballs[1],q2);
1328 quats_to_rotmat(q1,q2,r2);
1330 mult_rotmat(r2,r1,mat);
1333 /* Project the points from 4D to 3D. */
1334 for (i=0; i<=NUMV; i++)
1336 for (j=0; j<=NUMU; j++)
1341 y[l] = (mat[l][0]*kb->x[o][0]+mat[l][1]*kb->x[o][1]+
1342 mat[l][2]*kb->x[o][2]+mat[l][3]*kb->x[o][3]);
1343 yu[l] = (mat[l][0]*kb->xu[o][0]+mat[l][1]*kb->xu[o][1]+
1344 mat[l][2]*kb->xu[o][2]+mat[l][3]*kb->xu[o][3]);
1345 yv[l] = (mat[l][0]*kb->xv[o][0]+mat[l][1]*kb->xv[o][1]+
1346 mat[l][2]*kb->xv[o][2]+mat[l][3]*kb->xv[o][3]);
1348 if (projection_4d == DISP_4D_ORTHOGRAPHIC)
1352 kb->pp[o][l] = (y[l]+kb->offset4d[l])+kb->offset3d[l];
1359 s = y[3]+kb->offset4d[3];
1364 r = y[l]+kb->offset4d[l];
1365 kb->pp[o][l] = r*q+kb->offset3d[l];
1366 pu[l] = (yu[l]*s-r*yu[3])*t;
1367 pv[l] = (yv[l]*s-r*yv[3])*t;
1370 kb->pn[o][0] = pu[1]*pv[2]-pu[2]*pv[1];
1371 kb->pn[o][1] = pu[2]*pv[0]-pu[0]*pv[2];
1372 kb->pn[o][2] = pu[0]*pv[1]-pu[1]*pv[0];
1373 t = 1.0/sqrt(kb->pn[o][0]*kb->pn[o][0]+kb->pn[o][1]*kb->pn[o][1]+
1374 kb->pn[o][2]*kb->pn[o][2]);
1381 if (colors == COLORS_TWOSIDED)
1383 glColor3fv(mat_diff_red);
1384 if (display_mode == DISP_TRANSPARENT)
1386 glMaterialfv(GL_FRONT,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_red);
1387 glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_green);
1391 glMaterialfv(GL_FRONT,GL_AMBIENT_AND_DIFFUSE,mat_diff_red);
1392 glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,mat_diff_green);
1395 glBindTexture(GL_TEXTURE_2D,kb->tex_name);
1397 for (i=0; i<NUMV; i++)
1399 if (appearance == APPEARANCE_BANDS && ((i & (NUMB-1)) >= NUMB/2))
1401 if (display_mode == DISP_WIREFRAME)
1402 glBegin(GL_QUAD_STRIP);
1404 glBegin(GL_TRIANGLE_STRIP);
1405 for (j=0; j<=NUMU; j++)
1407 for (k=0; k<=1; k++)
1412 glNormal3fv(kb->pn[o]);
1413 glTexCoord2fv(kb->tex[o]);
1414 if (colors != COLORS_TWOSIDED)
1416 glColor3fv(kb->col[o]);
1417 glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,kb->col[o]);
1419 glVertex3fv(kb->pp[o]);
1430 /* Generate a texture image that shows the orientation reversal. */
1431 static void gen_texture(ModeInfo *mi)
1433 kleinstruct *kb = &klein[MI_SCREEN(mi)];
1435 glGenTextures(1,&kb->tex_name);
1436 glBindTexture(GL_TEXTURE_2D,kb->tex_name);
1437 glPixelStorei(GL_UNPACK_ALIGNMENT,1);
1438 glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_WRAP_S,GL_REPEAT);
1439 glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_WRAP_T,GL_REPEAT);
1440 glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_MAG_FILTER,GL_LINEAR);
1441 glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_MIN_FILTER,GL_LINEAR);
1442 glTexEnvf(GL_TEXTURE_ENV,GL_TEXTURE_ENV_MODE,GL_MODULATE);
1443 glTexImage2D(GL_TEXTURE_2D,0,GL_RGB,TEX_DIMENSION,TEX_DIMENSION,0,
1444 GL_LUMINANCE,GL_UNSIGNED_BYTE,texture);
1448 static void init(ModeInfo *mi)
1450 static const GLfloat light_ambient[] = { 0.0, 0.0, 0.0, 1.0 };
1451 static const GLfloat light_diffuse[] = { 1.0, 1.0, 1.0, 1.0 };
1452 static const GLfloat light_specular[] = { 1.0, 1.0, 1.0, 1.0 };
1453 static const GLfloat light_position[] = { 1.0, 1.0, 1.0, 0.0 };
1454 static const GLfloat mat_specular[] = { 1.0, 1.0, 1.0, 1.0 };
1455 kleinstruct *kb = &klein[MI_SCREEN(mi)];
1457 if (walk_speed == 0.0)
1460 if (view == VIEW_TURN)
1462 kb->alpha = frand(360.0);
1463 kb->beta = frand(360.0);
1464 kb->delta = frand(360.0);
1473 if (bottle_type == KLEIN_BOTTLE_FIGURE_8)
1478 kb->umove = frand(2.0*M_PI);
1479 kb->vmove = frand(2.0*M_PI);
1484 if (bottle_type == KLEIN_BOTTLE_FIGURE_8)
1486 kb->offset4d[0] = 0.0;
1487 kb->offset4d[1] = 0.0;
1488 kb->offset4d[2] = 0.0;
1489 kb->offset4d[3] = 1.5;
1490 kb->offset3d[0] = 0.0;
1491 kb->offset3d[1] = 0.0;
1492 if (projection_4d == DISP_4D_ORTHOGRAPHIC)
1493 kb->offset3d[2] = -2.1;
1495 kb->offset3d[2] = -1.9;
1496 kb->offset3d[3] = 0.0;
1500 kb->offset4d[0] = 0.0;
1501 kb->offset4d[1] = 0.0;
1502 kb->offset4d[2] = 0.0;
1503 if (projection_4d == DISP_4D_PERSPECTIVE &&
1504 projection_3d == DISP_3D_ORTHOGRAPHIC)
1505 kb->offset4d[3] = 1.5;
1507 kb->offset4d[3] = 1.1;
1508 kb->offset3d[0] = 0.0;
1509 kb->offset3d[1] = 0.0;
1510 if (projection_4d == DISP_4D_ORTHOGRAPHIC)
1511 kb->offset3d[2] = -2.0;
1513 kb->offset3d[2] = -5.0;
1514 kb->offset3d[3] = 0.0;
1518 if (bottle_type == KLEIN_BOTTLE_FIGURE_8)
1519 setup_figure8(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
1521 setup_lawson(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
1524 glEnable(GL_TEXTURE_2D);
1526 glDisable(GL_TEXTURE_2D);
1528 glMatrixMode(GL_PROJECTION);
1530 if (projection_3d == DISP_3D_PERSPECTIVE ||
1531 view == VIEW_WALK || view == VIEW_WALKTURN)
1533 if (view == VIEW_WALK || view == VIEW_WALKTURN)
1534 gluPerspective(60.0,1.0,0.01,10.0);
1536 gluPerspective(60.0,1.0,0.1,10.0);
1540 glOrtho(-1.0,1.0,-1.0,1.0,0.1,10.0);
1542 glMatrixMode(GL_MODELVIEW);
1545 if (display_mode == DISP_WIREFRAME)
1547 glDisable(GL_DEPTH_TEST);
1548 glShadeModel(GL_FLAT);
1549 glPolygonMode(GL_FRONT_AND_BACK,GL_LINE);
1550 glDisable(GL_LIGHTING);
1551 glDisable(GL_LIGHT0);
1552 glDisable(GL_BLEND);
1554 else if (display_mode == DISP_SURFACE)
1556 glEnable(GL_DEPTH_TEST);
1557 glDepthFunc(GL_LESS);
1558 glShadeModel(GL_SMOOTH);
1559 glPolygonMode(GL_FRONT_AND_BACK,GL_FILL);
1560 glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE);
1561 glEnable(GL_LIGHTING);
1562 glEnable(GL_LIGHT0);
1563 glLightfv(GL_LIGHT0,GL_AMBIENT,light_ambient);
1564 glLightfv(GL_LIGHT0,GL_DIFFUSE,light_diffuse);
1565 glLightfv(GL_LIGHT0,GL_SPECULAR,light_specular);
1566 glLightfv(GL_LIGHT0,GL_POSITION,light_position);
1567 glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mat_specular);
1568 glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,50.0);
1569 glDepthMask(GL_TRUE);
1570 glDisable(GL_BLEND);
1572 else if (display_mode == DISP_TRANSPARENT)
1574 glDisable(GL_DEPTH_TEST);
1575 glShadeModel(GL_SMOOTH);
1576 glPolygonMode(GL_FRONT_AND_BACK,GL_FILL);
1577 glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE);
1578 glEnable(GL_LIGHTING);
1579 glEnable(GL_LIGHT0);
1580 glLightfv(GL_LIGHT0,GL_AMBIENT,light_ambient);
1581 glLightfv(GL_LIGHT0,GL_DIFFUSE,light_diffuse);
1582 glLightfv(GL_LIGHT0,GL_SPECULAR,light_specular);
1583 glLightfv(GL_LIGHT0,GL_POSITION,light_position);
1584 glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mat_specular);
1585 glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,50.0);
1586 glDepthMask(GL_FALSE);
1588 glBlendFunc(GL_SRC_ALPHA,GL_ONE);
1592 glDisable(GL_DEPTH_TEST);
1593 glShadeModel(GL_FLAT);
1594 glPolygonMode(GL_FRONT_AND_BACK,GL_LINE);
1595 glDisable(GL_LIGHTING);
1596 glDisable(GL_LIGHT0);
1597 glDisable(GL_BLEND);
1602 /* Redisplay the Klein bottle. */
1603 static void display_klein(ModeInfo *mi)
1605 kleinstruct *kb = &klein[MI_SCREEN(mi)];
1607 if (!kb->button_pressed)
1609 if (view == VIEW_TURN)
1611 kb->alpha += speed_wx * kb->speed_scale;
1612 if (kb->alpha >= 360.0)
1614 kb->beta += speed_wy * kb->speed_scale;
1615 if (kb->beta >= 360.0)
1617 kb->delta += speed_wz * kb->speed_scale;
1618 if (kb->delta >= 360.0)
1620 kb->zeta += speed_xy * kb->speed_scale;
1621 if (kb->zeta >= 360.0)
1623 kb->eta += speed_xz * kb->speed_scale;
1624 if (kb->eta >= 360.0)
1626 kb->theta += speed_yz * kb->speed_scale;
1627 if (kb->theta >= 360.0)
1630 if (view == VIEW_WALKTURN)
1632 kb->zeta += speed_xy * kb->speed_scale;
1633 if (kb->zeta >= 360.0)
1635 kb->eta += speed_xz * kb->speed_scale;
1636 if (kb->eta >= 360.0)
1638 kb->theta += speed_yz * kb->speed_scale;
1639 if (kb->theta >= 360.0)
1642 if (view == VIEW_WALK || view == VIEW_WALKTURN)
1644 kb->dvmove = cos(walk_direction*M_PI/180.0)*walk_speed*M_PI/4096.0;
1645 kb->vmove += kb->dvmove;
1646 if (kb->vmove >= 2.0*M_PI)
1648 kb->vmove -= 2.0*M_PI;
1649 kb->umove = 2.0*M_PI-kb->umove;
1650 kb->side = -kb->side;
1652 kb->dumove = (kb->side*sin(walk_direction*M_PI/180.0)*
1653 walk_speed*M_PI/4096.0);
1654 kb->umove += kb->dumove;
1655 if (kb->umove >= 2.0*M_PI)
1656 kb->umove -= 2.0*M_PI;
1657 if (kb->umove < 0.0)
1658 kb->umove += 2.0*M_PI;
1662 glMatrixMode(GL_PROJECTION);
1664 if (projection_3d == DISP_3D_PERSPECTIVE ||
1665 view == VIEW_WALK || view == VIEW_WALKTURN)
1667 if (view == VIEW_WALK || view == VIEW_WALKTURN)
1668 gluPerspective(60.0,kb->aspect,0.01,10.0);
1670 gluPerspective(60.0,kb->aspect,0.1,10.0);
1674 if (kb->aspect >= 1.0)
1675 glOrtho(-kb->aspect,kb->aspect,-1.0,1.0,0.1,10.0);
1677 glOrtho(-1.0,1.0,-1.0/kb->aspect,1.0/kb->aspect,0.1,10.0);
1679 glMatrixMode(GL_MODELVIEW);
1682 if (bottle_type == KLEIN_BOTTLE_FIGURE_8)
1683 mi->polygon_count = figure8(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
1685 mi->polygon_count = lawson(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
1689 ENTRYPOINT void reshape_klein(ModeInfo *mi, int width, int height)
1691 kleinstruct *kb = &klein[MI_SCREEN(mi)];
1693 kb->WindW = (GLint)width;
1694 kb->WindH = (GLint)height;
1695 glViewport(0,0,width,height);
1696 kb->aspect = (GLfloat)width/(GLfloat)height;
1700 ENTRYPOINT Bool klein_handle_event(ModeInfo *mi, XEvent *event)
1702 Display *display = MI_DISPLAY(mi);
1703 kleinstruct *kb = &klein[MI_SCREEN(mi)];
1706 if (event->xany.type == ButtonPress &&
1707 event->xbutton.button == Button1)
1709 kb->button_pressed = True;
1710 gltrackball_start(kb->trackballs[kb->current_trackball],
1711 event->xbutton.x, event->xbutton.y,
1712 MI_WIDTH(mi), MI_HEIGHT(mi));
1715 else if (event->xany.type == ButtonRelease &&
1716 event->xbutton.button == Button1)
1718 kb->button_pressed = False;
1721 else if (event->xany.type == KeyPress)
1723 sym = XKeycodeToKeysym(display,event->xkey.keycode,0);
1724 if (sym == XK_Shift_L || sym == XK_Shift_R)
1726 kb->current_trackball = 1;
1727 if (kb->button_pressed)
1728 gltrackball_start(kb->trackballs[kb->current_trackball],
1729 event->xbutton.x, event->xbutton.y,
1730 MI_WIDTH(mi), MI_HEIGHT(mi));
1734 else if (event->xany.type == KeyRelease)
1736 sym = XKeycodeToKeysym(display,event->xkey.keycode,0);
1737 if (sym == XK_Shift_L || sym == XK_Shift_R)
1739 kb->current_trackball = 0;
1740 if (kb->button_pressed)
1741 gltrackball_start(kb->trackballs[kb->current_trackball],
1742 event->xbutton.x, event->xbutton.y,
1743 MI_WIDTH(mi), MI_HEIGHT(mi));
1747 else if (event->xany.type == MotionNotify && kb->button_pressed)
1749 gltrackball_track(kb->trackballs[kb->current_trackball],
1750 event->xmotion.x, event->xmotion.y,
1751 MI_WIDTH(mi), MI_HEIGHT(mi));
1760 *-----------------------------------------------------------------------------
1761 *-----------------------------------------------------------------------------
1763 *-----------------------------------------------------------------------------
1764 *-----------------------------------------------------------------------------
1768 *-----------------------------------------------------------------------------
1769 * Initialize klein. Called each time the window changes.
1770 *-----------------------------------------------------------------------------
1773 ENTRYPOINT void init_klein(ModeInfo *mi)
1779 klein = (kleinstruct *)calloc(MI_NUM_SCREENS(mi),
1780 sizeof(kleinstruct));
1784 kb = &klein[MI_SCREEN(mi)];
1787 kb->trackballs[0] = gltrackball_init();
1788 kb->trackballs[1] = gltrackball_init();
1789 kb->current_trackball = 0;
1790 kb->button_pressed = False;
1792 /* Set the Klein bottle. */
1793 if (!strcasecmp(klein_bottle,"random"))
1795 bottle_type = random() % NUM_KLEIN_BOTTLES;
1797 else if (!strcasecmp(klein_bottle,"figure-8"))
1799 bottle_type = KLEIN_BOTTLE_FIGURE_8;
1801 else if (!strcasecmp(klein_bottle,"lawson"))
1803 bottle_type = KLEIN_BOTTLE_LAWSON;
1807 bottle_type = random() % NUM_KLEIN_BOTTLES;
1810 /* Set the display mode. */
1811 if (!strcasecmp(mode,"random"))
1813 display_mode = random() % NUM_DISPLAY_MODES;
1815 else if (!strcasecmp(mode,"wireframe"))
1817 display_mode = DISP_WIREFRAME;
1819 else if (!strcasecmp(mode,"surface"))
1821 display_mode = DISP_SURFACE;
1823 else if (!strcasecmp(mode,"transparent"))
1825 display_mode = DISP_TRANSPARENT;
1829 display_mode = random() % NUM_DISPLAY_MODES;
1832 /* Orientation marks don't make sense in wireframe mode. */
1833 if (display_mode == DISP_WIREFRAME)
1836 /* Set the appearance. */
1837 if (!strcasecmp(appear,"random"))
1839 appearance = random() % NUM_APPEARANCES;
1841 else if (!strcasecmp(appear,"solid"))
1843 appearance = APPEARANCE_SOLID;
1845 else if (!strcasecmp(appear,"bands"))
1847 appearance = APPEARANCE_BANDS;
1851 appearance = random() % NUM_APPEARANCES;
1854 /* Set the color mode. */
1855 if (!strcasecmp(color_mode,"random"))
1857 colors = random() % NUM_COLORS;
1859 else if (!strcasecmp(color_mode,"two-sided"))
1861 colors = COLORS_TWOSIDED;
1863 else if (!strcasecmp(color_mode,"rainbow"))
1865 colors = COLORS_RAINBOW;
1867 else if (!strcasecmp(color_mode,"depth"))
1869 colors = COLORS_DEPTH;
1873 colors = random() % NUM_COLORS;
1876 /* Set the view mode. */
1877 if (!strcasecmp(view_mode,"random"))
1879 view = random() % NUM_VIEW_MODES;
1881 else if (!strcasecmp(view_mode,"walk"))
1885 else if (!strcasecmp(view_mode,"turn"))
1889 else if (!strcasecmp(view_mode,"walk-turn"))
1891 view = VIEW_WALKTURN;
1895 view = random() % NUM_VIEW_MODES;
1898 /* Set the 3d projection mode. */
1899 if (!strcasecmp(proj_3d,"random"))
1901 /* Orthographic projection only makes sense in turn mode. */
1902 if (view == VIEW_TURN)
1903 projection_3d = random() % NUM_DISP_3D_MODES;
1905 projection_3d = DISP_3D_PERSPECTIVE;
1907 else if (!strcasecmp(proj_3d,"perspective"))
1909 projection_3d = DISP_3D_PERSPECTIVE;
1911 else if (!strcasecmp(proj_3d,"orthographic"))
1913 projection_3d = DISP_3D_ORTHOGRAPHIC;
1917 /* Orthographic projection only makes sense in turn mode. */
1918 if (view == VIEW_TURN)
1919 projection_3d = random() % NUM_DISP_3D_MODES;
1921 projection_3d = DISP_3D_PERSPECTIVE;
1924 /* Set the 4d projection mode. */
1925 if (!strcasecmp(proj_4d,"random"))
1927 projection_4d = random() % NUM_DISP_4D_MODES;
1929 else if (!strcasecmp(proj_4d,"perspective"))
1931 projection_4d = DISP_4D_PERSPECTIVE;
1933 else if (!strcasecmp(proj_4d,"orthographic"))
1935 projection_4d = DISP_4D_ORTHOGRAPHIC;
1939 projection_4d = random() % NUM_DISP_4D_MODES;
1942 /* Modify the speeds to a useful range in walk-and-turn mode. */
1943 if (view == VIEW_WALKTURN)
1953 /* make multiple screens rotate at slightly different rates. */
1954 kb->speed_scale = 0.9 + frand(0.3);
1956 if ((kb->glx_context = init_GL(mi)) != NULL)
1958 reshape_klein(mi,MI_WIDTH(mi),MI_HEIGHT(mi));
1959 glDrawBuffer(GL_BACK);
1969 *-----------------------------------------------------------------------------
1970 * Called by the mainline code periodically to update the display.
1971 *-----------------------------------------------------------------------------
1973 ENTRYPOINT void draw_klein(ModeInfo *mi)
1975 Display *display = MI_DISPLAY(mi);
1976 Window window = MI_WINDOW(mi);
1981 kb = &klein[MI_SCREEN(mi)];
1983 MI_IS_DRAWN(mi) = True;
1984 if (!kb->glx_context)
1987 glXMakeCurrent(display,window,*(kb->glx_context));
1989 glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
1999 glXSwapBuffers(display,window);
2004 *-----------------------------------------------------------------------------
2005 * The display is being taken away from us. Free up malloc'ed
2006 * memory and X resources that we've alloc'ed. Only called
2007 * once, we must zap everything for every screen.
2008 *-----------------------------------------------------------------------------
2011 ENTRYPOINT void release_klein(ModeInfo *mi)
2017 for (screen = 0; screen < MI_NUM_SCREENS(mi); screen++)
2019 kleinstruct *kb = &klein[screen];
2021 if (kb->glx_context)
2022 kb->glx_context = (GLXContext *)NULL;
2024 (void) free((void *)klein);
2025 klein = (kleinstruct *)NULL;
2031 ENTRYPOINT void change_klein(ModeInfo *mi)
2033 kleinstruct *kb = &klein[MI_SCREEN(mi)];
2035 if (!kb->glx_context)
2038 glXMakeCurrent(MI_DISPLAY(mi),MI_WINDOW(mi),*(kb->glx_context));
2041 #endif /* !STANDALONE */
2043 XSCREENSAVER_MODULE ("Klein", klein)