static const char sccsid[] = "@(#)klein.c 1.1 08/10/04 xlockmore";
#endif
-/* Copyright (c) 2005-2009 Carsten Steger <carsten@mirsanmir.org>. */
+/* Copyright (c) 2005-2014 Carsten Steger <carsten@mirsanmir.org>. */
/*
* Permission to use, copy, modify, and distribute this software and its
* REVISION HISTORY:
* C. Steger - 08/10/04: Initial version
* C. Steger - 09/08/03: Changes to the parameter handling
+ * C. Steger - 13/12/25: Added the squeezed torus Klein bottle
+ * C. Steger - 14/10/03: Moved the curlicue texture to curlicue.h
*/
/*
- * This program shows two different Klein bottles in 4d: the figure-8 Klein
- * bottle or the Lawson Klein bottle. You can walk on the Klein bottle, see
- * it turn in 4d, or walk on it while it turns in 4d. The figure-8 Klein
- * bottle is well known in its 3d form. The 4d form used in this program is
- * an extension of the 3d form to 4d that does not intersect itself in 4d
- * (which can be seen in the depth colors mode). The Lawson Klein bottle,
+ * This program shows three different Klein bottles in 4d: the figure-8 Klein
+ * bottle, the squeezed torus Klein bottle, or the Lawson Klein bottle. You
+ * can walk on the Klein bottle, see it turn in 4d, or walk on it while it
+ * turns in 4d. The figure-8 Klein bottle is well known in its 3d form. The
+ * 4d form used in this program is an extension of the 3d form to 4d that
+ * does not intersect itself in 4d (which can be seen in the depth colors
+ * mode). The squeezed torus Klein bottle also does not intersect itself in
+ * 4d (which can be seen in the depth colors mode). The Lawson Klein bottle,
* on the other hand, does intersect itself in 4d. Its primary use is that
* it has a nice appearance for walking and for turning in 3d. The Klein
* bottle is a non-orientable surface. To make this apparent, the two-sided
* Klein bottle. For example, the Lawson Klein bottle looks nicest when
* projected perspectively. The figure-8 Klein bottle, on the other
* hand, looks nicer while walking when projected orthographically from 4d.
- * The projected Klein bottle can then be projected to the screen either
- * perspectively or orthographically. When using the walking modes,
- * perspective projection to the screen should be used. There are three
- * display modes for the Klein bottle: mesh (wireframe), solid, or
+ * For the squeezed torus Klein bottle, both projection modes give equally
+ * acceptable projections. The projected Klein bottle can then be projected
+ * to the screen either perspectively or orthographically. When using the
+ * walking modes, perspective projection to the screen should be used. There
+ * are three display modes for the Klein bottle: mesh (wireframe), solid, or
* transparent. Furthermore, the appearance of the Klein bottle can be as
* a solid object or as a set of see-through bands. Finally, the colors
* with with the Klein bottle is drawn can be set to two-sided, rainbow, or
* combined with the see-through bands mode or with the orientation markers
* drawn. The third mode draws the Klein bottle with colors that are chosen
* according to the 4d "depth" of the points. This mode enables you to see
- * that the figure-8 Klein bottle does not intersect itself in 4d, while the
- * Lawson Klein bottle does intersect itself. The rotation speed for each
- * of the six planes around which the Klein bottle rotates can be chosen.
- * For the walk-and-turn more, only the rotation speeds around the true 4d
- * planes are used (the xy, xz, and yz planes). Furthermore, in the walking
- * modes the walking direction in the 2d base square of the Klein bottle and
- * the walking speed can be chosen. This program is somewhat inspired by
- * Thomas Banchoff's book "Beyond the Third Dimension: Geometry, Computer
- * Graphics, and Higher Dimensions", Scientific American Library, 1990.
+ * that the figure-8 and squeezed torus Klein bottles do not intersect
+ * themselves in 4d, while the Lawson Klein bottle does intersect itself.
+ * The rotation speed for each of the six planes around which the Klein
+ * bottle rotates can be chosen. For the walk-and-turn more, only the
+ * rotation speeds around the true 4d planes are used (the xy, xz, and yz
+ * planes). Furthermore, in the walking modes the walking direction in the
+ * 2d base square of the Klein bottle and the walking speed can be chosen.
+ * This program is somewhat inspired by Thomas Banchoff's book "Beyond the
+ * Third Dimension: Geometry, Computer Graphics, and Higher Dimensions",
+ * Scientific American Library, 1990.
*/
+#include "curlicue.h"
+
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
-#define KLEIN_BOTTLE_FIGURE_8 0
-#define KLEIN_BOTTLE_LAWSON 1
-#define NUM_KLEIN_BOTTLES 2
-
-#define DISP_WIREFRAME 0
-#define DISP_SURFACE 1
-#define DISP_TRANSPARENT 2
-#define NUM_DISPLAY_MODES 3
-
-#define APPEARANCE_SOLID 0
-#define APPEARANCE_BANDS 1
-#define NUM_APPEARANCES 2
-
-#define COLORS_TWOSIDED 0
-#define COLORS_RAINBOW 1
-#define COLORS_DEPTH 2
-#define NUM_COLORS 3
-
-#define VIEW_WALK 0
-#define VIEW_TURN 1
-#define VIEW_WALKTURN 2
-#define NUM_VIEW_MODES 3
-
-#define DISP_3D_PERSPECTIVE 0
-#define DISP_3D_ORTHOGRAPHIC 1
-#define NUM_DISP_3D_MODES 2
-
-#define DISP_4D_PERSPECTIVE 0
-#define DISP_4D_ORTHOGRAPHIC 1
-#define NUM_DISP_4D_MODES 2
-
-#define DEF_KLEIN_BOTTLE "random"
-#define DEF_DISPLAY_MODE "random"
-#define DEF_APPEARANCE "random"
-#define DEF_COLORS "random"
-#define DEF_VIEW_MODE "random"
-#define DEF_MARKS "False"
-#define DEF_PROJECTION_3D "random"
-#define DEF_PROJECTION_4D "random"
-#define DEF_SPEEDWX "1.1"
-#define DEF_SPEEDWY "1.3"
-#define DEF_SPEEDWZ "1.5"
-#define DEF_SPEEDXY "1.7"
-#define DEF_SPEEDXZ "1.9"
-#define DEF_SPEEDYZ "2.1"
-#define DEF_WALK_DIRECTION "7.0"
-#define DEF_WALK_SPEED "20.0"
+#define KLEIN_BOTTLE_FIGURE_8 0
+#define KLEIN_BOTTLE_SQUEEZED_TORUS 1
+#define KLEIN_BOTTLE_LAWSON 2
+#define NUM_KLEIN_BOTTLES 3
+
+#define DISP_WIREFRAME 0
+#define DISP_SURFACE 1
+#define DISP_TRANSPARENT 2
+#define NUM_DISPLAY_MODES 3
+
+#define APPEARANCE_SOLID 0
+#define APPEARANCE_BANDS 1
+#define NUM_APPEARANCES 2
+
+#define COLORS_TWOSIDED 0
+#define COLORS_RAINBOW 1
+#define COLORS_DEPTH 2
+#define NUM_COLORS 3
+
+#define VIEW_WALK 0
+#define VIEW_TURN 1
+#define VIEW_WALKTURN 2
+#define NUM_VIEW_MODES 3
+
+#define DISP_3D_PERSPECTIVE 0
+#define DISP_3D_ORTHOGRAPHIC 1
+#define NUM_DISP_3D_MODES 2
+
+#define DISP_4D_PERSPECTIVE 0
+#define DISP_4D_ORTHOGRAPHIC 1
+#define NUM_DISP_4D_MODES 2
+
+#define DEF_KLEIN_BOTTLE "random"
+#define DEF_DISPLAY_MODE "random"
+#define DEF_APPEARANCE "random"
+#define DEF_COLORS "random"
+#define DEF_VIEW_MODE "random"
+#define DEF_MARKS "False"
+#define DEF_PROJECTION_3D "random"
+#define DEF_PROJECTION_4D "random"
+#define DEF_SPEEDWX "1.1"
+#define DEF_SPEEDWY "1.3"
+#define DEF_SPEEDWZ "1.5"
+#define DEF_SPEEDXY "1.7"
+#define DEF_SPEEDXZ "1.9"
+#define DEF_SPEEDYZ "2.1"
+#define DEF_WALK_DIRECTION "7.0"
+#define DEF_WALK_SPEED "20.0"
#ifdef STANDALONE
# define DEFAULTS "*delay: 10000 \n" \
"*showFPS: False \n" \
# define refresh_klein 0
+# define release_klein 0
# include "xlockmore.h" /* from the xscreensaver distribution */
#else /* !STANDALONE */
# include "xlock.h" /* from the xlockmore distribution */
#ifdef USE_GL
-#include <X11/keysym.h>
+#ifndef HAVE_JWXYZ
+# include <X11/keysym.h>
+#endif
#include "gltrackball.h"
#ifdef USE_MODULES
ModStruct klein_description =
-{"klein", "init_klein", "draw_klein", "release_klein",
+{"klein", "init_klein", "draw_klein", NULL,
"draw_klein", "change_klein", NULL, &klein_opts,
25000, 1, 1, 1, 1.0, 4, "",
"Rotate a Klein bottle in 4d or walk on it", 0, NULL};
static char *klein_bottle;
-static int bottle_type;
static char *mode;
-static int display_mode;
static char *appear;
-static int appearance;
static char *color_mode;
-static int colors;
static char *view_mode;
-static int view;
static Bool marks;
static char *proj_3d;
-static int projection_3d;
static char *proj_4d;
-static int projection_4d;
static float speed_wx;
static float speed_wy;
static float speed_wz;
{
{"-klein-bottle", ".kleinBottle", XrmoptionSepArg, 0 },
{"-figure-8", ".kleinBottle", XrmoptionNoArg, "figure-8" },
+ {"-squeezed-torus", ".kleinBottle", XrmoptionNoArg, "squeezed-torus" },
{"-lawson", ".kleinBottle", XrmoptionNoArg, "lawson" },
{"-mode", ".displayMode", XrmoptionSepArg, 0 },
{"-wireframe", ".displayMode", XrmoptionNoArg, "wireframe" },
{sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, NULL};
-/* Radius of the Figure 8 Klein bottle */
+/* Radius of the figure-8 Klein bottle */
#define FIGURE_8_RADIUS 2.0
+/* Radius of the squeezed torus Klein bottle */
+#define SQUEEZED_TORUS_RADIUS 2.0
+
/* Offset by which we walk above the Klein bottle */
#define DELTAY 0.02
typedef struct {
GLint WindH, WindW;
GLXContext *glx_context;
+ /* Options */
+ int bottle_type;
+ int display_mode;
+ int appearance;
+ int colors;
+ int view;
+ int projection_3d;
+ int projection_4d;
/* 4D rotation angles */
float alpha, beta, delta, zeta, eta, theta;
/* Movement parameters */
static kleinstruct *klein = (kleinstruct *) NULL;
-/* A texture map containing a "curlicue" */
-#define TEX_DIMENSION 64
-static const unsigned char texture[TEX_DIMENSION*TEX_DIMENSION] = {
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 58, 43, 43, 43, 43, 45, 70, 70, 70,
- 70, 70, 70, 70, 74, 98, 98, 98,100,194,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 30,186,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 1,111,244,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 43,198,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 5,123,248,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 50,209,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,246,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
- 74,252,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,138, 4,
- 66,229,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
- 1,170,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,153, 0, 0,
- 0, 53,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 6,188,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,213, 7, 0, 0,
- 0, 0,226,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 45, 0, 0, 0, 0, 0, 47, 0, 0,
- 0, 0, 22,225,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,254, 54, 0, 0, 0,
- 0, 81,254,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 45, 0, 0, 0, 0, 56,247, 82, 0,
- 0, 0, 0, 59,253,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,152, 0, 0, 0, 0,
- 52,243,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 45, 0, 0, 0, 8,215,255,250, 56,
- 0, 0, 0, 0,142,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,241, 19, 0, 0, 0, 15,
- 220,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 45, 0, 0, 0,129,255,255,255,230,
- 23, 0, 0, 0, 12,230,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,131, 0, 0, 0, 0,157,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 45, 0, 0, 49,250,255,255,255,255,
- 171, 0, 0, 0, 0,112,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,246, 19, 0, 0, 0, 54,253,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 45, 0, 5,208,255,255,255,255,255,
- 255, 77, 0, 0, 0, 9,231,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,163, 0, 0, 0, 0,186,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 45, 0,121,255,255,255,255,255,255,
- 255,211, 2, 0, 0, 0,134,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255, 69, 0, 0, 0, 50,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 45, 41,247,255,255,255,255,255,255,
- 255,255, 73, 0, 0, 0, 38,254,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,237, 4, 0, 0, 0,145,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255, 52,201,255,255,255,255,255,255,255,
- 255,255,169, 0, 0, 0, 0,216,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,181, 0, 0, 0, 0,229,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,186,255,255,255,255,255,255,255,255,
- 255,255,247, 7, 0, 0, 0,150,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,130, 0, 0, 0, 42,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255, 67, 0, 0, 0, 91,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255, 79, 0, 0, 0, 95,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,120, 0, 0, 0, 56,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255, 55, 0, 0, 0,130,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,157, 0, 0, 0, 21,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255, 34, 0, 0, 0,161,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,179, 0, 0, 0, 2,250,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255, 27, 0, 0, 0,168,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,200, 0, 0, 0, 0,249,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255, 27, 0, 0, 0,168,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,200, 0, 0, 0, 0,249,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255, 27, 0, 0, 0,163,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,183, 0, 0, 0, 0,249,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255, 42, 0, 0, 0,135,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,161, 0, 0, 0, 17,254,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255, 76, 0, 0, 0,100,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,126, 0, 0, 0, 48,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,114, 0, 0, 0, 53,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255, 78, 0, 0, 0, 84,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,165, 0, 0, 0, 3,241,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,252, 16, 0, 0, 0,139,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,228, 0, 0, 0, 0,161,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,192, 0, 0, 0, 0,198,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255, 46, 0, 0, 0, 67,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255, 93, 0, 0, 0, 21,250,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,139, 0, 0, 0, 1,211,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,226, 7, 0, 0, 0,108,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,230, 6, 0, 0, 0, 79,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,106, 0, 0, 0, 1,206,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255, 97, 0, 0, 0, 0,183,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 202, 3, 0, 0, 0, 67,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,221, 8, 0, 0, 0, 27,
- 235,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,243,
- 40, 0, 0, 0, 0,198,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,126, 0, 0, 0, 0,
- 71,252,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,253, 85,
- 0, 0, 0, 0, 96,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,247, 44, 0, 0, 0,
- 0, 91,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,116, 0,
- 0, 0, 0, 25,233,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,216, 11, 0, 0,
- 0, 0, 90,251,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,252,112, 0, 0,
- 0, 0, 4,191,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,174, 4, 0,
- 0, 0, 0, 72,235,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,242, 84, 0, 0, 0,
- 0, 0,146,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,150, 1,
- 0, 0, 0, 0, 27,181,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,194, 39, 0, 0, 0, 0,
- 0,120,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,151,
- 4, 0, 0, 0, 0, 0, 77,209,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,216, 92, 1, 0, 0, 0, 0, 0,
- 125,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 175, 12, 0, 0, 0, 0, 0, 1, 70,164,241,255,255,255,255,255,
- 255,255,255,255,255,242,171, 77, 2, 0, 0, 0, 0, 0, 4,150,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,214, 41, 0, 0, 0, 0, 0, 0, 0, 4, 48, 98,138,163,163,
- 163,163,140,103, 55, 5, 0, 0, 0, 0, 0, 0, 0, 30,199,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,245,125, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3,105,240,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,222,100, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 83,210,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,228,136, 45, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 37,125,220,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,225,166,112, 74, 43, 32, 12,
- 8, 32, 40, 71,105,162,218,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
- 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
-};
-
-
/* Add a rotation around the wx-plane to the matrix m. */
static void rotatewx(float m[4][4], float phi)
{
/* Compute a fully saturated and bright color based on an angle. */
-static void color(double angle, float col[4])
+static void color(kleinstruct *kb, double angle, float col[4])
{
int s;
double t;
- if (colors == COLORS_TWOSIDED)
+ if (kb->colors == COLORS_TWOSIDED)
return;
if (angle >= 0.0)
col[2] = 1.0-t;
break;
}
- if (display_mode == DISP_TRANSPARENT)
+ if (kb->display_mode == DISP_TRANSPARENT)
col[3] = 0.7;
else
col[3] = 1.0;
k = i*(NUMV+1)+j;
u = -ur*j/NUMU+umin;
v = vr*i/NUMV+vmin;
- if (colors == COLORS_DEPTH)
- color((cos(u)+1.0)*M_PI*2.0/3.0,kb->col[k]);
+ if (kb->colors == COLORS_DEPTH)
+ color(kb,(cos(u)+1.0)*M_PI*2.0/3.0,kb->col[k]);
else
- color(v,kb->col[k]);
+ color(kb,v,kb->col[k]);
kb->tex[k][0] = -32*u/(2.0*M_PI);
kb->tex[k][1] = 32*v/(2.0*M_PI);
cu = cos(u);
}
+/* Set up the squeezed torus Klein bottle coordinates, colors, and texture. */
+static void setup_squeezed_torus(ModeInfo *mi, double umin, double umax,
+ double vmin, double vmax)
+{
+ int i, j, k, l;
+ double u, v, ur, vr;
+ double cu, su, cv, sv, cv2, sv2;
+ kleinstruct *kb = &klein[MI_SCREEN(mi)];
+
+ ur = umax-umin;
+ vr = vmax-vmin;
+ for (i=0; i<=NUMU; i++)
+ {
+ for (j=0; j<=NUMV; j++)
+ {
+ k = i*(NUMV+1)+j;
+ u = -ur*j/NUMU+umin;
+ v = vr*i/NUMV+vmin;
+ if (kb->colors == COLORS_DEPTH)
+ color(kb,(sin(u)*sin(0.5*v)+1.0)*M_PI*2.0/3.0,kb->col[k]);
+ else
+ color(kb,v,kb->col[k]);
+ kb->tex[k][0] = -32*u/(2.0*M_PI);
+ kb->tex[k][1] = 32*v/(2.0*M_PI);
+ cu = cos(u);
+ su = sin(u);
+ cv = cos(v);
+ sv = sin(v);
+ cv2 = cos(0.5*v);
+ sv2 = sin(0.5*v);
+ kb->x[k][0] = (SQUEEZED_TORUS_RADIUS+cu)*cv;
+ kb->x[k][1] = (SQUEEZED_TORUS_RADIUS+cu)*sv;
+ kb->x[k][2] = su*cv2;
+ kb->x[k][3] = su*sv2;
+ kb->xu[k][0] = -su*cv;
+ kb->xu[k][1] = -su*sv;
+ kb->xu[k][2] = cu*cv2;
+ kb->xu[k][3] = cu*sv2;
+ kb->xv[k][0] = -(SQUEEZED_TORUS_RADIUS+cu)*sv;
+ kb->xv[k][1] = (SQUEEZED_TORUS_RADIUS+cu)*cv;
+ kb->xv[k][2] = -0.5*su*sv2;
+ kb->xv[k][3] = 0.5*su*cv2;
+ for (l=0; l<4; l++)
+ {
+ kb->x[k][l] /= SQUEEZED_TORUS_RADIUS+1.25;
+ kb->xu[k][l] /= SQUEEZED_TORUS_RADIUS+1.25;
+ kb->xv[k][l] /= SQUEEZED_TORUS_RADIUS+1.25;
+ }
+ }
+ }
+}
+
+
/* Set up the Lawson Klein bottle coordinates, colors, and texture. */
static void setup_lawson(ModeInfo *mi, double umin, double umax, double vmin,
double vmax)
k = i*(NUMU+1)+j;
u = -ur*j/NUMU+umin;
v = vr*i/NUMV+vmin;
- if (colors == COLORS_DEPTH)
- color((sin(u)*cos(0.5*v)+1.0)*M_PI*2.0/3.0,kb->col[k]);
+ if (kb->colors == COLORS_DEPTH)
+ color(kb,(sin(u)*cos(0.5*v)+1.0)*M_PI*2.0/3.0,kb->col[k]);
else
- color(v,kb->col[k]);
+ color(kb,v,kb->col[k]);
kb->tex[k][0] = -32*u/(2.0*M_PI);
kb->tex[k][1] = 32*v/(2.0*M_PI);
cu = cos(u);
float q1[4], q2[4], r1[4][4], r2[4][4];
kleinstruct *kb = &klein[MI_SCREEN(mi)];
- if (view == VIEW_WALK || view == VIEW_WALKTURN)
+ if (kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN)
{
/* Compute the rotation that rotates the Klein bottle in 4D without the
trackball rotations. */
yv[l] = (mat[l][0]*xxv[0]+mat[l][1]*xxv[1]+
mat[l][2]*xxv[2]+mat[l][3]*xxv[3]);
}
- if (projection_4d == DISP_4D_ORTHOGRAPHIC)
+ if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC)
{
for (l=0; l<3; l++)
{
| -pm[0] -pm[1] -pm[2] |
*/
kb->alpha = atan2(-n[2],-pm[2])*180/M_PI;
- kb->beta = atan2( -b[2],sqrt(b[0]*b[0]+b[1]*b[1]))*180/M_PI;
+ kb->beta = atan2(-b[2],sqrt(b[0]*b[0]+b[1]*b[1]))*180/M_PI;
kb->delta = atan2(b[1],-b[0])*180/M_PI;
/* Compute the rotation that rotates the Klein bottle in 4D. */
r += mat[l][m]*xx[m];
y[l] = r;
}
- if (projection_4d == DISP_4D_ORTHOGRAPHIC)
+ if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC)
{
for (l=0; l<3; l++)
p[l] = y[l]+kb->offset4d[l];
yv[l] = (mat[l][0]*kb->xv[o][0]+mat[l][1]*kb->xv[o][1]+
mat[l][2]*kb->xv[o][2]+mat[l][3]*kb->xv[o][3]);
}
- if (projection_4d == DISP_4D_ORTHOGRAPHIC)
+ if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC)
{
for (l=0; l<3; l++)
{
}
}
- if (colors == COLORS_TWOSIDED)
+ if (kb->colors == COLORS_TWOSIDED)
{
glColor3fv(mat_diff_red);
- if (display_mode == DISP_TRANSPARENT)
+ if (kb->display_mode == DISP_TRANSPARENT)
{
glMaterialfv(GL_FRONT,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_red);
glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_green);
for (i=0; i<NUMU; i++)
{
- if (appearance == APPEARANCE_BANDS && ((i & (NUMB-1)) >= NUMB/2))
+ if (kb->appearance == APPEARANCE_BANDS && ((i & (NUMB-1)) >= NUMB/2))
continue;
- if (display_mode == DISP_WIREFRAME)
+ if (kb->display_mode == DISP_WIREFRAME)
glBegin(GL_QUAD_STRIP);
else
glBegin(GL_TRIANGLE_STRIP);
o = l*(NUMV+1)+m;
glNormal3fv(kb->pn[o]);
glTexCoord2fv(kb->tex[o]);
- if (colors != COLORS_TWOSIDED)
+ if (kb->colors != COLORS_TWOSIDED)
+ {
+ glColor3fv(kb->col[o]);
+ glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,kb->col[o]);
+ }
+ glVertex3fv(kb->pp[o]);
+ polys++;
+ }
+ }
+ glEnd();
+ }
+ polys /= 2;
+ return polys;
+}
+
+
+/* Draw a squeezed torus Klein bottle projected into 3D. */
+static int squeezed_torus(ModeInfo *mi, double umin, double umax, double vmin,
+ double vmax)
+{
+ int polys = 0;
+ static const GLfloat mat_diff_red[] = { 1.0, 0.0, 0.0, 1.0 };
+ static const GLfloat mat_diff_green[] = { 0.0, 1.0, 0.0, 1.0 };
+ static const GLfloat mat_diff_trans_red[] = { 1.0, 0.0, 0.0, 0.7 };
+ static const GLfloat mat_diff_trans_green[] = { 0.0, 1.0, 0.0, 0.7 };
+ float p[3], pu[3], pv[3], pm[3], n[3], b[3], mat[4][4];
+ int i, j, k, l, m, o;
+ double u, v;
+ double xx[4], xxu[4], xxv[4], y[4], yu[4], yv[4];
+ double q, r, s, t;
+ double cu, su, cv, sv, cv2, sv2;
+ float q1[4], q2[4], r1[4][4], r2[4][4];
+ kleinstruct *kb = &klein[MI_SCREEN(mi)];
+
+ if (kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN)
+ {
+ /* Compute the rotation that rotates the Klein bottle in 4D without the
+ trackball rotations. */
+ rotateall4d(kb->zeta,kb->eta,kb->theta,mat);
+
+ u = kb->umove;
+ v = kb->vmove;
+ cu = cos(u);
+ su = sin(u);
+ cv = cos(v);
+ sv = sin(v);
+ cv2 = cos(0.5*v);
+ sv2 = sin(0.5*v);
+ xx[0] = (SQUEEZED_TORUS_RADIUS+cu)*cv;
+ xx[1] = (SQUEEZED_TORUS_RADIUS+cu)*sv;
+ xx[2] = su*cv2;
+ xx[3] = su*sv2;
+ xxu[0] = -su*cv;
+ xxu[1] = -su*sv;
+ xxu[2] = cu*cv2;
+ xxu[3] = cu*sv2;
+ xxv[0] = -(SQUEEZED_TORUS_RADIUS+cu)*sv;
+ xxv[1] = (SQUEEZED_TORUS_RADIUS+cu)*cv;
+ xxv[2] = -0.5*su*sv2;
+ xxv[3] = 0.5*su*cv2;
+ for (l=0; l<4; l++)
+ {
+ xx[l] /= SQUEEZED_TORUS_RADIUS+1.25;
+ xxu[l] /= SQUEEZED_TORUS_RADIUS+1.25;
+ xxv[l] /= SQUEEZED_TORUS_RADIUS+1.25;
+ }
+ for (l=0; l<4; l++)
+ {
+ y[l] = (mat[l][0]*xx[0]+mat[l][1]*xx[1]+
+ mat[l][2]*xx[2]+mat[l][3]*xx[3]);
+ yu[l] = (mat[l][0]*xxu[0]+mat[l][1]*xxu[1]+
+ mat[l][2]*xxu[2]+mat[l][3]*xxu[3]);
+ yv[l] = (mat[l][0]*xxv[0]+mat[l][1]*xxv[1]+
+ mat[l][2]*xxv[2]+mat[l][3]*xxv[3]);
+ }
+ if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC)
+ {
+ for (l=0; l<3; l++)
+ {
+ p[l] = y[l]+kb->offset4d[l];
+ pu[l] = yu[l];
+ pv[l] = yv[l];
+ }
+ }
+ else
+ {
+ s = y[3]+kb->offset4d[3];
+ q = 1.0/s;
+ t = q*q;
+ for (l=0; l<3; l++)
+ {
+ r = y[l]+kb->offset4d[l];
+ p[l] = r*q;
+ pu[l] = (yu[l]*s-r*yu[3])*t;
+ pv[l] = (yv[l]*s-r*yv[3])*t;
+ }
+ }
+ n[0] = pu[1]*pv[2]-pu[2]*pv[1];
+ n[1] = pu[2]*pv[0]-pu[0]*pv[2];
+ n[2] = pu[0]*pv[1]-pu[1]*pv[0];
+ t = 1.0/(kb->side*4.0*sqrt(n[0]*n[0]+n[1]*n[1]+n[2]*n[2]));
+ n[0] *= t;
+ n[1] *= t;
+ n[2] *= t;
+ pm[0] = pu[0]*kb->dumove+pv[0]*kb->dvmove;
+ pm[1] = pu[1]*kb->dumove+pv[1]*kb->dvmove;
+ pm[2] = pu[2]*kb->dumove+pv[2]*kb->dvmove;
+ t = 1.0/(4.0*sqrt(pm[0]*pm[0]+pm[1]*pm[1]+pm[2]*pm[2]));
+ pm[0] *= t;
+ pm[1] *= t;
+ pm[2] *= t;
+ b[0] = n[1]*pm[2]-n[2]*pm[1];
+ b[1] = n[2]*pm[0]-n[0]*pm[2];
+ b[2] = n[0]*pm[1]-n[1]*pm[0];
+ t = 1.0/(4.0*sqrt(b[0]*b[0]+b[1]*b[1]+b[2]*b[2]));
+ b[0] *= t;
+ b[1] *= t;
+ b[2] *= t;
+
+ /* Compute alpha, beta, delta from the three basis vectors.
+ | -b[0] -b[1] -b[2] |
+ m = | n[0] n[1] n[2] |
+ | -pm[0] -pm[1] -pm[2] |
+ */
+ kb->alpha = atan2(-n[2],-pm[2])*180/M_PI;
+ kb->beta = atan2(-b[2],sqrt(b[0]*b[0]+b[1]*b[1]))*180/M_PI;
+ kb->delta = atan2(b[1],-b[0])*180/M_PI;
+
+ /* Compute the rotation that rotates the Klein bottle in 4D. */
+ rotateall(kb->alpha,kb->beta,kb->delta,kb->zeta,kb->eta,kb->theta,mat);
+
+ u = kb->umove;
+ v = kb->vmove;
+ cu = cos(u);
+ su = sin(u);
+ cv = cos(v);
+ sv = sin(v);
+ cv2 = cos(0.5*v);
+ sv2 = sin(0.5*v);
+ xx[0] = (SQUEEZED_TORUS_RADIUS+cu)*cv;
+ xx[1] = (SQUEEZED_TORUS_RADIUS+cu)*sv;
+ xx[2] = su*cv2;
+ xx[3] = su*sv2;
+ for (l=0; l<4; l++)
+ xx[l] /= SQUEEZED_TORUS_RADIUS+1.25;
+ for (l=0; l<4; l++)
+ {
+ r = 0.0;
+ for (m=0; m<4; m++)
+ r += mat[l][m]*xx[m];
+ y[l] = r;
+ }
+ if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC)
+ {
+ for (l=0; l<3; l++)
+ p[l] = y[l]+kb->offset4d[l];
+ }
+ else
+ {
+ s = y[3]+kb->offset4d[3];
+ for (l=0; l<3; l++)
+ p[l] = (y[l]+kb->offset4d[l])/s;
+ }
+
+ kb->offset3d[0] = -p[0];
+ kb->offset3d[1] = -p[1]-DELTAY;
+ kb->offset3d[2] = -p[2];
+ }
+ else
+ {
+ /* Compute the rotation that rotates the Klein bottle in 4D, including
+ the trackball rotations. */
+ rotateall(kb->alpha,kb->beta,kb->delta,kb->zeta,kb->eta,kb->theta,r1);
+
+ gltrackball_get_quaternion(kb->trackballs[0],q1);
+ gltrackball_get_quaternion(kb->trackballs[1],q2);
+ quats_to_rotmat(q1,q2,r2);
+
+ mult_rotmat(r2,r1,mat);
+ }
+
+ /* Project the points from 4D to 3D. */
+ for (i=0; i<=NUMU; i++)
+ {
+ for (j=0; j<=NUMV; j++)
+ {
+ o = i*(NUMV+1)+j;
+ for (l=0; l<4; l++)
+ {
+ y[l] = (mat[l][0]*kb->x[o][0]+mat[l][1]*kb->x[o][1]+
+ mat[l][2]*kb->x[o][2]+mat[l][3]*kb->x[o][3]);
+ yu[l] = (mat[l][0]*kb->xu[o][0]+mat[l][1]*kb->xu[o][1]+
+ mat[l][2]*kb->xu[o][2]+mat[l][3]*kb->xu[o][3]);
+ yv[l] = (mat[l][0]*kb->xv[o][0]+mat[l][1]*kb->xv[o][1]+
+ mat[l][2]*kb->xv[o][2]+mat[l][3]*kb->xv[o][3]);
+ }
+ if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC)
+ {
+ for (l=0; l<3; l++)
+ {
+ kb->pp[o][l] = (y[l]+kb->offset4d[l])+kb->offset3d[l];
+ pu[l] = yu[l];
+ pv[l] = yv[l];
+ }
+ }
+ else
+ {
+ s = y[3]+kb->offset4d[3];
+ q = 1.0/s;
+ t = q*q;
+ for (l=0; l<3; l++)
+ {
+ r = y[l]+kb->offset4d[l];
+ kb->pp[o][l] = r*q+kb->offset3d[l];
+ pu[l] = (yu[l]*s-r*yu[3])*t;
+ pv[l] = (yv[l]*s-r*yv[3])*t;
+ }
+ }
+ kb->pn[o][0] = pu[1]*pv[2]-pu[2]*pv[1];
+ kb->pn[o][1] = pu[2]*pv[0]-pu[0]*pv[2];
+ kb->pn[o][2] = pu[0]*pv[1]-pu[1]*pv[0];
+ t = 1.0/sqrt(kb->pn[o][0]*kb->pn[o][0]+kb->pn[o][1]*kb->pn[o][1]+
+ kb->pn[o][2]*kb->pn[o][2]);
+ kb->pn[o][0] *= t;
+ kb->pn[o][1] *= t;
+ kb->pn[o][2] *= t;
+ }
+ }
+
+ if (kb->colors == COLORS_TWOSIDED)
+ {
+ glColor3fv(mat_diff_red);
+ if (kb->display_mode == DISP_TRANSPARENT)
+ {
+ glMaterialfv(GL_FRONT,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_red);
+ glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_green);
+ }
+ else
+ {
+ glMaterialfv(GL_FRONT,GL_AMBIENT_AND_DIFFUSE,mat_diff_red);
+ glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,mat_diff_green);
+ }
+ }
+ glBindTexture(GL_TEXTURE_2D,kb->tex_name);
+
+ for (i=0; i<NUMU; i++)
+ {
+ if (kb->appearance == APPEARANCE_BANDS && ((i & (NUMB-1)) >= NUMB/2))
+ continue;
+ if (kb->display_mode == DISP_WIREFRAME)
+ glBegin(GL_QUAD_STRIP);
+ else
+ glBegin(GL_TRIANGLE_STRIP);
+ for (j=0; j<=NUMV; j++)
+ {
+ for (k=0; k<=1; k++)
+ {
+ l = (i+k);
+ m = j;
+ o = l*(NUMV+1)+m;
+ glNormal3fv(kb->pn[o]);
+ glTexCoord2fv(kb->tex[o]);
+ if (kb->colors != COLORS_TWOSIDED)
{
glColor3fv(kb->col[o]);
glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,kb->col[o]);
float q1[4], q2[4], r1[4][4], r2[4][4];
kleinstruct *kb = &klein[MI_SCREEN(mi)];
- if (view == VIEW_WALK || view == VIEW_WALKTURN)
+ if (kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN)
{
/* Compute the rotation that rotates the Klein bottle in 4D without the
trackball rotations. */
yv[l] = (mat[l][0]*xxv[0]+mat[l][1]*xxv[1]+
mat[l][2]*xxv[2]+mat[l][3]*xxv[3]);
}
- if (projection_4d == DISP_4D_ORTHOGRAPHIC)
+ if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC)
{
for (l=0; l<3; l++)
{
| -pm[0] -pm[1] -pm[2] |
*/
kb->alpha = atan2(-n[2],-pm[2])*180/M_PI;
- kb->beta = atan2( -b[2],sqrt(b[0]*b[0]+b[1]*b[1]))*180/M_PI;
+ kb->beta = atan2(-b[2],sqrt(b[0]*b[0]+b[1]*b[1]))*180/M_PI;
kb->delta = atan2(b[1],-b[0])*180/M_PI;
/* Compute the rotation that rotates the Klein bottle in 4D. */
r += mat[l][m]*xx[m];
y[l] = r;
}
- if (projection_4d == DISP_4D_ORTHOGRAPHIC)
+ if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC)
{
for (l=0; l<3; l++)
p[l] = y[l]+kb->offset4d[l];
yv[l] = (mat[l][0]*kb->xv[o][0]+mat[l][1]*kb->xv[o][1]+
mat[l][2]*kb->xv[o][2]+mat[l][3]*kb->xv[o][3]);
}
- if (projection_4d == DISP_4D_ORTHOGRAPHIC)
+ if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC)
{
for (l=0; l<3; l++)
{
}
}
- if (colors == COLORS_TWOSIDED)
+ if (kb->colors == COLORS_TWOSIDED)
{
glColor3fv(mat_diff_red);
- if (display_mode == DISP_TRANSPARENT)
+ if (kb->display_mode == DISP_TRANSPARENT)
{
glMaterialfv(GL_FRONT,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_red);
glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_green);
for (i=0; i<NUMV; i++)
{
- if (appearance == APPEARANCE_BANDS && ((i & (NUMB-1)) >= NUMB/2))
+ if (kb->appearance == APPEARANCE_BANDS && ((i & (NUMB-1)) >= NUMB/2))
continue;
- if (display_mode == DISP_WIREFRAME)
+ if (kb->display_mode == DISP_WIREFRAME)
glBegin(GL_QUAD_STRIP);
else
glBegin(GL_TRIANGLE_STRIP);
o = l*(NUMU+1)+m;
glNormal3fv(kb->pn[o]);
glTexCoord2fv(kb->tex[o]);
- if (colors != COLORS_TWOSIDED)
+ if (kb->colors != COLORS_TWOSIDED)
{
glColor3fv(kb->col[o]);
glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,kb->col[o]);
if (walk_speed == 0.0)
walk_speed = 20.0;
- if (view == VIEW_TURN)
+ if (kb->view == VIEW_TURN)
{
kb->alpha = frand(360.0);
kb->beta = frand(360.0);
kb->delta = 0.0;
}
kb->zeta = 0.0;
- if (bottle_type == KLEIN_BOTTLE_FIGURE_8)
+ if (kb->bottle_type == KLEIN_BOTTLE_FIGURE_8 ||
+ kb->bottle_type == KLEIN_BOTTLE_SQUEEZED_TORUS)
kb->eta = 0.0;
else
kb->eta = 45.0;
kb->dvmove = 0.0;
kb->side = 1;
- if (bottle_type == KLEIN_BOTTLE_FIGURE_8)
+ if (kb->bottle_type == KLEIN_BOTTLE_FIGURE_8)
{
kb->offset4d[0] = 0.0;
kb->offset4d[1] = 0.0;
kb->offset4d[3] = 1.5;
kb->offset3d[0] = 0.0;
kb->offset3d[1] = 0.0;
- if (projection_4d == DISP_4D_ORTHOGRAPHIC)
+ if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC)
kb->offset3d[2] = -2.1;
else
kb->offset3d[2] = -1.9;
kb->offset3d[3] = 0.0;
}
- else
+ else if (kb->bottle_type == KLEIN_BOTTLE_SQUEEZED_TORUS)
+ {
+ kb->offset4d[0] = 0.0;
+ kb->offset4d[1] = 0.0;
+ kb->offset4d[2] = 0.0;
+ kb->offset4d[3] = 1.4;
+ kb->offset3d[0] = 0.0;
+ kb->offset3d[1] = 0.0;
+ kb->offset3d[2] = -2.0;
+ kb->offset3d[3] = 0.0;
+ }
+ else /* kb->bottle_type == KLEIN_BOTTLE_LAWSON */
{
kb->offset4d[0] = 0.0;
kb->offset4d[1] = 0.0;
kb->offset4d[2] = 0.0;
- if (projection_4d == DISP_4D_PERSPECTIVE &&
- projection_3d == DISP_3D_ORTHOGRAPHIC)
+ if (kb->projection_4d == DISP_4D_PERSPECTIVE &&
+ kb->projection_3d == DISP_3D_ORTHOGRAPHIC)
kb->offset4d[3] = 1.5;
else
kb->offset4d[3] = 1.1;
kb->offset3d[0] = 0.0;
kb->offset3d[1] = 0.0;
- if (projection_4d == DISP_4D_ORTHOGRAPHIC)
+ if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC)
kb->offset3d[2] = -2.0;
else
kb->offset3d[2] = -5.0;
}
gen_texture(mi);
- if (bottle_type == KLEIN_BOTTLE_FIGURE_8)
+ if (kb->bottle_type == KLEIN_BOTTLE_FIGURE_8)
setup_figure8(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
- else
+ else if (kb->bottle_type == KLEIN_BOTTLE_SQUEEZED_TORUS)
+ setup_squeezed_torus(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
+ else /* kb->bottle_type == KLEIN_BOTTLE_LAWSON */
setup_lawson(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
if (marks)
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
- if (projection_3d == DISP_3D_PERSPECTIVE ||
- view == VIEW_WALK || view == VIEW_WALKTURN)
+ if (kb->projection_3d == DISP_3D_PERSPECTIVE ||
+ kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN)
{
- if (view == VIEW_WALK || view == VIEW_WALKTURN)
+ if (kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN)
gluPerspective(60.0,1.0,0.01,10.0);
else
gluPerspective(60.0,1.0,0.1,10.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
- if (display_mode == DISP_WIREFRAME)
- {
- glDisable(GL_DEPTH_TEST);
- glShadeModel(GL_FLAT);
- glPolygonMode(GL_FRONT_AND_BACK,GL_LINE);
- glDisable(GL_LIGHTING);
- glDisable(GL_LIGHT0);
- glDisable(GL_BLEND);
- }
- else if (display_mode == DISP_SURFACE)
+# ifdef HAVE_JWZGLES /* #### glPolygonMode other than GL_FILL unimplemented */
+ if (kb->display_mode == DISP_WIREFRAME)
+ kb->display_mode = DISP_SURFACE;
+# endif
+
+ if (kb->display_mode == DISP_SURFACE)
{
glEnable(GL_DEPTH_TEST);
glDepthFunc(GL_LESS);
glDepthMask(GL_TRUE);
glDisable(GL_BLEND);
}
- else if (display_mode == DISP_TRANSPARENT)
+ else if (kb->display_mode == DISP_TRANSPARENT)
{
glDisable(GL_DEPTH_TEST);
glShadeModel(GL_SMOOTH);
glEnable(GL_BLEND);
glBlendFunc(GL_SRC_ALPHA,GL_ONE);
}
- else
+ else /* kb->display_mode == DISP_WIREFRAME */
{
glDisable(GL_DEPTH_TEST);
glShadeModel(GL_FLAT);
if (!kb->button_pressed)
{
- if (view == VIEW_TURN)
+ if (kb->view == VIEW_TURN)
{
kb->alpha += speed_wx * kb->speed_scale;
if (kb->alpha >= 360.0)
if (kb->theta >= 360.0)
kb->theta -= 360.0;
}
- if (view == VIEW_WALKTURN)
+ if (kb->view == VIEW_WALKTURN)
{
kb->zeta += speed_xy * kb->speed_scale;
if (kb->zeta >= 360.0)
if (kb->theta >= 360.0)
kb->theta -= 360.0;
}
- if (view == VIEW_WALK || view == VIEW_WALKTURN)
+ if (kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN)
{
kb->dvmove = cos(walk_direction*M_PI/180.0)*walk_speed*M_PI/4096.0;
kb->vmove += kb->dvmove;
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
- if (projection_3d == DISP_3D_PERSPECTIVE ||
- view == VIEW_WALK || view == VIEW_WALKTURN)
+ if (kb->projection_3d == DISP_3D_PERSPECTIVE ||
+ kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN)
{
- if (view == VIEW_WALK || view == VIEW_WALKTURN)
+ if (kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN)
gluPerspective(60.0,kb->aspect,0.01,10.0);
else
gluPerspective(60.0,kb->aspect,0.1,10.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
- if (bottle_type == KLEIN_BOTTLE_FIGURE_8)
+ if (kb->bottle_type == KLEIN_BOTTLE_FIGURE_8)
mi->polygon_count = figure8(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
- else
+ else if (kb->bottle_type == KLEIN_BOTTLE_SQUEEZED_TORUS)
+ mi->polygon_count = squeezed_torus(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
+ else /* kb->bottle_type == KLEIN_BOTTLE_LAWSON */
mi->polygon_count = lawson(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
}
ENTRYPOINT Bool klein_handle_event(ModeInfo *mi, XEvent *event)
{
- Display *display = MI_DISPLAY(mi);
kleinstruct *kb = &klein[MI_SCREEN(mi)];
- KeySym sym;
+ KeySym sym = 0;
+ char c = 0;
+
+ if (event->xany.type == KeyPress || event->xany.type == KeyRelease)
+ XLookupString (&event->xkey, &c, 1, &sym, 0);
if (event->xany.type == ButtonPress &&
event->xbutton.button == Button1)
}
else if (event->xany.type == KeyPress)
{
- sym = XKeycodeToKeysym(display,event->xkey.keycode,0);
if (sym == XK_Shift_L || sym == XK_Shift_R)
{
kb->current_trackball = 1;
}
else if (event->xany.type == KeyRelease)
{
- sym = XKeycodeToKeysym(display,event->xkey.keycode,0);
if (sym == XK_Shift_L || sym == XK_Shift_R)
{
kb->current_trackball = 0;
{
kleinstruct *kb;
- if (klein == NULL)
- {
- klein = (kleinstruct *)calloc(MI_NUM_SCREENS(mi),
- sizeof(kleinstruct));
- if (klein == NULL)
- return;
- }
+ MI_INIT(mi, klein, NULL);
kb = &klein[MI_SCREEN(mi)];
- kb->trackballs[0] = gltrackball_init();
- kb->trackballs[1] = gltrackball_init();
+ kb->trackballs[0] = gltrackball_init(True);
+ kb->trackballs[1] = gltrackball_init(True);
kb->current_trackball = 0;
kb->button_pressed = False;
/* Set the Klein bottle. */
if (!strcasecmp(klein_bottle,"random"))
{
- bottle_type = random() % NUM_KLEIN_BOTTLES;
+ kb->bottle_type = random() % NUM_KLEIN_BOTTLES;
}
else if (!strcasecmp(klein_bottle,"figure-8"))
{
- bottle_type = KLEIN_BOTTLE_FIGURE_8;
+ kb->bottle_type = KLEIN_BOTTLE_FIGURE_8;
+ }
+ else if (!strcasecmp(klein_bottle,"squeezed-torus"))
+ {
+ kb->bottle_type = KLEIN_BOTTLE_SQUEEZED_TORUS;
}
else if (!strcasecmp(klein_bottle,"lawson"))
{
- bottle_type = KLEIN_BOTTLE_LAWSON;
+ kb->bottle_type = KLEIN_BOTTLE_LAWSON;
}
else
{
- bottle_type = random() % NUM_KLEIN_BOTTLES;
+ kb->bottle_type = random() % NUM_KLEIN_BOTTLES;
}
/* Set the display mode. */
if (!strcasecmp(mode,"random"))
{
- display_mode = random() % NUM_DISPLAY_MODES;
+ kb->display_mode = random() % NUM_DISPLAY_MODES;
}
else if (!strcasecmp(mode,"wireframe"))
{
- display_mode = DISP_WIREFRAME;
+ kb->display_mode = DISP_WIREFRAME;
}
else if (!strcasecmp(mode,"surface"))
{
- display_mode = DISP_SURFACE;
+ kb->display_mode = DISP_SURFACE;
}
else if (!strcasecmp(mode,"transparent"))
{
- display_mode = DISP_TRANSPARENT;
+ kb->display_mode = DISP_TRANSPARENT;
}
else
{
- display_mode = random() % NUM_DISPLAY_MODES;
+ kb->display_mode = random() % NUM_DISPLAY_MODES;
}
/* Orientation marks don't make sense in wireframe mode. */
- if (display_mode == DISP_WIREFRAME)
+ if (kb->display_mode == DISP_WIREFRAME)
marks = False;
/* Set the appearance. */
if (!strcasecmp(appear,"random"))
{
- appearance = random() % NUM_APPEARANCES;
+ kb->appearance = random() % NUM_APPEARANCES;
}
else if (!strcasecmp(appear,"solid"))
{
- appearance = APPEARANCE_SOLID;
+ kb->appearance = APPEARANCE_SOLID;
}
else if (!strcasecmp(appear,"bands"))
{
- appearance = APPEARANCE_BANDS;
+ kb->appearance = APPEARANCE_BANDS;
}
else
{
- appearance = random() % NUM_APPEARANCES;
+ kb->appearance = random() % NUM_APPEARANCES;
}
/* Set the color mode. */
if (!strcasecmp(color_mode,"random"))
{
- colors = random() % NUM_COLORS;
+ kb->colors = random() % NUM_COLORS;
}
else if (!strcasecmp(color_mode,"two-sided"))
{
- colors = COLORS_TWOSIDED;
+ kb->colors = COLORS_TWOSIDED;
}
else if (!strcasecmp(color_mode,"rainbow"))
{
- colors = COLORS_RAINBOW;
+ kb->colors = COLORS_RAINBOW;
}
else if (!strcasecmp(color_mode,"depth"))
{
- colors = COLORS_DEPTH;
+ kb->colors = COLORS_DEPTH;
}
else
{
- colors = random() % NUM_COLORS;
+ kb->colors = random() % NUM_COLORS;
}
/* Set the view mode. */
if (!strcasecmp(view_mode,"random"))
{
- view = random() % NUM_VIEW_MODES;
+ kb->view = random() % NUM_VIEW_MODES;
}
else if (!strcasecmp(view_mode,"walk"))
{
- view = VIEW_WALK;
+ kb->view = VIEW_WALK;
}
else if (!strcasecmp(view_mode,"turn"))
{
- view = VIEW_TURN;
+ kb->view = VIEW_TURN;
}
else if (!strcasecmp(view_mode,"walk-turn"))
{
- view = VIEW_WALKTURN;
+ kb->view = VIEW_WALKTURN;
}
else
{
- view = random() % NUM_VIEW_MODES;
+ kb->view = random() % NUM_VIEW_MODES;
}
/* Set the 3d projection mode. */
if (!strcasecmp(proj_3d,"random"))
{
/* Orthographic projection only makes sense in turn mode. */
- if (view == VIEW_TURN)
- projection_3d = random() % NUM_DISP_3D_MODES;
+ if (kb->view == VIEW_TURN)
+ kb->projection_3d = random() % NUM_DISP_3D_MODES;
else
- projection_3d = DISP_3D_PERSPECTIVE;
+ kb->projection_3d = DISP_3D_PERSPECTIVE;
}
else if (!strcasecmp(proj_3d,"perspective"))
{
- projection_3d = DISP_3D_PERSPECTIVE;
+ kb->projection_3d = DISP_3D_PERSPECTIVE;
}
else if (!strcasecmp(proj_3d,"orthographic"))
{
- projection_3d = DISP_3D_ORTHOGRAPHIC;
+ kb->projection_3d = DISP_3D_ORTHOGRAPHIC;
}
else
{
/* Orthographic projection only makes sense in turn mode. */
- if (view == VIEW_TURN)
- projection_3d = random() % NUM_DISP_3D_MODES;
+ if (kb->view == VIEW_TURN)
+ kb->projection_3d = random() % NUM_DISP_3D_MODES;
else
- projection_3d = DISP_3D_PERSPECTIVE;
+ kb->projection_3d = DISP_3D_PERSPECTIVE;
}
/* Set the 4d projection mode. */
if (!strcasecmp(proj_4d,"random"))
{
- projection_4d = random() % NUM_DISP_4D_MODES;
+ kb->projection_4d = random() % NUM_DISP_4D_MODES;
}
else if (!strcasecmp(proj_4d,"perspective"))
{
- projection_4d = DISP_4D_PERSPECTIVE;
+ kb->projection_4d = DISP_4D_PERSPECTIVE;
}
else if (!strcasecmp(proj_4d,"orthographic"))
{
- projection_4d = DISP_4D_ORTHOGRAPHIC;
+ kb->projection_4d = DISP_4D_ORTHOGRAPHIC;
}
else
{
- projection_4d = random() % NUM_DISP_4D_MODES;
+ kb->projection_4d = random() % NUM_DISP_4D_MODES;
}
/* Modify the speeds to a useful range in walk-and-turn mode. */
- if (view == VIEW_WALKTURN)
+ if (kb->view == VIEW_WALKTURN)
{
speed_wx *= 0.2;
speed_wy *= 0.2;
}
-/*
- *-----------------------------------------------------------------------------
- * The display is being taken away from us. Free up malloc'ed
- * memory and X resources that we've alloc'ed. Only called
- * once, we must zap everything for every screen.
- *-----------------------------------------------------------------------------
- */
-
-ENTRYPOINT void release_klein(ModeInfo *mi)
-{
- if (klein != NULL)
- {
- int screen;
-
- for (screen = 0; screen < MI_NUM_SCREENS(mi); screen++)
- {
- kleinstruct *kb = &klein[screen];
-
- if (kb->glx_context)
- kb->glx_context = (GLXContext *)NULL;
- }
- (void) free((void *)klein);
- klein = (kleinstruct *)NULL;
- }
- FreeAllGL(mi);
-}
-
#ifndef STANDALONE
ENTRYPOINT void change_klein(ModeInfo *mi)
{
projects / xscreensaver / blobdiff