--- /dev/null
+/* projectiveplane --- Shows a 4d embedding of the real projective plane
+ that rotates in 4d or on which you can walk */
+
+#if 0
+static const char sccsid[] = "@(#)projectiveplane.c 1.1 14/01/01 xlockmore";
+#endif
+
+/* Copyright (c) 2005-2014 Carsten Steger <carsten@mirsanmir.org>. */
+
+/*
+ * Permission to use, copy, modify, and distribute this software and its
+ * documentation for any purpose and without fee is hereby granted,
+ * provided that the above copyright notice appear in all copies and that
+ * both that copyright notice and this permission notice appear in
+ * supporting documentation.
+ *
+ * This file is provided AS IS with no warranties of any kind. The author
+ * shall have no liability with respect to the infringement of copyrights,
+ * trade secrets or any patents by this file or any part thereof. In no
+ * event will the author be liable for any lost revenue or profits or
+ * other special, indirect and consequential damages.
+ *
+ * REVISION HISTORY:
+ * C. Steger - 14/01/03: Initial version
+ */
+
+/*
+ * This program shows a 4d embedding of the real projective plane.
+ * You can walk on the projective plane, see it turn in 4d, or walk on
+ * it while it turns in 4d. The fact that the surface is an embedding
+ * of the real projective plane in 4d can be seen in the depth colors
+ * mode: set all rotation speeds to 0 and the projection mode to 4d
+ * orthographic projection. In its default orientation, the embedding
+ * of the real projective plane will then project to the Roman
+ * surface, which has three lines of self-intersection. However, at
+ * the three lines of self-intersection the parts of the surface that
+ * intersect have different colors, i.e., different 4d depths.
+ *
+ * The real projective plane is a non-orientable surface. To make
+ * this apparent, the two-sided color mode can be used.
+ * Alternatively, orientation markers (curling arrows) can be drawn as
+ * a texture map on the surface of the projective plane. While
+ * walking on the projective plane, you will notice that the
+ * orientation of the curling arrows changes (which it must because
+ * the projective plane is non-orientable).
+ *
+ * The real projective plane is a model for the projective geometry in
+ * 2d space. One point can be singled out as the origin. A line can
+ * be singled out as the line at infinity, i.e., a line that lies at
+ * an infinite distance to the origin. The line at infinity is
+ * topologically a circle. Points on the line at infinity are also
+ * used to model directions in projective geometry. The origin can be
+ * visualized in different manners. When using distance colors, the
+ * origin is the point that is displayed as fully saturated red, which
+ * is easier to see as the center of the reddish area on the
+ * projective plane. Alternatively, when using distance bands, the
+ * origin is the center of the only band that projects to a disc.
+ * When using direction bands, the origin is the point where all
+ * direction bands collapse to a point. Finally, when orientation
+ * markers are being displayed, the origin the the point where all
+ * orientation markers are compressed to a point. The line at
+ * infinity can also be visualized in different ways. When using
+ * distance colors, the line at infinity is the line that is displayed
+ * as fully saturated magenta. When two-sided colors are used, the
+ * line at infinity lies at the points where the red and green "sides"
+ * of the projective plane meet (of course, the real projective plane
+ * only has one side, so this is a design choice of the
+ * visualization). Alternatively, when orientation markers are being
+ * displayed, the line at infinity is the place where the orientation
+ * markers change their orientation.
+ *
+ * Note that when the projective plane is displayed with bands, the
+ * orientation markers are placed in the middle of the bands. For
+ * distance bands, the bands are chosen in such a way that the band at
+ * the origin is only half as wide as the remaining bands, which
+ * results in a disc being displayed at the origin that has the same
+ * diameter as the remaining bands. This choice, however, also
+ * implies that the band at infinity is half as wide as the other
+ * bands. Since the projective plane is attached to itself (in a
+ * complicated fashion) at the line at infinity, effectively the band
+ * at infinity is again as wide as the remaining bands. However,
+ * since the orientation markers are displayed in the middle of the
+ * bands, this means that only one half of the orientation markers
+ * will be displayed twice at the line at infinity if distance bands
+ * are used. If direction bands are used or if the projective plane
+ * is displayed as a solid surface, the orientation markers are
+ * displayed fully at the respective sides of the line at infinity.
+ *
+ * The program projects the 4d projective plane to 3d using either a
+ * perspective or an orthographic projection. Which of the two
+ * alternatives looks more appealing is up to you. However, two
+ * famous surfaces are obtained if orthographic 4d projection is used:
+ * The Roman surface and the cross cap. If the projective plane is
+ * rotated in 4d, the result of the projection for certain rotations
+ * is a Roman surface and for certain rotations it is a cross cap.
+ * The easiest way to see this is to set all rotation speeds to 0 and
+ * the rotation speed around the yz plane to a value different from 0.
+ * However, for any 4d rotation speeds, the projections will generally
+ * cycle between the Roman surface and the cross cap. The difference
+ * is where the origin and the line at infinity will lie with respect
+ * to the self-intersections in the projections to 3d.
+ *
+ * The projected projective plane can then be projected to the screen
+ * either perspectively or orthographically. When using the walking
+ * modes, perspective projection to the screen will be used.
+ *
+ * There are three display modes for the projective plane: mesh
+ * (wireframe), solid, or transparent. Furthermore, the appearance of
+ * the projective plane can be as a solid object or as a set of
+ * see-through bands. The bands can be distance bands, i.e., bands
+ * that lie at increasing distances from the origin, or direction
+ * bands, i.e., bands that lie at increasing angles with respect to
+ * the origin.
+ *
+ * When the projective plane is displayed with direction bands, you
+ * will be able to see that each direction band (modulo the "pinching"
+ * at the origin) is a Moebius strip, which also shows that the
+ * projective plane is non-orientable.
+ *
+ * Finally, the colors with with the projective plane is drawn can be
+ * set to two-sided, distance, direction, or depth. In two-sided
+ * mode, the projective plane is drawn with red on one "side" and
+ * green on the "other side". As described above, the projective
+ * plane only has one side, so the color jumps from red to green along
+ * the line at infinity. This mode enables you to see that the
+ * projective plane is non-orientable. In distance mode, the
+ * projective plane is displayed with fully saturated colors that
+ * depend on the distance of the points on the projective plane to the
+ * origin. The origin is displayed in red, the line at infinity is
+ * displayed in magenta. If the projective plane is displayed as
+ * distance bands, each band will be displayed with a different color.
+ * In direction mode, the projective plane is displayed with fully
+ * saturated colors that depend on the angle of the points on the
+ * projective plane with respect to the origin. Angles in opposite
+ * directions to the origin (e.g., 15 and 205 degrees) are displayed
+ * in the same color since they are projectively equivalent. If the
+ * projective plane is displayed as direction bands, each band will be
+ * displayed with a different color. Finally, in depth mode the
+ * projective plane with colors chosen depending on the 4d "depth"
+ * (i.e., the w coordinate) of the points on the projective plane at
+ * its default orientation in 4d. As discussed above, this mode
+ * enables you to see that the projective plane does not intersect
+ * itself in 4d.
+ *
+ * The rotation speed for each of the six planes around which the
+ * projective plane 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 projective plane and the walking speed can be
+ * chosen. The walking direction is measured as an angle in degrees
+ * in the 2d square that forms the coordinate system of the surface of
+ * the projective plane. A value of 0 or 180 means that the walk is
+ * along a circle at a randomly chosen distance from the origin
+ * (parallel to a distance band). A value of 90 or 270 means that the
+ * walk is directly from the origin to the line at infinity and back
+ * (analogous to a direction band). Any other value results in a
+ * curved path from the origin to the line at infinity and back.
+ *
+ * This program is somewhat inspired by Thomas Banchoff's book "Beyond
+ * the Third Dimension: Geometry, Computer Graphics, and Higher
+ * Dimensions", Scientific American Library, 1990.
+ */
+
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+
+#define DISP_WIREFRAME 0
+#define DISP_SURFACE 1
+#define DISP_TRANSPARENT 2
+#define NUM_DISPLAY_MODES 3
+
+#define APPEARANCE_SOLID 0
+#define APPEARANCE_DISTANCE_BANDS 1
+#define APPEARANCE_DIRECTION_BANDS 2
+#define NUM_APPEARANCES 3
+
+#define COLORS_TWOSIDED 0
+#define COLORS_DISTANCE 1
+#define COLORS_DIRECTION 2
+#define COLORS_DEPTH 3
+#define NUM_COLORS 4
+
+#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_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 "83.0"
+#define DEF_WALK_SPEED "20.0"
+
+#ifdef STANDALONE
+# define DEFAULTS "*delay: 10000 \n" \
+ "*showFPS: False \n" \
+
+# define refresh_projectiveplane 0
+# include "xlockmore.h" /* from the xscreensaver distribution */
+#else /* !STANDALONE */
+# include "xlock.h" /* from the xlockmore distribution */
+#endif /* !STANDALONE */
+
+#ifdef USE_GL
+
+#ifndef HAVE_COCOA
+# include <X11/keysym.h>
+#endif
+
+#include "gltrackball.h"
+
+#include <float.h>
+
+
+#ifdef USE_MODULES
+ModStruct projectiveplane_description =
+{"projectiveplane", "init_projectiveplane", "draw_projectiveplane",
+ "release_projectiveplane", "draw_projectiveplane", "change_projectiveplane",
+ NULL, &projectiveplane_opts, 25000, 1, 1, 1, 1.0, 4, "",
+ "Rotate a 4d embedding of the real projective plane in 4d or walk on it",
+ 0, NULL};
+
+#endif
+
+
+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;
+static float speed_xy;
+static float speed_xz;
+static float speed_yz;
+static float walk_direction;
+static float walk_speed;
+
+
+static XrmOptionDescRec opts[] =
+{
+ {"-mode", ".displayMode", XrmoptionSepArg, 0 },
+ {"-wireframe", ".displayMode", XrmoptionNoArg, "wireframe" },
+ {"-surface", ".displayMode", XrmoptionNoArg, "surface" },
+ {"-transparent", ".displayMode", XrmoptionNoArg, "transparent" },
+ {"-appearance", ".appearance", XrmoptionSepArg, 0 },
+ {"-solid", ".appearance", XrmoptionNoArg, "solid" },
+ {"-distance-bands", ".appearance", XrmoptionNoArg, "distance-bands" },
+ {"-direction-bands", ".appearance", XrmoptionNoArg, "direction-bands" },
+ {"-colors", ".colors", XrmoptionSepArg, 0 },
+ {"-twosided-colors", ".colors", XrmoptionNoArg, "two-sided" },
+ {"-distance-colors", ".colors", XrmoptionNoArg, "distance" },
+ {"-direction-colors", ".colors", XrmoptionNoArg, "direction" },
+ {"-depth-colors", ".colors", XrmoptionNoArg, "depth" },
+ {"-view-mode", ".viewMode", XrmoptionSepArg, 0 },
+ {"-walk", ".viewMode", XrmoptionNoArg, "walk" },
+ {"-turn", ".viewMode", XrmoptionNoArg, "turn" },
+ {"-walk-turn", ".viewMode", XrmoptionNoArg, "walk-turn" },
+ {"-orientation-marks", ".marks", XrmoptionNoArg, "on"},
+ {"+orientation-marks", ".marks", XrmoptionNoArg, "off"},
+ {"-projection-3d", ".projection3d", XrmoptionSepArg, 0 },
+ {"-perspective-3d", ".projection3d", XrmoptionNoArg, "perspective" },
+ {"-orthographic-3d", ".projection3d", XrmoptionNoArg, "orthographic" },
+ {"-projection-4d", ".projection4d", XrmoptionSepArg, 0 },
+ {"-perspective-4d", ".projection4d", XrmoptionNoArg, "perspective" },
+ {"-orthographic-4d", ".projection4d", XrmoptionNoArg, "orthographic" },
+ {"-speed-wx", ".speedwx", XrmoptionSepArg, 0 },
+ {"-speed-wy", ".speedwy", XrmoptionSepArg, 0 },
+ {"-speed-wz", ".speedwz", XrmoptionSepArg, 0 },
+ {"-speed-xy", ".speedxy", XrmoptionSepArg, 0 },
+ {"-speed-xz", ".speedxz", XrmoptionSepArg, 0 },
+ {"-speed-yz", ".speedyz", XrmoptionSepArg, 0 },
+ {"-walk-direction", ".walkDirection", XrmoptionSepArg, 0 },
+ {"-walk-speed", ".walkSpeed", XrmoptionSepArg, 0 }
+};
+
+static argtype vars[] =
+{
+ { &mode, "displayMode", "DisplayMode", DEF_DISPLAY_MODE, t_String },
+ { &appear, "appearance", "Appearance", DEF_APPEARANCE, t_String },
+ { &color_mode, "colors", "Colors", DEF_COLORS, t_String },
+ { &view_mode, "viewMode", "ViewMode", DEF_VIEW_MODE, t_String },
+ { &marks, "marks", "Marks", DEF_MARKS, t_Bool },
+ { &proj_3d, "projection3d", "Projection3d", DEF_PROJECTION_3D, t_String },
+ { &proj_4d, "projection4d", "Projection4d", DEF_PROJECTION_4D, t_String },
+ { &speed_wx, "speedwx", "Speedwx", DEF_SPEEDWX, t_Float},
+ { &speed_wy, "speedwy", "Speedwy", DEF_SPEEDWY, t_Float},
+ { &speed_wz, "speedwz", "Speedwz", DEF_SPEEDWZ, t_Float},
+ { &speed_xy, "speedxy", "Speedxy", DEF_SPEEDXY, t_Float},
+ { &speed_xz, "speedxz", "Speedxz", DEF_SPEEDXZ, t_Float},
+ { &speed_yz, "speedyz", "Speedyz", DEF_SPEEDYZ, t_Float},
+ { &walk_direction, "walkDirection", "WalkDirection", DEF_WALK_DIRECTION, t_Float},
+ { &walk_speed, "walkSpeed", "WalkSpeed", DEF_WALK_SPEED, t_Float}
+};
+
+ENTRYPOINT ModeSpecOpt projectiveplane_opts =
+{sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, NULL};
+
+
+/* Offset by which we walk above the projective plane */
+#define DELTAY 0.01
+
+/* Number of subdivisions of the projective plane */
+#define NUMU 128
+#define NUMV 128
+
+/* Number of subdivisions per band */
+#define NUMB 8
+
+
+typedef struct {
+ GLint WindH, WindW;
+ GLXContext *glx_context;
+ /* 4D rotation angles */
+ float alpha, beta, delta, zeta, eta, theta;
+ /* Movement parameters */
+ float umove, vmove, dumove, dvmove;
+ int side, dir;
+ /* The viewing offset in 4d */
+ float offset4d[4];
+ /* The viewing offset in 3d */
+ float offset3d[4];
+ /* The 4d coordinates of the projective plane and their derivatives */
+ float x[(NUMU+1)*(NUMV+1)][4];
+ float xu[(NUMU+1)*(NUMV+1)][4];
+ float xv[(NUMU+1)*(NUMV+1)][4];
+ float pp[(NUMU+1)*(NUMV+1)][3];
+ float pn[(NUMU+1)*(NUMV+1)][3];
+ /* The precomputed colors of the projective plane */
+ float col[(NUMU+1)*(NUMV+1)][4];
+ /* The precomputed texture coordinates of the projective plane */
+ float tex[(NUMU+1)*(NUMV+1)][2];
+ /* The "curlicue" texture */
+ GLuint tex_name;
+ /* Aspect ratio of the current window */
+ float aspect;
+ /* Trackball states */
+ trackball_state *trackballs[2];
+ int current_trackball;
+ Bool button_pressed;
+ /* A random factor to modify the rotation speeds */
+ float speed_scale;
+} projectiveplanestruct;
+
+static projectiveplanestruct *projectiveplane = (projectiveplanestruct *) 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,
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+ 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
+ 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
+ 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
+ 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
+ 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
+ 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
+ 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
+ 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
+ 255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
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+ 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,
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+ 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 50,209,255,255,255,255,255,255,255,255,255,255,255,255,255,
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+ 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,
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+ 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,
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+ 255,255,255,255,255,255,255, 18, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 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,
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+ 255,255,255,255,255,255,255, 45, 0, 0, 0, 0, 56,247, 82, 0,
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+ 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)
+{
+ float c, s, u, v;
+ int i;
+
+ phi *= M_PI/180.0;
+ c = cos(phi);
+ s = sin(phi);
+ for (i=0; i<4; i++)
+ {
+ u = m[i][1];
+ v = m[i][2];
+ m[i][1] = c*u+s*v;
+ m[i][2] = -s*u+c*v;
+ }
+}
+
+
+/* Add a rotation around the wy-plane to the matrix m. */
+static void rotatewy(float m[4][4], float phi)
+{
+ float c, s, u, v;
+ int i;
+
+ phi *= M_PI/180.0;
+ c = cos(phi);
+ s = sin(phi);
+ for (i=0; i<4; i++)
+ {
+ u = m[i][0];
+ v = m[i][2];
+ m[i][0] = c*u-s*v;
+ m[i][2] = s*u+c*v;
+ }
+}
+
+
+/* Add a rotation around the wz-plane to the matrix m. */
+static void rotatewz(float m[4][4], float phi)
+{
+ float c, s, u, v;
+ int i;
+
+ phi *= M_PI/180.0;
+ c = cos(phi);
+ s = sin(phi);
+ for (i=0; i<4; i++)
+ {
+ u = m[i][0];
+ v = m[i][1];
+ m[i][0] = c*u+s*v;
+ m[i][1] = -s*u+c*v;
+ }
+}
+
+
+/* Add a rotation around the xy-plane to the matrix m. */
+static void rotatexy(float m[4][4], float phi)
+{
+ float c, s, u, v;
+ int i;
+
+ phi *= M_PI/180.0;
+ c = cos(phi);
+ s = sin(phi);
+ for (i=0; i<4; i++)
+ {
+ u = m[i][2];
+ v = m[i][3];
+ m[i][2] = c*u+s*v;
+ m[i][3] = -s*u+c*v;
+ }
+}
+
+
+/* Add a rotation around the xz-plane to the matrix m. */
+static void rotatexz(float m[4][4], float phi)
+{
+ float c, s, u, v;
+ int i;
+
+ phi *= M_PI/180.0;
+ c = cos(phi);
+ s = sin(phi);
+ for (i=0; i<4; i++)
+ {
+ u = m[i][1];
+ v = m[i][3];
+ m[i][1] = c*u-s*v;
+ m[i][3] = s*u+c*v;
+ }
+}
+
+
+/* Add a rotation around the yz-plane to the matrix m. */
+static void rotateyz(float m[4][4], float phi)
+{
+ float c, s, u, v;
+ int i;
+
+ phi *= M_PI/180.0;
+ c = cos(phi);
+ s = sin(phi);
+ for (i=0; i<4; i++)
+ {
+ u = m[i][0];
+ v = m[i][3];
+ m[i][0] = c*u-s*v;
+ m[i][3] = s*u+c*v;
+ }
+}
+
+
+/* Compute the rotation matrix m from the rotation angles. */
+static void rotateall(float al, float be, float de, float ze, float et,
+ float th, float m[4][4])
+{
+ int i, j;
+
+ for (i=0; i<4; i++)
+ for (j=0; j<4; j++)
+ m[i][j] = (i==j);
+ rotatewx(m,al);
+ rotatewy(m,be);
+ rotatewz(m,de);
+ rotatexy(m,ze);
+ rotatexz(m,et);
+ rotateyz(m,th);
+}
+
+
+/* Compute the rotation matrix m from the 4d rotation angles. */
+static void rotateall4d(float ze, float et, float th, float m[4][4])
+{
+ int i, j;
+
+ for (i=0; i<4; i++)
+ for (j=0; j<4; j++)
+ m[i][j] = (i==j);
+ rotatexy(m,ze);
+ rotatexz(m,et);
+ rotateyz(m,th);
+}
+
+
+/* Multiply two rotation matrices: o=m*n. */
+static void mult_rotmat(float m[4][4], float n[4][4], float o[4][4])
+{
+ int i, j, k;
+
+ for (i=0; i<4; i++)
+ {
+ for (j=0; j<4; j++)
+ {
+ o[i][j] = 0.0;
+ for (k=0; k<4; k++)
+ o[i][j] += m[i][k]*n[k][j];
+ }
+ }
+}
+
+
+/* Compute a 4D rotation matrix from two unit quaternions. */
+static void quats_to_rotmat(float p[4], float q[4], float m[4][4])
+{
+ double al, be, de, ze, et, th;
+ double r00, r01, r02, r12, r22;
+
+ r00 = 1.0-2.0*(p[1]*p[1]+p[2]*p[2]);
+ r01 = 2.0*(p[0]*p[1]+p[2]*p[3]);
+ r02 = 2.0*(p[2]*p[0]-p[1]*p[3]);
+ r12 = 2.0*(p[1]*p[2]+p[0]*p[3]);
+ r22 = 1.0-2.0*(p[1]*p[1]+p[0]*p[0]);
+
+ al = atan2(-r12,r22)*180.0/M_PI;
+ be = atan2(r02,sqrt(r00*r00+r01*r01))*180.0/M_PI;
+ de = atan2(-r01,r00)*180.0/M_PI;
+
+ r00 = 1.0-2.0*(q[1]*q[1]+q[2]*q[2]);
+ r01 = 2.0*(q[0]*q[1]+q[2]*q[3]);
+ r02 = 2.0*(q[2]*q[0]-q[1]*q[3]);
+ r12 = 2.0*(q[1]*q[2]+q[0]*q[3]);
+ r22 = 1.0-2.0*(q[1]*q[1]+q[0]*q[0]);
+
+ et = atan2(-r12,r22)*180.0/M_PI;
+ th = atan2(r02,sqrt(r00*r00+r01*r01))*180.0/M_PI;
+ ze = atan2(-r01,r00)*180.0/M_PI;
+
+ rotateall(al,be,de,ze,et,-th,m);
+}
+
+
+/* Compute a fully saturated and bright color based on an angle. */
+static void color(double angle, float col[4])
+{
+ int s;
+ double t;
+
+ if (colors == COLORS_TWOSIDED)
+ return;
+
+ if (angle >= 0.0)
+ angle = fmod(angle,2.0*M_PI);
+ else
+ angle = fmod(angle,-2.0*M_PI);
+ s = floor(angle/(M_PI/3));
+ t = angle/(M_PI/3)-s;
+ if (s >= 6)
+ s = 0;
+ switch (s)
+ {
+ case 0:
+ col[0] = 1.0;
+ col[1] = t;
+ col[2] = 0.0;
+ break;
+ case 1:
+ col[0] = 1.0-t;
+ col[1] = 1.0;
+ col[2] = 0.0;
+ break;
+ case 2:
+ col[0] = 0.0;
+ col[1] = 1.0;
+ col[2] = t;
+ break;
+ case 3:
+ col[0] = 0.0;
+ col[1] = 1.0-t;
+ col[2] = 1.0;
+ break;
+ case 4:
+ col[0] = t;
+ col[1] = 0.0;
+ col[2] = 1.0;
+ break;
+ case 5:
+ col[0] = 1.0;
+ col[1] = 0.0;
+ col[2] = 1.0-t;
+ break;
+ }
+ if (display_mode == DISP_TRANSPARENT)
+ col[3] = 0.7;
+ else
+ col[3] = 1.0;
+}
+
+
+/* Set up the projective plane coordinates, colors, and texture. */
+static void setup_projective_plane(ModeInfo *mi, double umin, double umax,
+ double vmin, double vmax)
+{
+ int i, j, k;
+ double u, v, ur, vr;
+ double cu, su, cv2, sv2, cv4, sv4, c2u, s2u;
+ projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)];
+
+ ur = umax-umin;
+ vr = vmax-vmin;
+ for (i=0; i<=NUMV; i++)
+ {
+ for (j=0; j<=NUMU; j++)
+ {
+ k = i*(NUMU+1)+j;
+ if (appearance != APPEARANCE_DIRECTION_BANDS)
+ u = -ur*j/NUMU+umin;
+ else
+ u = ur*j/NUMU+umin;
+ v = vr*i/NUMV+vmin;
+ cu = cos(u);
+ su = sin(u);
+ c2u = cos(2.0*u);
+ s2u = sin(2.0*u);
+ sv2 = sin(0.5*v);
+ cv4 = cos(0.25*v);
+ sv4 = sin(0.25*v);
+ if (colors == COLORS_DEPTH)
+ color(((su*su*sv4*sv4-cv4*cv4)+1.0)*M_PI*2.0/3.0,pp->col[k]);
+ else if (colors == COLORS_DIRECTION)
+ color(2.0*M_PI+fmod(2.0*u,2.0*M_PI),pp->col[k]);
+ else /* colors == COLORS_DISTANCE */
+ color(v*(5.0/6.0),pp->col[k]);
+ pp->tex[k][0] = -32*u/(2.0*M_PI);
+ if (appearance != APPEARANCE_DISTANCE_BANDS)
+ pp->tex[k][1] = 32*v/(2.0*M_PI);
+ else
+ pp->tex[k][1] = 32*v/(2.0*M_PI)-0.5;
+ pp->x[k][0] = 0.5*s2u*sv4*sv4;
+ pp->x[k][1] = 0.5*su*sv2;
+ pp->x[k][2] = 0.5*cu*sv2;
+ pp->x[k][3] = 0.5*(su*su*sv4*sv4-cv4*cv4);
+ /* Avoid degenerate tangential plane basis vectors. */
+ if (v < FLT_EPSILON)
+ v = FLT_EPSILON;
+ cv2 = cos(0.5*v);
+ sv2 = sin(0.5*v);
+ sv4 = sin(0.25*v);
+ pp->xu[k][0] = c2u*sv4*sv4;
+ pp->xu[k][1] = 0.5*cu*sv2;
+ pp->xu[k][2] = -0.5*su*sv2;
+ pp->xu[k][3] = 0.5*s2u*sv4*sv4;
+ pp->xv[k][0] = 0.125*s2u*sv2;
+ pp->xv[k][1] = 0.25*su*cv2;
+ pp->xv[k][2] = 0.25*cu*cv2;
+ pp->xv[k][3] = 0.125*(su*su+1.0)*sv2;
+ }
+ }
+}
+
+
+/* Draw a 4d embedding of the projective plane projected into 3D. */
+static int projective_plane(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, cv2, sv2, cv4, sv4, c2u, s2u;
+ float q1[4], q2[4], r1[4][4], r2[4][4];
+ projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)];
+
+ if (view == VIEW_WALK || view == VIEW_WALKTURN)
+ {
+ /* Compute the rotation that rotates the projective plane in 4D without
+ the trackball rotations. */
+ rotateall4d(pp->zeta,pp->eta,pp->theta,mat);
+
+ u = pp->umove;
+ v = pp->vmove;
+ cu = cos(u);
+ su = sin(u);
+ c2u = cos(2.0*u);
+ s2u = sin(2.0*u);
+ sv2 = sin(0.5*v);
+ cv4 = cos(0.25*v);
+ sv4 = sin(0.25*v);
+ xx[0] = 0.5*s2u*sv4*sv4;
+ xx[1] = 0.5*su*sv2;
+ xx[2] = 0.5*cu*sv2;
+ xx[3] = 0.5*(su*su*sv4*sv4-cv4*cv4);
+ /* Avoid degenerate tangential plane basis vectors. */
+ if (v < FLT_EPSILON)
+ v = FLT_EPSILON;
+ cv2 = cos(0.5*v);
+ sv2 = sin(0.5*v);
+ sv4 = sin(0.25*v);
+ xxu[0] = c2u*sv4*sv4;
+ xxu[1] = 0.5*cu*sv2;
+ xxu[2] = -0.5*su*sv2;
+ xxu[3] = 0.5*s2u*sv4*sv4;
+ xxv[0] = 0.125*s2u*sv2;
+ xxv[1] = 0.25*su*cv2;
+ xxv[2] = 0.25*cu*cv2;
+ xxv[3] = 0.125*(su*su+1.0)*sv2;
+ 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 (projection_4d == DISP_4D_ORTHOGRAPHIC)
+ {
+ for (l=0; l<3; l++)
+ {
+ p[l] = y[l]+pp->offset4d[l];
+ pu[l] = yu[l];
+ pv[l] = yv[l];
+ }
+ }
+ else
+ {
+ s = y[3]+pp->offset4d[3];
+ q = 1.0/s;
+ t = q*q;
+ for (l=0; l<3; l++)
+ {
+ r = y[l]+pp->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/(pp->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]*pp->dumove+pv[0]*pp->dvmove;
+ pm[1] = pu[1]*pp->dumove+pv[1]*pp->dvmove;
+ pm[2] = pu[2]*pp->dumove+pv[2]*pp->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] |
+ */
+ pp->alpha = atan2(-n[2],-pm[2])*180/M_PI;
+ pp->beta = atan2(-b[2],sqrt(b[0]*b[0]+b[1]*b[1]))*180/M_PI;
+ pp->delta = atan2(b[1],-b[0])*180/M_PI;
+
+ /* Compute the rotation that rotates the projective plane in 4D. */
+ rotateall(pp->alpha,pp->beta,pp->delta,pp->zeta,pp->eta,pp->theta,mat);
+
+ u = pp->umove;
+ v = pp->vmove;
+ cu = cos(u);
+ su = sin(u);
+ s2u = sin(2.0*u);
+ sv2 = sin(0.5*v);
+ cv4 = cos(0.25*v);
+ sv4 = sin(0.25*v);
+ xx[0] = 0.5*s2u*sv4*sv4;
+ xx[1] = 0.5*su*sv2;
+ xx[2] = 0.5*cu*sv2;
+ xx[3] = 0.5*(su*su*sv4*sv4-cv4*cv4);
+ 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 (projection_4d == DISP_4D_ORTHOGRAPHIC)
+ {
+ for (l=0; l<3; l++)
+ p[l] = y[l]+pp->offset4d[l];
+ }
+ else
+ {
+ s = y[3]+pp->offset4d[3];
+ for (l=0; l<3; l++)
+ p[l] = (y[l]+pp->offset4d[l])/s;
+ }
+
+ pp->offset3d[0] = -p[0];
+ pp->offset3d[1] = -p[1]-DELTAY;
+ pp->offset3d[2] = -p[2];
+ }
+ else
+ {
+ /* Compute the rotation that rotates the projective plane in 4D,
+ including the trackball rotations. */
+ rotateall(pp->alpha,pp->beta,pp->delta,pp->zeta,pp->eta,pp->theta,r1);
+
+ gltrackball_get_quaternion(pp->trackballs[0],q1);
+ gltrackball_get_quaternion(pp->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<=NUMV; i++)
+ {
+ for (j=0; j<=NUMU; j++)
+ {
+ o = i*(NUMU+1)+j;
+ for (l=0; l<4; l++)
+ {
+ y[l] = (mat[l][0]*pp->x[o][0]+mat[l][1]*pp->x[o][1]+
+ mat[l][2]*pp->x[o][2]+mat[l][3]*pp->x[o][3]);
+ yu[l] = (mat[l][0]*pp->xu[o][0]+mat[l][1]*pp->xu[o][1]+
+ mat[l][2]*pp->xu[o][2]+mat[l][3]*pp->xu[o][3]);
+ yv[l] = (mat[l][0]*pp->xv[o][0]+mat[l][1]*pp->xv[o][1]+
+ mat[l][2]*pp->xv[o][2]+mat[l][3]*pp->xv[o][3]);
+ }
+ if (projection_4d == DISP_4D_ORTHOGRAPHIC)
+ {
+ for (l=0; l<3; l++)
+ {
+ pp->pp[o][l] = (y[l]+pp->offset4d[l])+pp->offset3d[l];
+ pu[l] = yu[l];
+ pv[l] = yv[l];
+ }
+ }
+ else
+ {
+ s = y[3]+pp->offset4d[3];
+ q = 1.0/s;
+ t = q*q;
+ for (l=0; l<3; l++)
+ {
+ r = y[l]+pp->offset4d[l];
+ pp->pp[o][l] = r*q+pp->offset3d[l];
+ pu[l] = (yu[l]*s-r*yu[3])*t;
+ pv[l] = (yv[l]*s-r*yv[3])*t;
+ }
+ }
+ pp->pn[o][0] = pu[1]*pv[2]-pu[2]*pv[1];
+ pp->pn[o][1] = pu[2]*pv[0]-pu[0]*pv[2];
+ pp->pn[o][2] = pu[0]*pv[1]-pu[1]*pv[0];
+ t = 1.0/sqrt(pp->pn[o][0]*pp->pn[o][0]+pp->pn[o][1]*pp->pn[o][1]+
+ pp->pn[o][2]*pp->pn[o][2]);
+ pp->pn[o][0] *= t;
+ pp->pn[o][1] *= t;
+ pp->pn[o][2] *= t;
+ }
+ }
+
+ if (colors == COLORS_TWOSIDED)
+ {
+ glColor3fv(mat_diff_red);
+ if (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,pp->tex_name);
+
+ if (appearance != APPEARANCE_DIRECTION_BANDS)
+ {
+ for (i=0; i<NUMV; i++)
+ {
+ if (appearance == APPEARANCE_DISTANCE_BANDS &&
+ ((i & (NUMB-1)) >= NUMB/4) && ((i & (NUMB-1)) < 3*NUMB/4))
+ continue;
+ if (display_mode == DISP_WIREFRAME)
+ glBegin(GL_QUAD_STRIP);
+ else
+ glBegin(GL_TRIANGLE_STRIP);
+ for (j=0; j<=NUMU; j++)
+ {
+ for (k=0; k<=1; k++)
+ {
+ l = (i+k);
+ m = j;
+ o = l*(NUMU+1)+m;
+ glNormal3fv(pp->pn[o]);
+ glTexCoord2fv(pp->tex[o]);
+ if (colors != COLORS_TWOSIDED)
+ {
+ glColor3fv(pp->col[o]);
+ glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,pp->col[o]);
+ }
+ glVertex3fv(pp->pp[o]);
+ polys++;
+ }
+ }
+ glEnd();
+ }
+ }
+ else /* appearance == APPEARANCE_DIRECTION_BANDS */
+ {
+ for (j=0; j<NUMU; j++)
+ {
+ if ((j & (NUMB-1)) >= NUMB/2)
+ continue;
+ if (display_mode == DISP_WIREFRAME)
+ glBegin(GL_QUAD_STRIP);
+ else
+ glBegin(GL_TRIANGLE_STRIP);
+ for (i=0; i<=NUMV; i++)
+ {
+ for (k=0; k<=1; k++)
+ {
+ l = i;
+ m = (j+k);
+ o = l*(NUMU+1)+m;
+ glNormal3fv(pp->pn[o]);
+ glTexCoord2fv(pp->tex[o]);
+ if (colors != COLORS_TWOSIDED)
+ {
+ glColor3fv(pp->col[o]);
+ glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,pp->col[o]);
+ }
+ glVertex3fv(pp->pp[o]);
+ polys++;
+ }
+ }
+ glEnd();
+ }
+ }
+
+ polys /= 2;
+ return polys;
+}
+
+
+/* Generate a texture image that shows the orientation reversal. */
+static void gen_texture(ModeInfo *mi)
+{
+ projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)];
+
+ glGenTextures(1,&pp->tex_name);
+ glBindTexture(GL_TEXTURE_2D,pp->tex_name);
+ glPixelStorei(GL_UNPACK_ALIGNMENT,1);
+ glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_WRAP_S,GL_REPEAT);
+ glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_WRAP_T,GL_REPEAT);
+ glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_MAG_FILTER,GL_LINEAR);
+ glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_MIN_FILTER,GL_LINEAR);
+ glTexEnvf(GL_TEXTURE_ENV,GL_TEXTURE_ENV_MODE,GL_MODULATE);
+ glTexImage2D(GL_TEXTURE_2D,0,GL_RGB,TEX_DIMENSION,TEX_DIMENSION,0,
+ GL_LUMINANCE,GL_UNSIGNED_BYTE,texture);
+}
+
+
+static void init(ModeInfo *mi)
+{
+ static const GLfloat light_ambient[] = { 0.0, 0.0, 0.0, 1.0 };
+ static const GLfloat light_diffuse[] = { 1.0, 1.0, 1.0, 1.0 };
+ static const GLfloat light_specular[] = { 1.0, 1.0, 1.0, 1.0 };
+ static const GLfloat light_position[] = { 1.0, 1.0, 1.0, 0.0 };
+ static const GLfloat mat_specular[] = { 1.0, 1.0, 1.0, 1.0 };
+ projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)];
+
+ if (walk_speed == 0.0)
+ walk_speed = 20.0;
+
+ if (view == VIEW_TURN)
+ {
+ pp->alpha = frand(360.0);
+ pp->beta = frand(360.0);
+ pp->delta = frand(360.0);
+ pp->zeta = 0.0;
+ pp->eta = 0.0;
+ pp->theta = 0.0;
+ }
+ else
+ {
+ pp->alpha = 0.0;
+ pp->beta = 0.0;
+ pp->delta = 0.0;
+ pp->zeta = 120.0;
+ pp->eta = 180.0;
+ pp->theta = 90.0;
+ }
+ pp->umove = frand(2.0*M_PI);
+ pp->vmove = frand(2.0*M_PI);
+ pp->dumove = 0.0;
+ pp->dvmove = 0.0;
+ pp->side = 1;
+ if (sin(walk_direction*M_PI/180.0) >= 0.0)
+ pp->dir = 1;
+ else
+ pp->dir = -1;
+
+ pp->offset4d[0] = 0.0;
+ pp->offset4d[1] = 0.0;
+ pp->offset4d[2] = 0.0;
+ pp->offset4d[3] = 1.2;
+ pp->offset3d[0] = 0.0;
+ pp->offset3d[1] = 0.0;
+ pp->offset3d[2] = -1.2;
+ pp->offset3d[3] = 0.0;
+
+ gen_texture(mi);
+ setup_projective_plane(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
+
+ if (marks)
+ glEnable(GL_TEXTURE_2D);
+ else
+ glDisable(GL_TEXTURE_2D);
+
+ glMatrixMode(GL_PROJECTION);
+ glLoadIdentity();
+ if (projection_3d == DISP_3D_PERSPECTIVE ||
+ view == VIEW_WALK || view == VIEW_WALKTURN)
+ {
+ if (view == VIEW_WALK || view == VIEW_WALKTURN)
+ gluPerspective(60.0,1.0,0.01,10.0);
+ else
+ gluPerspective(60.0,1.0,0.1,10.0);
+ }
+ else
+ {
+ glOrtho(-0.6,0.6,-0.6,0.6,0.1,10.0);
+ }
+ glMatrixMode(GL_MODELVIEW);
+ glLoadIdentity();
+
+# ifdef HAVE_JWZGLES /* #### glPolygonMode other than GL_FILL unimplemented */
+ if (display_mode == DISP_WIREFRAME)
+ display_mode = DISP_SURFACE;
+# endif
+
+ if (display_mode == DISP_SURFACE)
+ {
+ glEnable(GL_DEPTH_TEST);
+ glDepthFunc(GL_LESS);
+ glShadeModel(GL_SMOOTH);
+ glPolygonMode(GL_FRONT_AND_BACK,GL_FILL);
+ glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE);
+ glEnable(GL_LIGHTING);
+ glEnable(GL_LIGHT0);
+ glLightfv(GL_LIGHT0,GL_AMBIENT,light_ambient);
+ glLightfv(GL_LIGHT0,GL_DIFFUSE,light_diffuse);
+ glLightfv(GL_LIGHT0,GL_SPECULAR,light_specular);
+ glLightfv(GL_LIGHT0,GL_POSITION,light_position);
+ glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mat_specular);
+ glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,50.0);
+ glDepthMask(GL_TRUE);
+ glDisable(GL_BLEND);
+ }
+ else if (display_mode == DISP_TRANSPARENT)
+ {
+ glDisable(GL_DEPTH_TEST);
+ glShadeModel(GL_SMOOTH);
+ glPolygonMode(GL_FRONT_AND_BACK,GL_FILL);
+ glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE);
+ glEnable(GL_LIGHTING);
+ glEnable(GL_LIGHT0);
+ glLightfv(GL_LIGHT0,GL_AMBIENT,light_ambient);
+ glLightfv(GL_LIGHT0,GL_DIFFUSE,light_diffuse);
+ glLightfv(GL_LIGHT0,GL_SPECULAR,light_specular);
+ glLightfv(GL_LIGHT0,GL_POSITION,light_position);
+ glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mat_specular);
+ glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,50.0);
+ glDepthMask(GL_FALSE);
+ glEnable(GL_BLEND);
+ glBlendFunc(GL_SRC_ALPHA,GL_ONE);
+ }
+ else /* 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);
+ }
+}
+
+
+/* Redisplay the Klein bottle. */
+static void display_projectiveplane(ModeInfo *mi)
+{
+ projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)];
+
+ if (!pp->button_pressed)
+ {
+ if (view == VIEW_TURN)
+ {
+ pp->alpha += speed_wx * pp->speed_scale;
+ if (pp->alpha >= 360.0)
+ pp->alpha -= 360.0;
+ pp->beta += speed_wy * pp->speed_scale;
+ if (pp->beta >= 360.0)
+ pp->beta -= 360.0;
+ pp->delta += speed_wz * pp->speed_scale;
+ if (pp->delta >= 360.0)
+ pp->delta -= 360.0;
+ pp->zeta += speed_xy * pp->speed_scale;
+ if (pp->zeta >= 360.0)
+ pp->zeta -= 360.0;
+ pp->eta += speed_xz * pp->speed_scale;
+ if (pp->eta >= 360.0)
+ pp->eta -= 360.0;
+ pp->theta += speed_yz * pp->speed_scale;
+ if (pp->theta >= 360.0)
+ pp->theta -= 360.0;
+ }
+ if (view == VIEW_WALKTURN)
+ {
+ pp->zeta += speed_xy * pp->speed_scale;
+ if (pp->zeta >= 360.0)
+ pp->zeta -= 360.0;
+ pp->eta += speed_xz * pp->speed_scale;
+ if (pp->eta >= 360.0)
+ pp->eta -= 360.0;
+ pp->theta += speed_yz * pp->speed_scale;
+ if (pp->theta >= 360.0)
+ pp->theta -= 360.0;
+ }
+ if (view == VIEW_WALK || view == VIEW_WALKTURN)
+ {
+ pp->dvmove = (pp->dir*sin(walk_direction*M_PI/180.0)*
+ walk_speed*M_PI/4096.0);
+ pp->vmove += pp->dvmove;
+ if (pp->vmove > 2.0*M_PI)
+ {
+ pp->vmove = 4.0*M_PI-pp->vmove;
+ pp->umove = pp->umove-M_PI;
+ if (pp->umove < 0.0)
+ pp->umove += 2.0*M_PI;
+ pp->side = -pp->side;
+ pp->dir = -pp->dir;
+ pp->dvmove = -pp->dvmove;
+ }
+ if (pp->vmove < 0.0)
+ {
+ pp->vmove = -pp->vmove;
+ pp->umove = pp->umove-M_PI;
+ if (pp->umove < 0.0)
+ pp->umove += 2.0*M_PI;
+ pp->dir = -pp->dir;
+ pp->dvmove = -pp->dvmove;
+ }
+ pp->dumove = cos(walk_direction*M_PI/180.0)*walk_speed*M_PI/4096.0;
+ pp->umove += pp->dumove;
+ if (pp->umove >= 2.0*M_PI)
+ pp->umove -= 2.0*M_PI;
+ if (pp->umove < 0.0)
+ pp->umove += 2.0*M_PI;
+ }
+ }
+
+ glMatrixMode(GL_PROJECTION);
+ glLoadIdentity();
+ if (projection_3d == DISP_3D_PERSPECTIVE ||
+ view == VIEW_WALK || view == VIEW_WALKTURN)
+ {
+ if (view == VIEW_WALK || view == VIEW_WALKTURN)
+ gluPerspective(60.0,pp->aspect,0.01,10.0);
+ else
+ gluPerspective(60.0,pp->aspect,0.1,10.0);
+ }
+ else
+ {
+ if (pp->aspect >= 1.0)
+ glOrtho(-0.6*pp->aspect,0.6*pp->aspect,-0.6,0.6,0.1,10.0);
+ else
+ glOrtho(-0.6,0.6,-0.6/pp->aspect,0.6/pp->aspect,0.1,10.0);
+ }
+ glMatrixMode(GL_MODELVIEW);
+ glLoadIdentity();
+
+ mi->polygon_count = projective_plane(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
+}
+
+
+ENTRYPOINT void reshape_projectiveplane(ModeInfo *mi, int width, int height)
+{
+ projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)];
+
+ pp->WindW = (GLint)width;
+ pp->WindH = (GLint)height;
+ glViewport(0,0,width,height);
+ pp->aspect = (GLfloat)width/(GLfloat)height;
+}
+
+
+ENTRYPOINT Bool projectiveplane_handle_event(ModeInfo *mi, XEvent *event)
+{
+ projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)];
+ 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)
+ {
+ pp->button_pressed = True;
+ gltrackball_start(pp->trackballs[pp->current_trackball],
+ event->xbutton.x, event->xbutton.y,
+ MI_WIDTH(mi), MI_HEIGHT(mi));
+ return True;
+ }
+ else if (event->xany.type == ButtonRelease &&
+ event->xbutton.button == Button1)
+ {
+ pp->button_pressed = False;
+ return True;
+ }
+ else if (event->xany.type == KeyPress)
+ {
+ if (sym == XK_Shift_L || sym == XK_Shift_R)
+ {
+ pp->current_trackball = 1;
+ if (pp->button_pressed)
+ gltrackball_start(pp->trackballs[pp->current_trackball],
+ event->xbutton.x, event->xbutton.y,
+ MI_WIDTH(mi), MI_HEIGHT(mi));
+ return True;
+ }
+ }
+ else if (event->xany.type == KeyRelease)
+ {
+ if (sym == XK_Shift_L || sym == XK_Shift_R)
+ {
+ pp->current_trackball = 0;
+ if (pp->button_pressed)
+ gltrackball_start(pp->trackballs[pp->current_trackball],
+ event->xbutton.x, event->xbutton.y,
+ MI_WIDTH(mi), MI_HEIGHT(mi));
+ return True;
+ }
+ }
+ else if (event->xany.type == MotionNotify && pp->button_pressed)
+ {
+ gltrackball_track(pp->trackballs[pp->current_trackball],
+ event->xmotion.x, event->xmotion.y,
+ MI_WIDTH(mi), MI_HEIGHT(mi));
+ return True;
+ }
+
+ return False;
+}
+
+
+/*
+ *-----------------------------------------------------------------------------
+ *-----------------------------------------------------------------------------
+ * Xlock hooks.
+ *-----------------------------------------------------------------------------
+ *-----------------------------------------------------------------------------
+ */
+
+/*
+ *-----------------------------------------------------------------------------
+ * Initialize projectiveplane. Called each time the window changes.
+ *-----------------------------------------------------------------------------
+ */
+
+ENTRYPOINT void init_projectiveplane(ModeInfo *mi)
+{
+ projectiveplanestruct *pp;
+
+ if (projectiveplane == NULL)
+ {
+ projectiveplane =
+ (projectiveplanestruct *)calloc(MI_NUM_SCREENS(mi),
+ sizeof(projectiveplanestruct));
+ if (projectiveplane == NULL)
+ return;
+ }
+ pp = &projectiveplane[MI_SCREEN(mi)];
+
+
+ pp->trackballs[0] = gltrackball_init();
+ pp->trackballs[1] = gltrackball_init();
+ pp->current_trackball = 0;
+ pp->button_pressed = False;
+
+ /* Set the display mode. */
+ if (!strcasecmp(mode,"random"))
+ {
+ display_mode = random() % NUM_DISPLAY_MODES;
+ }
+ else if (!strcasecmp(mode,"wireframe"))
+ {
+ display_mode = DISP_WIREFRAME;
+ }
+ else if (!strcasecmp(mode,"surface"))
+ {
+ display_mode = DISP_SURFACE;
+ }
+ else if (!strcasecmp(mode,"transparent"))
+ {
+ display_mode = DISP_TRANSPARENT;
+ }
+ else
+ {
+ display_mode = random() % NUM_DISPLAY_MODES;
+ }
+
+ /* Orientation marks don't make sense in wireframe mode. */
+ if (display_mode == DISP_WIREFRAME)
+ marks = False;
+
+ /* Set the appearance. */
+ if (!strcasecmp(appear,"random"))
+ {
+ appearance = random() % NUM_APPEARANCES;
+ }
+ else if (!strcasecmp(appear,"solid"))
+ {
+ appearance = APPEARANCE_SOLID;
+ }
+ else if (!strcasecmp(appear,"distance-bands"))
+ {
+ appearance = APPEARANCE_DISTANCE_BANDS;
+ }
+ else if (!strcasecmp(appear,"direction-bands"))
+ {
+ appearance = APPEARANCE_DIRECTION_BANDS;
+ }
+ else
+ {
+ appearance = random() % NUM_APPEARANCES;
+ }
+
+ /* Set the color mode. */
+ if (!strcasecmp(color_mode,"random"))
+ {
+ colors = random() % NUM_COLORS;
+ }
+ else if (!strcasecmp(color_mode,"two-sided"))
+ {
+ colors = COLORS_TWOSIDED;
+ }
+ else if (!strcasecmp(color_mode,"distance"))
+ {
+ colors = COLORS_DISTANCE;
+ }
+ else if (!strcasecmp(color_mode,"direction"))
+ {
+ colors = COLORS_DIRECTION;
+ }
+ else if (!strcasecmp(color_mode,"depth"))
+ {
+ colors = COLORS_DEPTH;
+ }
+ else
+ {
+ colors = random() % NUM_COLORS;
+ }
+
+ /* Set the view mode. */
+ if (!strcasecmp(view_mode,"random"))
+ {
+ view = random() % NUM_VIEW_MODES;
+ }
+ else if (!strcasecmp(view_mode,"walk"))
+ {
+ view = VIEW_WALK;
+ }
+ else if (!strcasecmp(view_mode,"turn"))
+ {
+ view = VIEW_TURN;
+ }
+ else if (!strcasecmp(view_mode,"walk-turn"))
+ {
+ view = VIEW_WALKTURN;
+ }
+ else
+ {
+ 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;
+ else
+ projection_3d = DISP_3D_PERSPECTIVE;
+ }
+ else if (!strcasecmp(proj_3d,"perspective"))
+ {
+ projection_3d = DISP_3D_PERSPECTIVE;
+ }
+ else if (!strcasecmp(proj_3d,"orthographic"))
+ {
+ 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;
+ else
+ projection_3d = DISP_3D_PERSPECTIVE;
+ }
+
+ /* Set the 4d projection mode. */
+ if (!strcasecmp(proj_4d,"random"))
+ {
+ projection_4d = random() % NUM_DISP_4D_MODES;
+ }
+ else if (!strcasecmp(proj_4d,"perspective"))
+ {
+ projection_4d = DISP_4D_PERSPECTIVE;
+ }
+ else if (!strcasecmp(proj_4d,"orthographic"))
+ {
+ projection_4d = DISP_4D_ORTHOGRAPHIC;
+ }
+ else
+ {
+ projection_4d = random() % NUM_DISP_4D_MODES;
+ }
+
+ /* Modify the speeds to a useful range in walk-and-turn mode. */
+ if (view == VIEW_WALKTURN)
+ {
+ speed_wx *= 0.2;
+ speed_wy *= 0.2;
+ speed_wz *= 0.2;
+ speed_xy *= 0.2;
+ speed_xz *= 0.2;
+ speed_yz *= 0.2;
+ }
+
+ /* make multiple screens rotate at slightly different rates. */
+ pp->speed_scale = 0.9 + frand(0.3);
+
+ if ((pp->glx_context = init_GL(mi)) != NULL)
+ {
+ reshape_projectiveplane(mi,MI_WIDTH(mi),MI_HEIGHT(mi));
+ glDrawBuffer(GL_BACK);
+ init(mi);
+ }
+ else
+ {
+ MI_CLEARWINDOW(mi);
+ }
+}
+
+/*
+ *-----------------------------------------------------------------------------
+ * Called by the mainline code periodically to update the display.
+ *-----------------------------------------------------------------------------
+ */
+ENTRYPOINT void draw_projectiveplane(ModeInfo *mi)
+{
+ Display *display = MI_DISPLAY(mi);
+ Window window = MI_WINDOW(mi);
+ projectiveplanestruct *pp;
+
+ if (projectiveplane == NULL)
+ return;
+ pp = &projectiveplane[MI_SCREEN(mi)];
+
+ MI_IS_DRAWN(mi) = True;
+ if (!pp->glx_context)
+ return;
+
+ glXMakeCurrent(display,window,*(pp->glx_context));
+
+ glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
+ glLoadIdentity();
+
+ display_projectiveplane(mi);
+
+ if (MI_IS_FPS(mi))
+ do_fps (mi);
+
+ glFlush();
+
+ glXSwapBuffers(display,window);
+}
+
+
+/*
+ *-----------------------------------------------------------------------------
+ * 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_projectiveplane(ModeInfo *mi)
+{
+ if (projectiveplane != NULL)
+ {
+ int screen;
+
+ for (screen = 0; screen < MI_NUM_SCREENS(mi); screen++)
+ {
+ projectiveplanestruct *pp = &projectiveplane[screen];
+
+ if (pp->glx_context)
+ pp->glx_context = (GLXContext *)NULL;
+ }
+ (void) free((void *)projectiveplane);
+ projectiveplane = (projectiveplanestruct *)NULL;
+ }
+ FreeAllGL(mi);
+}
+
+#ifndef STANDALONE
+ENTRYPOINT void change_projectiveplane(ModeInfo *mi)
+{
+ projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)];
+
+ if (!pp->glx_context)
+ return;
+
+ glXMakeCurrent(MI_DISPLAY(mi),MI_WINDOW(mi),*(pp->glx_context));
+ init(mi);
+}
+#endif /* !STANDALONE */
+
+XSCREENSAVER_MODULE ("ProjectivePlane", projectiveplane)
+
+#endif /* USE_GL */
projects / xscreensaver / blobdiff