/* hypertorus --- Shows a hypertorus that rotates in 4d */
#if 0
-static const char sccsid[] = "@(#)hypertorus.c 1.1 03/05/18 xlockmore";
+static const char sccsid[] = "@(#)hypertorus.c 1.2 05/09/28 xlockmore";
#endif
-/* Copyright (c) 2003 Carsten Steger <carsten@mirsanmir.org>. */
+/* Copyright (c) 2003-2005 Carsten Steger <carsten@mirsanmir.org>. */
/*
* Permission to use, copy, modify, and distribute this software and its
*
* REVISION HISTORY:
* C. Steger - 03/05/18: Initial version
+ * C. Steger - 05/09/28: Added the spirals appearance mode
+ * and trackball support
*/
/*
* projected 3d torus can then be projected to the screen either perspectively
* or orthographically. There are three display modes for the torus: mesh
* (wireframe), solid, or transparent. Furthermore, the appearance of the
- * torus can be as a solid object or as a set of see-through bands. Finally,
- * the colors with with the torus is drawn can be set to either two-sided or
- * to colorwheel. In the first case, the torus is drawn with red on the
- * outside and green on the inside. This mode enables you to see that the
- * torus turns inside-out as it rotates in 4d. The second mode draws the
- * torus in a fully saturated color wheel. This gives a very nice effect
- * when combined with the see-through bands mode. The rotation speed for
- * each of the six planes around which the torus rotates can be chosen.
- * This program is very much inspired by Thomas Banchoff's book "Beyond the
- * Third Dimension: Geometry, Computer Graphics, and Higher Dimensions",
- * Scientific American Library, 1990.
+ * torus can be as a solid object or as a set of see-through bands or
+ * see-through spirals. Finally, the colors with with the torus is drawn can
+ * be set to either two-sided or to colorwheel. In the first case, the torus
+ * is drawn with red on the outside and green on the inside. This mode
+ * enables you to see that the torus turns inside-out as it rotates in 4d.
+ * The second mode draws the torus in a fully saturated color wheel. This
+ * gives a very nice effect when combined with the see-through bands or
+ * see-through spirals mode. The rotation speed for each of the six planes
+ * around which the torus rotates can be chosen. This program is very much
+ * 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_WIREFRAME_STR "0"
-#define DISP_SURFACE 1
-#define DISP_SURFACE_STR "1"
-#define DISP_TRANSPARENT 2
-#define DISP_TRANSPARENT_STR "2"
-
-#define APPEARANCE_SOLID 0
-#define APPEARANCE_SOLID_STR "0"
-#define APPEARANCE_BANDS 1
-#define APPEARANCE_BANDS_STR "1"
-
-#define COLORS_TWOSIDED 0
-#define COLORS_TWOSIDED_STR "0"
-#define COLORS_COLORWHEEL 1
-#define COLORS_COLORWHEEL_STR "1"
-
-#define DISP_3D_PERSPECTIVE 0
-#define DISP_3D_PERSPECTIVE_STR "0"
-#define DISP_3D_ORTHOGRAPHIC 1
-#define DISP_3D_ORTHOGRAPHIC_STR "1"
-
-#define DISP_4D_PERSPECTIVE 0
-#define DISP_4D_PERSPECTIVE_STR "0"
-#define DISP_4D_ORTHOGRAPHIC 1
-#define DISP_4D_ORTHOGRAPHIC_STR "1"
-
-#define DALPHA 1.1
-#define DALPHA_STR "1.1"
-#define DBETA 1.3
-#define DBETA_STR "1.3"
-#define DDELTA 1.5
-#define DDELTA_STR "1.5"
-#define DZETA 1.7
-#define DZETA_STR "1.7"
-#define DETA 1.9
-#define DETA_STR "1.9"
-#define DTHETA 2.1
-#define DTHETA_STR "2.1"
-
-#define DEF_DISPLAY_MODE DISP_SURFACE_STR
-#define DEF_APPEARANCE APPEARANCE_BANDS_STR
-#define DEF_COLORS COLORS_COLORWHEEL_STR
-#define DEF_3D_PROJECTION DISP_3D_PERSPECTIVE_STR
-#define DEF_4D_PROJECTION DISP_4D_PERSPECTIVE_STR
-#define DEF_DALPHA DALPHA_STR
-#define DEF_DBETA DBETA_STR
-#define DEF_DDELTA DDELTA_STR
-#define DEF_DZETA DZETA_STR
-#define DEF_DETA DETA_STR
-#define DEF_DTHETA DTHETA_STR
+#define DISP_WIREFRAME 0
+#define DISP_WIREFRAME_STR "0"
+#define DISP_SURFACE 1
+#define DISP_SURFACE_STR "1"
+#define DISP_TRANSPARENT 2
+#define DISP_TRANSPARENT_STR "2"
+
+#define APPEARANCE_SOLID 0
+#define APPEARANCE_SOLID_STR "0"
+#define APPEARANCE_BANDS 1
+#define APPEARANCE_BANDS_STR "1"
+#define APPEARANCE_SPIRALS 2
+#define APPEARANCE_SPIRALS_STR "2"
+#define APPEARANCE_SPIRALS_1 3
+#define APPEARANCE_SPIRALS_1_STR "3"
+#define APPEARANCE_SPIRALS_2 4
+#define APPEARANCE_SPIRALS_2_STR "4"
+#define APPEARANCE_SPIRALS_4 5
+#define APPEARANCE_SPIRALS_4_STR "5"
+#define APPEARANCE_SPIRALS_8 6
+#define APPEARANCE_SPIRALS_8_STR "6"
+#define APPEARANCE_SPIRALS_16 7
+#define APPEARANCE_SPIRALS_16_STR "7"
+
+#define COLORS_TWOSIDED 0
+#define COLORS_TWOSIDED_STR "0"
+#define COLORS_COLORWHEEL 1
+#define COLORS_COLORWHEEL_STR "1"
+
+#define DISP_3D_PERSPECTIVE 0
+#define DISP_3D_PERSPECTIVE_STR "0"
+#define DISP_3D_ORTHOGRAPHIC 1
+#define DISP_3D_ORTHOGRAPHIC_STR "1"
+
+#define DISP_4D_PERSPECTIVE 0
+#define DISP_4D_PERSPECTIVE_STR "0"
+#define DISP_4D_ORTHOGRAPHIC 1
+#define DISP_4D_ORTHOGRAPHIC_STR "1"
+
+#define DALPHA 1.1
+#define DALPHA_STR "1.1"
+#define DBETA 1.3
+#define DBETA_STR "1.3"
+#define DDELTA 1.5
+#define DDELTA_STR "1.5"
+#define DZETA 1.7
+#define DZETA_STR "1.7"
+#define DETA 1.9
+#define DETA_STR "1.9"
+#define DTHETA 2.1
+#define DTHETA_STR "2.1"
+
+#define DEF_DISPLAY_MODE DISP_SURFACE_STR
+#define DEF_APPEARANCE APPEARANCE_BANDS_STR
+#define DEF_COLORS COLORS_COLORWHEEL_STR
+#define DEF_3D_PROJECTION DISP_3D_PERSPECTIVE_STR
+#define DEF_4D_PROJECTION DISP_4D_PERSPECTIVE_STR
+#define DEF_DALPHA DALPHA_STR
+#define DEF_DBETA DBETA_STR
+#define DEF_DDELTA DDELTA_STR
+#define DEF_DZETA DZETA_STR
+#define DEF_DETA DETA_STR
+#define DEF_DTHETA DTHETA_STR
#ifdef STANDALONE
-# define PROGCLASS "Hypertorus"
-# define HACK_INIT init_hypertorus
-# define HACK_DRAW draw_hypertorus
-# define HACK_RESHAPE reshape_hypertorus
-# define hypertorus_opts xlockmore_opts
-# define DEFAULTS "*delay: 25000 \n" \
- "*showFPS: False \n" \
+# define PROGCLASS "Hypertorus"
+# define HACK_INIT init_hypertorus
+# define HACK_DRAW draw_hypertorus
+# define HACK_RESHAPE reshape_hypertorus
+# define HACK_HANDLE_EVENT hypertorus_handle_event
+# define EVENT_MASK PointerMotionMask|KeyReleaseMask
+# define hypertorus_opts xlockmore_opts
+# define DEFAULTS "*delay: 25000 \n" \
+ "*showFPS: False \n" \
# include "xlockmore.h" /* from the xscreensaver distribution */
#else /* !STANDALONE */
#ifdef USE_GL
+#include <X11/keysym.h>
#include <GL/gl.h>
#include <GL/glu.h>
+#include "gltrackball.h"
#ifdef USE_MODULES
static int display_mode;
static int appearance;
+static int num_spirals;
static int colors;
static int projection_3d;
static int projection_4d;
static float alpha, beta, delta, zeta, eta, theta;
static float aspect;
-static const float offset4d[4] = {
- 0.0, 0.0, 0.0, 2.0
-};
+/* Trackball states */
+trackball_state *trackballs[2];
+int current_trackball;
+Bool button_pressed;
-static const float offset3d[4] = {
- 0.0, 0.0, -2.0, 0.0
-};
+static const float offset4d[4] = { 0.0, 0.0, 0.0, 2.0 };
+static const float offset3d[4] = { 0.0, 0.0, -2.0, 0.0 };
static XrmOptionDescRec opts[] =
APPEARANCE_SOLID_STR },
{"-bands", ".hypertorus.appearance", XrmoptionNoArg,
APPEARANCE_BANDS_STR },
+ {"-spirals-1", ".hypertorus.appearance", XrmoptionNoArg,
+ APPEARANCE_SPIRALS_1_STR },
+ {"-spirals-2", ".hypertorus.appearance", XrmoptionNoArg,
+ APPEARANCE_SPIRALS_2_STR },
+ {"-spirals-4", ".hypertorus.appearance", XrmoptionNoArg,
+ APPEARANCE_SPIRALS_4_STR },
+ {"-spirals-8", ".hypertorus.appearance", XrmoptionNoArg,
+ APPEARANCE_SPIRALS_8_STR },
+ {"-spirals-16", ".hypertorus.appearance", XrmoptionNoArg,
+ APPEARANCE_SPIRALS_16_STR },
{"-twosided", ".hypertorus.colors", XrmoptionNoArg,
COLORS_TWOSIDED_STR },
{"-colorwheel", ".hypertorus.colors", XrmoptionNoArg,
{ "-transparent", "display the torus as a transparent surface" },
{ "-solid", "display the torus as a solid object" },
{ "-bands", "display the torus as see-through bands" },
+ { "-spirals-{1,2,4,8,16}", "display the torus as see-through spirals" },
{ "-twosided", "display the torus with two colors" },
{ "-colorwheel", "display the torus with a smooth color wheel" },
{ "-perspective-3d", "project the torus perspectively from 3d to 2d" },
}
+/* 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);
+}
+
+
+/* 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]);
+
+ ze = atan2(-r12,r22)*180.0/M_PI;
+ et = atan2(r02,sqrt(r00*r00+r01*r01))*180.0/M_PI;
+ th = 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)
{
break;
}
if (display_mode == DISP_TRANSPARENT)
- color[3] = 0.5;
+ color[3] = 0.7;
else
color[3] = 1.0;
glColor3fv(color);
}
-/* Draw a hyperturus projected into 3D. */
+/* Draw a hypertorus projected into 3D. Note that the spirals appearance
+ will only work correctly if numu and numv are set to 64 or any higher
+ power of 2. Similarly, the banded appearance will only work correctly
+ if numu and numv are divisible by 4. */
static void hypertorus(double umin, double umax, double vmin, double vmax,
int numu, int numv)
{
static GLfloat mat_diff_red[] = { 1.0, 0.0, 0.0, 1.0 };
static GLfloat mat_diff_green[] = { 0.0, 1.0, 0.0, 1.0 };
- static GLfloat mat_diff_trans_red[] = { 1.0, 0.0, 0.0, 0.5 };
- static GLfloat mat_diff_trans_green[] = { 0.0, 1.0, 0.0, 0.5 };
+ static GLfloat mat_diff_trans_red[] = { 1.0, 0.0, 0.0, 0.7 };
+ static GLfloat mat_diff_trans_green[] = { 0.0, 1.0, 0.0, 0.7 };
float p[3], pu[3], pv[3], n[3], mat[4][4];
- int i, j, k, l, m;
+ int i, j, k, l, m, b, skew;
double u, v, ur, vr;
double cu, su, cv, sv;
double xx[4], xxu[4], xxv[4], x[4], xu[4], xv[4];
double r, s, t;
+ float q1[4], q2[4], r1[4][4], r2[4][4];
- /* Compute the rotation that rotates the hypercube in 4D. */
- for (i=0; i<4; i++)
- for (j=0; j<4; j++)
- mat[i][j] = (i==j);
- rotatewx(mat,alpha);
- rotatewy(mat,beta);
- rotatewz(mat,delta);
- rotatexy(mat,zeta);
- rotatexz(mat,eta);
- rotateyz(mat,theta);
+ rotateall(alpha,beta,delta,zeta,eta,theta,r1);
+
+ gltrackball_get_quaternion(trackballs[0],q1);
+ gltrackball_get_quaternion(trackballs[1],q2);
+ quats_to_rotmat(q1,q2,r2);
+
+ mult_rotmat(r2,r1,mat);
if (colors != COLORS_COLORWHEEL)
{
}
}
+ skew = num_spirals;
ur = umax-umin;
vr = vmax-vmin;
for (i=0; i<numu; i++)
{
- if (appearance == APPEARANCE_BANDS && ((i & 3) >= 2))
+ if ((appearance == APPEARANCE_BANDS ||
+ appearance == APPEARANCE_SPIRALS) && ((i & 3) >= 2))
continue;
if (display_mode == DISP_WIREFRAME)
glBegin(GL_QUAD_STRIP);
m = j;
u = ur*l/numu+umin;
v = vr*m/numv+vmin;
- color(u);
+ if (appearance == APPEARANCE_SPIRALS)
+ {
+ u += 4.0*skew/numv*v;
+ b = ((i/4)&(skew-1))*(numu/(4*skew));
+ color(ur*4*b/numu+umin);
+ }
+ else
+ {
+ color(u);
+ }
cu = cos(u);
su = sin(u);
cv = cos(v);
static GLfloat light_position[] = { 1.0, 1.0, 1.0, 0.0 };
static GLfloat mat_specular[] = { 1.0, 1.0, 1.0, 1.0 };
+ if (appearance >= APPEARANCE_SPIRALS_1)
+ {
+ num_spirals = 1<<(appearance-APPEARANCE_SPIRALS_1);
+ appearance = APPEARANCE_SPIRALS;
+ }
+ else
+ {
+ num_spirals = 0;
+ }
+
alpha = 0.0;
beta = 0.0;
delta = 0.0;
/* Redisplay the hypertorus. */
static void display_hypertorus(void)
{
- alpha += speed_wx;
- if (alpha >= 360.0)
- alpha -= 360.0;
- beta += speed_wy;
- if (beta >= 360.0)
- beta -= 360.0;
- delta += speed_wz;
- if (delta >= 360.0)
- delta -= 360.0;
- zeta += speed_xy;
- if (zeta >= 360.0)
- zeta -= 360.0;
- eta += speed_xz;
- if (eta >= 360.0)
- eta -= 360.0;
- theta += speed_yz;
- if (theta >= 360.0)
- theta -= 360.0;
+ if (!button_pressed)
+ {
+ alpha += speed_wx;
+ if (alpha >= 360.0)
+ alpha -= 360.0;
+ beta += speed_wy;
+ if (beta >= 360.0)
+ beta -= 360.0;
+ delta += speed_wz;
+ if (delta >= 360.0)
+ delta -= 360.0;
+ zeta += speed_xy;
+ if (zeta >= 360.0)
+ zeta -= 360.0;
+ eta += speed_xz;
+ if (eta >= 360.0)
+ eta -= 360.0;
+ theta += speed_yz;
+ if (theta >= 360.0)
+ theta -= 360.0;
+ }
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
- if (display_mode == DISP_WIREFRAME)
- hypertorus(0.0,2.0*M_PI,0.0,2.0*M_PI,40,40);
- else
- hypertorus(0.0,2.0*M_PI,0.0,2.0*M_PI,60,60);
+ hypertorus(0.0,2.0*M_PI,0.0,2.0*M_PI,64,64);
}
}
+Bool hypertorus_handle_event(ModeInfo *mi, XEvent *event)
+{
+ Display *display = MI_DISPLAY(mi);
+ KeySym sym;
+
+ if (event->xany.type == ButtonPress &&
+ event->xbutton.button == Button1)
+ {
+ button_pressed = True;
+ gltrackball_start(trackballs[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)
+ {
+ button_pressed = False;
+ return True;
+ }
+ else if (event->xany.type == KeyPress)
+ {
+ sym = XKeycodeToKeysym(display,event->xkey.keycode,0);
+ if (sym == XK_Shift_L || sym == XK_Shift_R)
+ {
+ current_trackball = 1;
+ if (button_pressed)
+ gltrackball_start(trackballs[current_trackball],
+ event->xbutton.x, event->xbutton.y,
+ MI_WIDTH(mi), MI_HEIGHT(mi));
+ return True;
+ }
+ }
+ else if (event->xany.type == KeyRelease)
+ {
+ sym = XKeycodeToKeysym(display,event->xkey.keycode,0);
+ if (sym == XK_Shift_L || sym == XK_Shift_R)
+ {
+ current_trackball = 0;
+ if (button_pressed)
+ gltrackball_start(trackballs[current_trackball],
+ event->xbutton.x, event->xbutton.y,
+ MI_WIDTH(mi), MI_HEIGHT(mi));
+ return True;
+ }
+ }
+ else if (event->xany.type == MotionNotify && button_pressed)
+ {
+ gltrackball_track(trackballs[current_trackball],
+ event->xmotion.x, event->xmotion.y,
+ MI_WIDTH(mi), MI_HEIGHT(mi));
+ return True;
+ }
+
+ return False;
+}
+
+
/*
*-----------------------------------------------------------------------------
*-----------------------------------------------------------------------------
}
hp = &hyper[MI_SCREEN(mi)];
+ trackballs[0] = gltrackball_init();
+ trackballs[1] = gltrackball_init();
+ current_trackball = 0;
+ button_pressed = False;
+
if ((hp->glx_context = init_GL(mi)) != NULL)
{
reshape_hypertorus(mi,MI_WIDTH(mi),MI_HEIGHT(mi));
projects / xscreensaver / blobdiff