static const char sccsid[] = "@(#)klein.c 1.1 08/10/04 xlockmore";
#endif
-/* Copyright (c) 2005-2009 Carsten Steger <carsten@mirsanmir.org>. */
+/* Copyright (c) 2005-2013 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
*/
/*
- * 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.
*/
#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" \
{
{"-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
}
+/* 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 (colors == COLORS_DEPTH)
+ color((sin(u)*sin(0.5*v)+1.0)*M_PI*2.0/3.0,kb->col[k]);
+ else
+ color(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)
| -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. */
}
+/* 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 (view == VIEW_WALK || 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 (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 (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 (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 (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,kb->tex_name);
+
+ for (i=0; i<NUMU; i++)
+ {
+ if (appearance == APPEARANCE_BANDS && ((i & (NUMB-1)) >= NUMB/2))
+ continue;
+ if (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 (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 Lawson Klein bottle projected into 3D. */
static int lawson(ModeInfo *mi, double umin, double umax, double vmin,
double vmax)
| -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. */
kb->delta = 0.0;
}
kb->zeta = 0.0;
- if (bottle_type == KLEIN_BOTTLE_FIGURE_8)
+ if (bottle_type == KLEIN_BOTTLE_FIGURE_8 ||
+ bottle_type == KLEIN_BOTTLE_SQUEEZED_TORUS)
kb->eta = 0.0;
else
kb->eta = 45.0;
kb->offset3d[2] = -1.9;
kb->offset3d[3] = 0.0;
}
- else
+ else if (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 /* bottle_type == KLEIN_BOTTLE_LAWSON */
{
kb->offset4d[0] = 0.0;
kb->offset4d[1] = 0.0;
gen_texture(mi);
if (bottle_type == KLEIN_BOTTLE_FIGURE_8)
setup_figure8(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
- else
+ else if (bottle_type == KLEIN_BOTTLE_SQUEEZED_TORUS)
+ setup_squeezed_torus(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
+ else /* bottle_type == KLEIN_BOTTLE_LAWSON */
setup_lawson(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
if (marks)
# ifdef HAVE_JWZGLES /* #### glPolygonMode other than GL_FILL unimplemented */
if (display_mode == DISP_WIREFRAME)
- display_mode = DISP_SURFACE;
+ display_mode = DISP_SURFACE;
# endif
if (display_mode == DISP_SURFACE)
if (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 (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 /* bottle_type == KLEIN_BOTTLE_LAWSON */
mi->polygon_count = lawson(mi,0.0,2.0*M_PI,0.0,2.0*M_PI);
}
{
bottle_type = KLEIN_BOTTLE_FIGURE_8;
}
+ else if (!strcasecmp(klein_bottle,"squeezed-torus"))
+ {
+ bottle_type = KLEIN_BOTTLE_SQUEEZED_TORUS;
+ }
else if (!strcasecmp(klein_bottle,"lawson"))
{
bottle_type = KLEIN_BOTTLE_LAWSON;
projects / xscreensaver / blobdiff