Original 5.40

1 files changed, 1803 insertions, 0 deletions

diff --git a/hacks/glx/geodesicgears.c b/hacks/glx/geodesicgears.c
new file mode 100644
index 0000000..ecc7f26
--- /dev/null
+++ b/hacks/glx/geodesicgears.c
@@ -0,0 +1,1803 @@
+/* geodesicgears, Copyright (c) 2014-2015 Jamie Zawinski <jwz@jwz.org>
+ *
+ * Permission to use, copy, modify, distribute, and sell this software and its
+ * documentation for any purpose is hereby granted without fee, provided that
+ * the above copyright notice appear in all copies and that both that
+ * copyright notice and this permission notice appear in supporting
+ * documentation.  No representations are made about the suitability of this
+ * software for any purpose.  It is provided "as is" without express or 
+ * implied warranty.
+ *
+ * Inspired by http://bugman123.com/Gears/
+ * and by http://kennethsnelson.net/PortraitOfAnAtom.pdf
+ */
+
+#define DEFAULTS	"*delay:	30000       \n" \
+			"*count:        4           \n" \
+			"*wireframe:    False       \n" \
+			"*showFPS:      False       \n" \
+		        "*texFontCacheSize: 100     \n" \
+			"*suppressRotationAnimation: True\n" \
+		"*font:  -*-helvetica-medium-r-normal-*-*-160-*-*-*-*-*-*\n" \
+
+# define release_geodesic 0
+#undef countof
+#define countof(x) (sizeof((x))/sizeof((*x)))
+
+#include "xlockmore.h"
+#include "involute.h"
+#include "colors.h"
+#include "normals.h"
+#include "rotator.h"
+#include "gltrackball.h"
+#include <ctype.h>
+#include "texfont.h"
+
+
+#ifdef USE_GL /* whole file */
+
+#include "gllist.h"
+
+#define DEF_SPIN        "True"
+#define DEF_WANDER      "True"
+#define DEF_SPEED       "1.0"
+#define DEF_LABELS      "False"
+#define DEF_NUMBERS     "False"
+#define DEF_TIMEOUT     "20"
+
+typedef struct { double a, o; } LL;	/* latitude + longitude */
+
+/* 10:6 is a mismesh. */
+
+static const struct {
+  enum { PRISM, OCTO, DECA, G14, G18, G32, G92, G182 } type;
+  const GLfloat args[5];
+} gear_templates[] = {
+  { PRISM },
+  { OCTO },
+  { DECA },
+  { G14 },
+  { G18 },
+  { G32, { 15, 6,  0.4535 }},		/* teeth1, teeth2, radius1 */
+  { G32, { 15, 12, 0.3560 }},
+  { G32, { 20, 6,  0.4850 }},
+  { G32, { 20, 12, 0.3995 }},		/* double of 10:6 */
+  { G32, { 20, 18, 0.3375 }},
+  { G32, { 25, 6,  0.5065 }},
+  { G32, { 25, 12, 0.4300 }},
+  { G32, { 25, 18, 0.3725 }},
+  { G32, { 25, 24, 0.3270 }},
+  { G32, { 30, 12, 0.4535 }},		/* double of 15:6 */
+  { G32, { 30, 18, 0.3995 }},
+  { G32, { 30, 24, 0.3560 }},		/* double of 15:12 */
+  { G32, { 30, 30, 0.3205 }},
+  { G32, { 35, 12, 0.4710 }},
+  { G32, { 35, 18, 0.4208 }},
+  { G32, { 35, 24, 0.3800 }},
+  { G32, { 35, 30, 0.3450 }},
+  { G32, { 35, 36, 0.3160 }},
+  { G32, { 40, 12, 0.4850 }},		/* double of 20:6 */
+  { G32, { 40, 24, 0.3995 }},		/* double of 10:6, 20:12 */
+/*{ G32, { 40, 36, 0.3375 }},*/		/* double of 20:18 */
+  { G32, { 50, 12, 0.5065 }},		/* double of 25:6 */
+  { G32, { 50, 24, 0.4300 }},		/* double of 25:12 */
+
+  /* These all have phase errors and don't always mesh properly.
+     Maybe we should just omit them? */
+
+  { G92, { 35, 36, 16, 0.2660, 0.366 }},	/* teeth1, 2, 3, r1, pitch3 */
+  { G92, { 25, 36, 11, 0.2270, 0.315 }},
+/*{ G92, { 15, 15,  8, 0.2650, 0.356 }},*/
+/*{ G92, { 20, 21,  8, 0.2760, 0.355 }},*/
+  { G92, { 25, 27, 16, 0.2320, 0.359 }},
+  { G92, { 20, 36, 11, 0.1875, 0.283 }},
+  { G92, { 30, 30, 16, 0.2585, 0.374 }}, 	/* double of 15:15:8 */
+  { G92, { 20, 33, 11, 0.1970, 0.293 }},
+/*{ G92, { 10, 12,  8, 0.2030, 0.345 }},*/
+  { G92, { 30, 33, 16, 0.2455, 0.354 }},
+/*{ G92, { 25, 24,  8, 0.3050, 0.375 }},*/
+  { G92, { 20, 24, 16, 0.2030, 0.346 }},
+};
+
+
+typedef struct sphere_gear sphere_gear;
+struct sphere_gear {
+  int id;			/* name, for debugging */
+  XYZ axis;			/* the vector on which this gear's axis lies */
+  int direction;		/* rotation, +1 or -1 */
+  GLfloat offset;		/* rotational degrees from parent gear */
+  sphere_gear *parent;		/* gear driving this one, or 0 for root */
+  sphere_gear **children;	/* gears driven by this one (no loops) */
+  sphere_gear **neighbors;	/* gears touching this one (circular!) */
+  int nchildren, children_size;
+  int nneighbors, neighbors_size;
+  const gear *g;		/* shape of this gear (shared) */
+};
+
+
+typedef struct {
+  GLXContext *glx_context;
+  rotator *rot;
+  trackball_state *trackball;
+  Bool button_down_p;
+  int ncolors;
+  XColor *colors;
+  GLfloat color1[4], color2[4];
+  texture_font_data *font;
+
+  int nshapes, shapes_size;	/* how many 'gear' objects there are */
+  int ngears, gears_size;	/* how many 'sphere_gear' objects there are */
+  gear *shapes;
+  sphere_gear *gears;
+
+  int which;
+  int mode;  /* 0 = normal, 1 = out, 2 = in */
+  int mode_tick;
+  int next;  /* 0 = random, -1 = back, 1 = forward */
+  time_t draw_time;
+  int draw_tick;
+  char *desc;
+
+  GLfloat th;		/* rotation of the root sphere_gear in degrees. */
+
+} geodesic_configuration;
+
+static geodesic_configuration *bps = NULL;
+
+static int timeout;
+static Bool do_spin;
+static GLfloat speed;
+static Bool do_wander;
+static Bool do_labels;
+static Bool do_numbers;
+
+static XrmOptionDescRec opts[] = {
+  { "-spin",      ".spin",   XrmoptionNoArg, "True"  },
+  { "+spin",      ".spin",   XrmoptionNoArg, "False" },
+  { "-speed",     ".speed",  XrmoptionSepArg, 0      },
+  { "-wander",    ".wander", XrmoptionNoArg, "True"  },
+  { "+wander",    ".wander", XrmoptionNoArg, "False" },
+  { "-labels",	  ".labels", XrmoptionNoArg, "True"  },
+  { "+labels",	  ".labels", XrmoptionNoArg, "False" },
+  { "-numbers",	  ".numbers",XrmoptionNoArg, "True"  },
+  { "+numbers",	  ".numbers",XrmoptionNoArg, "False" },
+  { "-timeout",	  ".timeout",XrmoptionSepArg, 0 },
+};
+
+static argtype vars[] = {
+  {&do_spin,   "spin",   "Spin",   DEF_SPIN,   t_Bool},
+  {&do_wander, "wander", "Wander", DEF_WANDER, t_Bool},
+  {&speed,     "speed",  "Speed",  DEF_SPEED,  t_Float},
+  {&do_labels, "labels", "Labels", DEF_LABELS, t_Bool},
+  {&do_numbers,"numbers","Numbers",DEF_NUMBERS,t_Bool},
+  {&timeout,   "timeout","Seconds",DEF_TIMEOUT,t_Int},
+};
+
+ENTRYPOINT ModeSpecOpt geodesic_opts = {
+  countof(opts), opts, countof(vars), vars, NULL};
+
+
+#undef BELLRAND
+#define BELLRAND(n) ((frand((n)) + frand((n)) + frand((n))) / 3)
+
+
+
+static XYZ
+cross_product (XYZ a, XYZ b)
+{
+  XYZ c;
+  c.x = (a.y * b.z) - (a.z * b.y);
+  c.y = (a.z * b.x) - (a.x * b.z);
+  c.z = (a.x * b.y) - (a.y * b.x);
+  return c;
+}
+
+
+static GLfloat
+dot_product (XYZ a, XYZ b)
+{
+  return (a.x * b.x) + (a.y * b.y) + (a.z * b.z);
+}
+
+
+static XYZ
+normalize (XYZ v)
+{
+  GLfloat d = sqrt ((v.x * v.x) + (v.y * v.y) + (v.z * v.z));
+  if (d == 0)
+    v.x = v.y = v.z = 0;
+  else
+    {
+      v.x /= d;
+      v.y /= d;
+      v.z /= d;
+    }
+  return v;
+}
+
+
+static XYZ
+polar_to_cartesian (LL v)
+{
+  XYZ p;
+  p.x = cos (v.a) * cos (v.o);
+  p.y = cos (v.a) * sin (v.o);
+  p.z = sin (v.a);
+  return p;
+}
+
+
+
+
+static gear *
+add_gear_shape (ModeInfo *mi, GLfloat radius, int teeth)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  int wire = MI_IS_WIREFRAME(mi);
+  gear *g;
+  int i;
+
+  if (bp->nshapes >= bp->shapes_size - 1)
+    {
+      bp->shapes_size = bp->shapes_size * 1.2 + 4;
+      bp->shapes = (gear *)
+        realloc (bp->shapes, bp->shapes_size * sizeof(*bp->shapes));
+    }
+  g = &bp->shapes[bp->nshapes++];
+
+  memset (g, 0, sizeof(*g));
+
+  g->r = radius;
+  g->nteeth = teeth;
+  g->ratio = 1;
+
+  g->tooth_h = g->r / (teeth * 0.4);
+
+  if (g->tooth_h > 0.06)  /* stubbier teeth when small tooth count. */
+    g->tooth_h *= 0.6;
+
+  g->thickness  = 0.05 + BELLRAND(0.15);
+  g->thickness2 = g->thickness / 4;
+  g->thickness3 = g->thickness;
+  g->size       = wire ? INVOLUTE_SMALL : INVOLUTE_LARGE;
+
+  /* Move the disc's origin inward to make the edge of the disc be tangent
+     to the unit sphere. */
+  g->z = 1 - sqrt (1 - (g->r * g->r));
+
+  /* #### This isn't quite right */
+  g->tooth_slope = 1 + ((g->z * 2) / g->r);
+
+
+  /* Decide on shape of gear interior:
+     - just a ring with teeth;
+     - that, plus a thinner in-set "plate" in the middle;
+     - that, plus a thin raised "lip" on the inner plate;
+     - or, a wide lip (really, a thicker third inner plate.)
+   */
+  if (wire)
+    ;
+  else if ((random() % 10) == 0)
+    {
+      /* inner_r can go all the way in; there's no inset disc. */
+      g->inner_r = (g->r * 0.3) + frand((g->r - g->tooth_h/2) * 0.6);
+      g->inner_r2 = 0;
+      g->inner_r3 = 0;
+    }
+  else
+    {
+      /* inner_r doesn't go in very far; inner_r2 is an inset disc. */
+      g->inner_r  = (g->r * 0.5)  + frand((g->r - g->tooth_h) * 0.4);
+      g->inner_r2 = (g->r * 0.1) + frand(g->inner_r * 0.5);
+      g->inner_r3 = 0;
+
+      if (g->inner_r2 > (g->r * 0.2))
+        {
+          int nn = (random() % 10);
+          if (nn <= 2)
+            g->inner_r3 = (g->r * 0.1) + frand(g->inner_r2 * 0.2);
+          else if (nn <= 7 && g->inner_r2 >= 0.1)
+            g->inner_r3 = g->inner_r2 - 0.01;
+        }
+    }
+
+  /* If we have three discs, sometimes make the middle disc be spokes.
+   */
+  if (g->inner_r3 && ((random() % 5) == 0))
+    {
+      g->spokes = 2 + BELLRAND (5);
+      g->spoke_thickness = 1 + frand(7.0);
+      if (g->spokes == 2 && g->spoke_thickness < 2)
+        g->spoke_thickness += 1;
+    }
+
+  /* Sometimes add little nubbly bits, if there is room.
+   */
+  if (!wire && g->nteeth > 5)
+    {
+      double size = 0;
+      involute_biggest_ring (g, 0, &size, 0);
+      if (size > g->r * 0.2 && (random() % 5) == 0)
+        {
+          g->nubs = 1 + (random() % 16);
+          if (g->nubs > 8) g->nubs = 1;
+        }
+    }
+
+  /* Decide how complex the polygon model should be.
+   */
+  {
+    double pix = g->tooth_h * MI_HEIGHT(mi); /* approx. tooth size in pixels */
+    if (pix <= 4)        g->size = INVOLUTE_SMALL;
+    else if (pix <= 8)   g->size = INVOLUTE_MEDIUM;
+    else if (pix <= 30)  g->size = INVOLUTE_LARGE;
+    else                 g->size = INVOLUTE_HUGE;
+  }
+
+  if (g->inner_r3 > g->inner_r2) abort();
+  if (g->inner_r2 > g->inner_r) abort();
+  if (g->inner_r  > g->r) abort();
+
+  i = random() % bp->ncolors;
+  g->color[0] = bp->colors[i].red    / 65536.0;
+  g->color[1] = bp->colors[i].green  / 65536.0;
+  g->color[2] = bp->colors[i].blue   / 65536.0;
+  g->color[3] = 1;
+
+  i = (i + bp->ncolors / 2) % bp->ncolors;
+  g->color2[0] = bp->colors[i].red    / 65536.0;
+  g->color2[1] = bp->colors[i].green  / 65536.0;
+  g->color2[2] = bp->colors[i].blue   / 65536.0;
+  g->color2[3] = 1;
+
+  g->dlist = glGenLists (1);
+  glNewList (g->dlist, GL_COMPILE);
+
+#if 1
+  {
+    gear G, *g2 = &G;
+    *g2 = *g;
+
+    /* Move the gear inward so that its outer edge is on the disc, instead
+       of its midpoint. */
+    g2->z += g2->thickness/2;
+
+    /* 'radius' is at the surface but 'g->r' is at the center, so we need
+       to reverse the slope computation that involute.c does. */
+    g2->r /= (1 + (g2->thickness * g2->tooth_slope / 2));
+
+    glPushMatrix();
+    glTranslatef(g2->x, g2->y, -g2->z);
+
+    /* Line up the center of the point of tooth 0 with "up". */
+    glRotatef (90, 0, 0, 1);
+    glRotatef (180, 0, 1, 0);
+    glRotatef (-360.0 / g2->nteeth / 4, 0, 0, 1);
+
+    g->polygons = draw_involute_gear (g2, wire);
+    glPopMatrix();
+  }
+# else  /* draw discs */
+  {
+    glPushMatrix();
+    glTranslatef(g->x, g->y, -g->z);
+    glLineWidth (2);
+    glFrontFace (GL_CCW);
+    glNormal3f(0, 0, 1);
+    glColor3f(0, 0, 0);
+    glDisable (GL_LIGHTING);
+
+    glBegin(GL_LINES);
+    glVertex3f (0, 0, 0);
+    glVertex3f (0, radius, 0);
+    glEnd();
+
+    glColor3f(0.5, 0.5, 0.5);
+    glBegin(wire ? GL_LINE_LOOP : GL_TRIANGLE_FAN);
+    {
+      GLfloat th;
+      GLfloat step = M_PI * 2 / 128;
+      /* radius *= 1.005; */
+      glVertex3f (0, 0, 0);
+      for (th = 0; th < M_PI * 2 + step; th += step)
+        {
+          GLfloat x = cos(th) * radius;
+          GLfloat y = sin(th) * radius;
+          glVertex3f (x, y, 0);
+        }
+    }
+    glEnd();
+    if (!wire) glEnable(GL_LIGHTING);
+    glPopMatrix();
+  }
+# endif /* 0 */
+
+  glEndList ();
+
+  return g;
+}
+
+
+static void
+add_sphere_gear (ModeInfo *mi, gear *g, XYZ axis)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  sphere_gear *gg;
+  int i;
+
+  axis = normalize (axis);
+
+  /* If there's already a gear on this axis, don't duplicate it. */
+  for (i = 0; i < bp->ngears; i++)
+    {
+      XYZ o = bp->gears[i].axis;
+      if (o.x == axis.x && o.y == axis.y && o.z == axis.z)
+        return;
+    }
+
+  if (bp->ngears >= bp->gears_size - 1)
+    {
+      bp->gears_size = bp->gears_size * 1.2 + 10;
+      bp->gears = (sphere_gear *)
+        realloc (bp->gears, bp->gears_size * sizeof(*bp->gears));
+    }
+
+  gg = &bp->gears[bp->ngears];
+  memset (gg, 0, sizeof(*gg));
+  gg->id = bp->ngears;
+  gg->axis = axis;
+  gg->direction = 0;
+  gg->g = g;
+  bp->ngears++;
+}
+
+
+static void
+free_sphere_gears (ModeInfo *mi)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  int i;
+  for (i = 0; i < bp->nshapes; i++)
+    {
+      if (bp->shapes[i].dlist)
+        glDeleteLists (bp->shapes[i].dlist, 1);
+    }
+  free (bp->shapes);
+  bp->nshapes = 0;
+  bp->shapes_size = 0;
+  bp->shapes = 0;
+
+  for (i = 0; i < bp->ngears; i++)
+    {
+      sphere_gear *g = &bp->gears[i];
+      if (g->children)
+        free (g->children);
+      if (g->neighbors)
+        free (g->neighbors);
+    }
+  free (bp->gears);
+  bp->ngears = 0;
+  bp->gears_size = 0;
+  bp->gears = 0;
+}
+
+
+
+/* Is the gear a member of the list?
+ */
+static Bool
+gear_list_member (sphere_gear *g, sphere_gear **list, int count)
+{
+  int i;
+  for (i = 0; i < count; i++)
+    if (list[i] == g) return True;
+  return False;
+}
+
+
+/* Add the gear to the list, resizing it as needed.
+ */
+static void
+gear_list_push (sphere_gear *g,
+                sphere_gear ***listP,
+                int *countP, int *sizeP)
+{
+  if (*countP >= (*sizeP) - 1)
+    {
+      *sizeP = (*sizeP) * 1.2 + 4;
+      *listP = (sphere_gear **) realloc (*listP, (*sizeP) * sizeof(**listP));
+    }
+  (*listP)[*countP] = g;
+  (*countP)++;
+}
+
+
+/* Mark child and parent as being mutual neighbors.
+ */
+static void
+link_neighbors (sphere_gear *parent, sphere_gear *child)
+{
+  if (child == parent) abort();
+
+  /* Add child to parent's list of neighbors */
+  if (! gear_list_member (child, parent->neighbors, parent->nneighbors))
+    {
+      gear_list_push (child,
+                      &parent->neighbors,
+                      &parent->nneighbors,
+                      &parent->neighbors_size);
+      /* fprintf(stderr, "neighbor %2d -> %2d  (%d)\n", parent->id, child->id,
+                parent->nneighbors); */
+    }
+
+  /* Add parent to child's list of neighbors */
+  if (! gear_list_member (parent, child->neighbors, child->nneighbors))
+    {
+      gear_list_push (parent,
+                      &child->neighbors,
+                      &child->nneighbors,
+                      &child->neighbors_size);
+      /* fprintf(stderr, "neighbor %2d <- %2d\n", parent->id, child->id); */
+    }
+}
+
+/* Mark child as having parent, and vice versa.
+ */
+static void
+link_child (sphere_gear *parent, sphere_gear *child)
+{
+  if (child == parent) abort();
+  if (child->parent) return;
+
+  gear_list_push (child,
+                  &parent->children,
+                  &parent->nchildren,
+                  &parent->children_size);
+  child->parent = parent;
+  /* fprintf(stderr, "child    %2d -> %2d  (%d)\n", parent->id, child->id,
+            parent->nchildren); */
+}
+
+
+
+static void link_children (sphere_gear *);
+
+static void
+link_children (sphere_gear *parent)
+{
+  int i;
+# if 1    /* depth first */
+  for (i = 0; i < parent->nneighbors; i++)
+    {
+      sphere_gear *child = parent->neighbors[i];
+      if (! child->parent)
+        {
+          link_child (parent, child);
+          link_children (child);
+        }
+    }
+# else   /* breadth first */
+  for (i = 0; i < parent->nneighbors; i++)
+    {
+      sphere_gear *child = parent->neighbors[i];
+      if (! child->parent)
+        link_child (parent, child);
+    }
+  for (i = 0; i < parent->nchildren; i++)
+    {
+      sphere_gear *child = parent->children[i];
+      link_children (child);
+    }
+# endif
+}
+
+
+
+/* Whether the two gears touch.
+ */
+static Bool
+gears_touch_p (ModeInfo *mi, sphere_gear *a, sphere_gear *b)
+{
+  /* We need to know if the two discs on the surface overlap.
+
+     Find the angle between the axis of each disc, and a point on its edge:
+     the axis between the hypotenuse and adjacent of a right triangle between
+     the disc's radius and the origin.
+
+		      R
+		    _____
+		   |_|  /
+		   |   /
+		1  |  /
+		   |t/    t = asin(R)
+		   |/
+
+     Find the angle between the axes of the two discs.
+
+		  |
+		  |    /    angle = acos (v1 dot v2)
+		1 |   /     axis  = v1 cross v2
+		  |  /  1
+		  | /
+		  |/
+
+     If the sum of the first two angles is less than the third angle,
+     they touch.
+   */
+  XYZ p1 = a->axis;
+  XYZ p2 = b->axis;
+  double t1 = asin (a->g->r);
+  double t2 = asin (b->g->r);
+  double th = acos (dot_product (p1, p2));
+
+  return (t1 + t2 >= th);
+}
+
+
+/* Set the rotation direction for the gear and its kids.
+ */
+static void
+orient_gears (ModeInfo *mi, sphere_gear *g)
+{
+  int i;
+  if (g->parent)
+    g->direction = -g->parent->direction;
+  for (i = 0; i < g->nchildren; i++)
+    orient_gears (mi, g->children[i]);
+}
+
+
+/* Returns the global model coordinates of the given tooth of a gear.
+ */
+static XYZ
+tooth_coords (const sphere_gear *s, int tooth)
+{
+  const gear *g = s->g;
+  GLfloat off = s->offset * (M_PI / 180) * g->ratio * s->direction;
+  GLfloat th = (tooth * M_PI * 2 / g->nteeth) - off;
+  XYZ axis;
+  GLfloat angle;
+  XYZ from = { 0, 1, 0 };
+  XYZ to = s->axis;
+  XYZ p0, p1, p2;
+  GLfloat x, y, z, C, S, m[4][4];
+
+  axis  = cross_product (from, to);
+  angle = acos (dot_product (from, to));
+
+  p0 = normalize (axis);
+  x = p0.x;
+  y = p0.y;
+  z = p0.z;
+  C = cos(angle);
+  S = sin(angle);
+
+  /* this is what glRotatef does */
+  m[0][0] = x*x * (1 - C) + C;
+  m[1][0] = x*y * (1 - C) - z*S;
+  m[2][0] = x*z * (1 - C) + y*S;
+  m[3][0] = 0;
+
+  m[0][1] = y*x * (1 - C) + z*S;
+  m[1][1] = y*y * (1 - C) + C;
+  m[2][1] = y*z * (1 - C) - x*S;
+  m[3][1] = 0;
+
+  m[0][2] = x*z * (1 - C) - y*S;
+  m[1][2] = y*z * (1 - C) + x*S;
+  m[2][2] = z*z * (1 - C) + C;
+  m[3][2] = 0;
+
+  m[0][3] = 0;
+  m[1][3] = 0;
+  m[2][3] = 0;
+  m[3][3] = 1;
+
+  /* The point to transform */
+  p1.x = g->r * sin (th);
+  p1.z = g->r * cos (th);
+  p1.y = 1 - g->z;
+  p1 = normalize (p1);
+
+  /* transformation result */
+  p2.x = p1.x * m[0][0] + p1.y * m[1][0] + p1.z * m[2][0] + m[3][0];
+  p2.y = p1.x * m[0][1] + p1.y * m[1][1] + p1.z * m[2][1] + m[3][1];
+  p2.z = p1.x * m[0][2] + p1.y * m[1][2] + p1.z * m[2][2] + m[3][2];
+
+  return p2;
+}
+
+
+/* Returns the number of the tooth of the first gear that is closest
+   to any tooth of its parent.  Also the position of the parent tooth.
+ */
+static int
+parent_tooth (const sphere_gear *s, XYZ *parent)
+{
+  const sphere_gear *s2 = s->parent;
+  int i, j;
+  GLfloat min_dist = 99999;
+  int min_tooth = 0;
+  XYZ min_parent = { 0, 0, 0 };
+
+  if (s2)
+    for (i = 0; i < s->g->nteeth; i++)
+      {
+        XYZ p1 = tooth_coords (s, i);
+        for (j = 0; j < s2->g->nteeth; j++)
+          {
+            XYZ p2 = tooth_coords (s2, j);
+            XYZ d;
+            GLfloat dist;
+            d.x = p1.x - p2.x;
+            d.y = p1.y - p2.y;
+            d.z = p1.z - p2.z;
+
+            dist = sqrt (d.x*d.x + d.y*d.y + d.z*d.z);
+            if (dist < min_dist)
+              {
+                min_dist = dist;
+                min_parent = p2;
+                min_tooth = i;
+              }
+          }
+      }
+  *parent = min_parent;
+  return min_tooth;
+}
+
+
+/* Make all of the gear's children's teeth mesh properly.
+ */
+static void align_gear_teeth (sphere_gear *s);
+static void
+align_gear_teeth (sphere_gear *s)
+{
+  int i;
+  XYZ pc;
+
+  if (s->parent)
+    {
+      /* Iterate this gear's offset until we find a value for it that
+         minimizes the distance between this gear's parent-pointing
+         tooth, and the corresponding tooth on the parent.
+      */
+      int pt = parent_tooth (s, &pc);
+      GLfloat range = 360 / s->g->nteeth;
+      GLfloat steps = 64;
+      GLfloat min_dist = 999999;
+      GLfloat min_off = 0;
+      GLfloat off;
+
+      for (off = -range/2; off < range/2; off += range/steps)
+        {
+          XYZ tc, d;
+          GLfloat dist;
+          s->offset = off;
+          tc = tooth_coords (s, pt);
+          d.x = pc.x - tc.x;
+          d.y = pc.y - tc.y;
+          d.z = pc.z - tc.z;
+          dist = sqrt (d.x*d.x + d.y*d.y + d.z*d.z);
+          if (dist < min_dist)
+            {
+              min_dist = dist;
+              min_off = off;
+            }
+        }
+
+      s->offset = min_off;
+    }
+
+  /* Now do the children.  We have to do it in parent/child order because
+     the offset we just computed for the parent affects everyone downstream.
+   */
+  for (i = 0; i < s->nchildren; i++)
+    align_gear_teeth (s->children[i]);
+}
+
+
+
+static void
+describe_gears (ModeInfo *mi)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  int gears_per_teeth[1000];
+  int i;
+  int lines = 0;
+  memset (gears_per_teeth, 0, sizeof(gears_per_teeth));
+  for (i = 0; i < bp->ngears; i++)
+    gears_per_teeth[bp->gears[i].g->nteeth]++;
+  if (bp->desc) free (bp->desc);
+  bp->desc = (char *) malloc (80 * bp->ngears);
+  *bp->desc = 0;
+  for (i = 0; i < countof(gears_per_teeth); i++)
+    if (gears_per_teeth[i])
+      {
+        sprintf (bp->desc + strlen(bp->desc),
+                 "%s%d gears with %d teeth",
+                 (lines > 0 ? ",\n" : ""),
+                 gears_per_teeth[i], i);
+        lines++;
+      }
+  if (lines > 1)
+    sprintf (bp->desc + strlen(bp->desc), ",\n%d gears total", bp->ngears);
+  strcat (bp->desc, ".");
+}
+
+
+/* Takes the gears and makes an arbitrary DAG of them in order to compute
+   direction and gear ratios.
+ */
+static void
+sort_gears (ModeInfo *mi)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  sphere_gear *root = 0;
+  int i, j;
+
+  /* For each gear, compare it against every other gear.
+     If they touch, mark them as being each others' neighbors.
+   */
+  for (i = 0; i < bp->ngears; i++)
+    {
+      sphere_gear *a = &bp->gears[i];
+      for (j = 0; j < bp->ngears; j++)
+        {
+          sphere_gear *b = &bp->gears[j];
+          if (a == b) continue;
+          if (gears_touch_p (mi, a, b))
+            link_neighbors (a, b);
+        }
+    }
+
+  bp->gears[0].parent = &bp->gears[0]; /* don't give this one a parent */
+  link_children (&bp->gears[0]);
+  bp->gears[0].parent = 0;
+
+
+# if 0
+  for (i = 0; i < bp->ngears; i++)
+    {
+      fprintf (stderr, "%2d: p = %2d; k(%d, %d) = ",
+               i,
+               bp->gears[i].parent ? bp->gears[i].parent->id : -1,
+               bp->gears[i].nneighbors,
+               bp->gears[i].nchildren);
+      for (j = 0; j < bp->gears[i].nneighbors; j++)
+        fprintf (stderr, "%2d ", (int) bp->gears[i].neighbors[j]->id);
+      fprintf (stderr, "\t\t");
+      if (j < 5) fprintf (stderr, "\t");
+      for (j = 0; j < bp->gears[i].nchildren; j++)
+        fprintf (stderr, "%2d ", (int) bp->gears[i].children[j]->id);
+      fprintf (stderr,"\n");
+    }
+  fprintf (stderr,"\n");
+# endif /* 0 */
+
+
+  /* If there is more than one gear with no parent, we fucked up. */
+
+  root = 0;
+  for (i = 0; i < bp->ngears; i++)
+    {
+      sphere_gear *g = &bp->gears[i];
+      if (!g->parent)
+        root = g;
+    }
+
+  if (! root) abort();
+
+  root->direction = 1;
+  orient_gears (mi, root);
+
+  /* If there are any gears with no direction, they aren't reachable. */
+  for (i = 0; i < bp->ngears; i++)
+    {
+      sphere_gear *g = &bp->gears[i];
+      if (g->direction == 0)
+        fprintf(stderr,"INTERNAL ERROR: unreachable: %d\n", g->id);
+    }
+
+  align_gear_teeth (root);
+  describe_gears (mi);
+}
+
+
+/* Create 5 identical gears arranged on the faces of a uniform
+   triangular prism.
+ */
+static void
+make_prism (ModeInfo *mi)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  gear *g;
+  XYZ a;
+  int i;
+  int teeth = 4 * (4 + (int) (BELLRAND(20)));
+  if (teeth % 4) abort();  /* must be a multiple of 4 */
+
+  g = add_gear_shape (mi, 0.7075, teeth);
+
+  a.x = 0; a.y = 0; a.z = 1;
+  add_sphere_gear (mi, g, a);
+  a.z = -1;
+  add_sphere_gear (mi, g, a);
+
+  a.z = 0;
+  for (i = 0; i < 3; i++)
+    {
+      GLfloat th = i * M_PI * 2 / 3;
+      a.x = cos (th);
+      a.y = sin (th);
+      add_sphere_gear (mi, g, a);
+    }
+
+  if (bp->ngears != 5) abort();
+}
+
+
+/* Create 8 identical gears arranged on the faces of an octohedron
+   (or alternately, arranged on the diagonals of a cube.)
+ */
+static void
+make_octo (ModeInfo *mi)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  static const XYZ verts[] = {{ -1, -1, -1 },
+                              { -1, -1,  1 },
+                              { -1,  1,  1 },
+                              { -1,  1, -1 },
+                              {  1, -1,  1 },
+                              {  1, -1, -1 },
+                              {  1,  1, -1 },
+                              {  1,  1,  1 }};
+  gear *g;
+  int i;
+  int teeth = 4 * (4 + (int) (BELLRAND(20)));
+  if (teeth % 4) abort();  /* must be a multiple of 4 */
+
+  g = add_gear_shape (mi, 0.578, teeth);
+  for (i = 0; i < countof(verts); i++)
+    add_sphere_gear (mi, g, verts[i]);
+
+  if (bp->ngears != 8) abort();
+}
+
+
+/* Create 10 identical gears arranged on the faces of ... something.
+   I'm not sure what polyhedron is the basis of this.
+ */
+static void
+make_deca (ModeInfo *mi)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  gear *g;
+  XYZ a;
+  int i, j;
+  int teeth = 4 * (4 + (int) (BELLRAND(15)));
+  if (teeth % 4) abort();  /* must be a multiple of 4 */
+
+  g = add_gear_shape (mi, 0.5415, teeth);
+
+  a.x = 0; a.y = 0; a.z = 1;
+  add_sphere_gear (mi, g, a);
+  a.z = -1;
+  add_sphere_gear (mi, g, a);
+
+  for (j = -1; j <= 1; j += 2)
+    {
+      GLfloat off = (j < 0 ? 0 : M_PI / 4);
+      LL v;
+      v.a = j * M_PI * 0.136;  /* #### Empirical. What is this? */
+      for (i = 0; i < 4; i++)
+        {
+          v.o = i * M_PI / 2 + off;
+          a = polar_to_cartesian (v);
+          add_sphere_gear (mi, g, a);
+        }
+    }
+  if (bp->ngears != 10) abort();
+}
+
+
+/* Create 14 identical gears arranged on the faces of ... something.
+   I'm not sure what polyhedron is the basis of this.
+ */
+static void
+make_14 (ModeInfo *mi)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  gear *g;
+  XYZ a;
+  int i;
+  GLfloat r = 0.4610;
+  int teeth = 6 * (2 + (int) (BELLRAND(4)));
+  if (teeth % 6) abort();  /* must be a multiple of 6. I think? */
+  /* mismeshes: 24 30 34 36 42 48 54 60 */
+
+  /* North, south */
+  g = add_gear_shape (mi, r, teeth);
+  a.x = 0; a.y = 0; a.z = 1;
+  add_sphere_gear (mi, g, a);
+  a.z = -1;
+  add_sphere_gear (mi, g, a);
+
+  /* Equator */
+  a.z = 0;
+  for (i = 0; i < 4; i++)
+    {
+      GLfloat th = i * M_PI * 2 / 4 + (M_PI / 4);
+      a.x = cos(th);
+      a.y = sin(th);
+      add_sphere_gear (mi, g, a);
+    }
+
+  /* The other 8 */
+  g = add_gear_shape (mi, r, teeth);
+
+  for (i = 0; i < 4; i++)
+    {
+      LL v;
+      v.a = M_PI * 0.197;  /* #### Empirical.  Also, wrong.  What is this? */
+      v.o = i * M_PI * 2 / 4;
+      a = polar_to_cartesian (v);
+      add_sphere_gear (mi, g, a);
+      v.a = -v.a;
+      a = polar_to_cartesian (v);
+      add_sphere_gear (mi, g, a);
+    }
+
+  if (bp->ngears != 14) abort();
+}
+
+
+/* Create 18 identical gears arranged on the faces of ... something.
+   I'm not sure what polyhedron is the basis of this.
+ */
+static void
+make_18 (ModeInfo *mi)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  gear *g, *g2;
+  XYZ a;
+  int i;
+  GLfloat r = 0.3830;
+  int sizes[] = { 8, 12, 16, 20 };  /* 10, 14, 18, 26 and 34 don't work */
+  int teeth = sizes[random() % countof(sizes)] * (1 + (random() % 4));
+
+  /* North, south */
+  g = add_gear_shape (mi, r, teeth);
+  a.x = 0; a.y = 0; a.z = 1;
+  add_sphere_gear (mi, g, a);
+  a.z = -1;
+  add_sphere_gear (mi, g, a);
+
+  /* Equator */
+  g2 = add_gear_shape (mi, r, teeth);
+  a.z = 0;
+  for (i = 0; i < 8; i++)
+    {
+      GLfloat th = i * M_PI * 2 / 8 + (M_PI / 4);
+      a.x = cos(th);
+      a.y = sin(th);
+      add_sphere_gear (mi, (i & 1 ? g : g2), a);
+    }
+
+  /* The other 16 */
+  g = add_gear_shape (mi, r, teeth);
+
+  for (i = 0; i < 4; i++)
+    {
+      LL v;
+      v.a = M_PI * 0.25;
+      v.o = i * M_PI * 2 / 4;
+      a = polar_to_cartesian (v);
+      add_sphere_gear (mi, g, a);
+      v.a = -v.a;
+      a = polar_to_cartesian (v);
+      add_sphere_gear (mi, g, a);
+    }
+
+  if (bp->ngears != 18) abort();
+}
+
+
+/* Create 32 gears arranged along a truncated icosahedron:
+   One gear on each of the 20 faces, and one on each of the 12 vertices.
+ */
+static void
+make_32 (ModeInfo *mi, const GLfloat *args)
+{
+  /* http://bugman123.com/Gears/32GearSpheres/ */
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  GLfloat th0 = atan (0.5);  /* lat division: 26.57 deg */
+  GLfloat s = M_PI / 5;	     /* lon division: 72 deg    */
+  int i;
+
+  int teeth1 = args[0];
+  int teeth2 = args[1];
+  GLfloat r1 = args[2];
+  GLfloat ratio = teeth2 / (GLfloat) teeth1;
+  GLfloat r2 = r1 * ratio;
+
+  gear *gear1, *gear2;
+
+  if (teeth1 % 5) abort();
+  if (teeth2 % 6) abort();
+
+  gear1 = add_gear_shape (mi, r1, teeth1);
+  gear2 = add_gear_shape (mi, r2, teeth2);
+  gear2->ratio = 1 / ratio;
+
+  {
+    XYZ a = { 0, 0, 1 };
+    XYZ b = { 0, 0, -1 };
+    add_sphere_gear (mi, gear1, a);
+    add_sphere_gear (mi, gear1, b);
+  }
+
+  for (i = 0; i < 10; i++)
+    {
+      GLfloat th1 = s * i;
+      GLfloat th2 = s * (i+1);
+      GLfloat th3 = s * (i+2);
+      LL v1, v2, v3, vc;
+      XYZ p1, p2, p3, pc, pc2;
+      v1.a = th0;    v1.o = th1;
+      v2.a = th0;    v2.o = th3;
+      v3.a = -th0;   v3.o = th2;
+      vc.a = M_PI/2; vc.o = th2;
+
+      if (! (i & 1)) /* southern hemisphere */
+        {
+          v1.a = -v1.a;
+          v2.a = -v2.a;
+          v3.a = -v3.a;
+          vc.a = -vc.a;
+        }
+
+      p1 = polar_to_cartesian (v1);
+      p2 = polar_to_cartesian (v2);
+      p3 = polar_to_cartesian (v3);
+      pc = polar_to_cartesian (vc);
+
+      /* Two faces: 123 and 12c. */
+
+      add_sphere_gear (mi, gear1, p1);	/* left shared point of 2 triangles */
+
+      pc2.x = (p1.x + p2.x + p3.x) / 3;	/* center of bottom triangle */
+      pc2.y = (p1.y + p2.y + p3.y) / 3;
+      pc2.z = (p1.z + p2.z + p3.z) / 3;
+      add_sphere_gear (mi, gear2, pc2);
+
+      pc2.x = (p1.x + p2.x + pc.x) / 3;	/* center of top triangle */
+      pc2.y = (p1.y + p2.y + pc.y) / 3;
+      pc2.z = (p1.z + p2.z + pc.z) / 3;
+      add_sphere_gear (mi, gear2, pc2);
+    }
+
+  if (bp->ngears != 32) abort();
+}
+
+
+/* Create 92 gears arranged along a geodesic sphere: 20 + 12 + 60.
+   (frequency 3v, class-I geodesic tessellation of an icosahedron)
+ */
+static void
+make_92 (ModeInfo *mi, const GLfloat *args)
+{
+  /* http://bugman123.com/Gears/92GearSpheres/ */
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  GLfloat th0 = atan (0.5);  /* lat division: 26.57 deg */
+  GLfloat s = M_PI / 5;	     /* lon division: 72 deg    */
+  int i;
+
+  int tscale = 2;	/* These don't mesh properly, so let's increase the
+                           number of teeth so that it's not so obvious. */
+
+  int teeth1 = args[0] * tscale;
+  int teeth2 = args[1] * tscale;
+  int teeth3 = args[2] * tscale;
+  GLfloat r1 = args[3];
+  GLfloat ratio2 = teeth2 / (GLfloat) teeth1;
+  GLfloat ratio3 = teeth3 / (GLfloat) teeth2;
+  GLfloat r2 = r1 * ratio2;
+  GLfloat r3 = r2 * ratio3;
+
+  GLfloat r4 = args[4];	/* #### Empirical. Not sure what its basis is. */
+  GLfloat r5 = 1 - r4;
+
+  gear *gear1, *gear2, *gear3;
+
+  gear1 = add_gear_shape (mi, r1, teeth1);
+  gear2 = add_gear_shape (mi, r2, teeth2);
+  gear3 = add_gear_shape (mi, r3, teeth3);
+  gear2->ratio = 1 / ratio2;
+  gear3->ratio = 1 / ratio3;
+
+  {
+    XYZ a = { 0, 0, 1 };
+    XYZ b = { 0, 0, -1 };
+    add_sphere_gear (mi, gear1, a);
+    add_sphere_gear (mi, gear1, b);
+  }
+
+  for (i = 0; i < 10; i++)
+    {
+      GLfloat th1 = s * i;
+      GLfloat th2 = s * (i+1);
+      GLfloat th3 = s * (i+2);
+      LL v1, v2, v3, vc;
+      XYZ p1, p2, p3, pc, pc2;
+      v1.a = th0;    v1.o = th1;
+      v2.a = th0;    v2.o = th3;
+      v3.a = -th0;   v3.o = th2;
+      vc.a = M_PI/2; vc.o = th2;
+
+      if (! (i & 1)) /* southern hemisphere */
+        {
+          v1.a = -v1.a;
+          v2.a = -v2.a;
+          v3.a = -v3.a;
+          vc.a = -vc.a;
+        }
+
+      p1 = polar_to_cartesian (v1);
+      p2 = polar_to_cartesian (v2);
+      p3 = polar_to_cartesian (v3);
+      pc = polar_to_cartesian (vc);
+
+      /* Two faces: 123 and 12c. */
+
+      add_sphere_gear (mi, gear1, p1);	/* left shared point of 2 triangles */
+
+      pc2.x = (p1.x + p2.x + p3.x) / 3;	/* center of bottom triangle */
+      pc2.y = (p1.y + p2.y + p3.y) / 3;
+      pc2.z = (p1.z + p2.z + p3.z) / 3;
+      add_sphere_gear (mi, gear2, pc2);
+
+      pc2.x = (p1.x + p2.x + pc.x) / 3;	/* center of top triangle */
+      pc2.y = (p1.y + p2.y + pc.y) / 3;
+      pc2.z = (p1.z + p2.z + pc.z) / 3;
+      add_sphere_gear (mi, gear2, pc2);
+
+      /* left edge of bottom triangle, 1/3 in */
+      pc2.x = p1.x + (p3.x - p1.x) * r4;
+      pc2.y = p1.y + (p3.y - p1.y) * r4;
+      pc2.z = p1.z + (p3.z - p1.z) * r4;
+      add_sphere_gear (mi, gear3, pc2);
+
+      /* left edge of bottom triangle, 2/3 in */
+      pc2.x = p1.x + (p3.x - p1.x) * r5;
+      pc2.y = p1.y + (p3.y - p1.y) * r5;
+      pc2.z = p1.z + (p3.z - p1.z) * r5;
+      add_sphere_gear (mi, gear3, pc2);
+
+      /* left edge of top triangle, 1/3 in */
+      pc2.x = p1.x + (pc.x - p1.x) * r4;
+      pc2.y = p1.y + (pc.y - p1.y) * r4;
+      pc2.z = p1.z + (pc.z - p1.z) * r4;
+      add_sphere_gear (mi, gear3, pc2);
+
+      /* left edge of top triangle, 2/3 in */
+      pc2.x = p1.x + (pc.x - p1.x) * r5;
+      pc2.y = p1.y + (pc.y - p1.y) * r5;
+      pc2.z = p1.z + (pc.z - p1.z) * r5;
+      add_sphere_gear (mi, gear3, pc2);
+
+      /* center of shared edge, 1/3 in */
+      pc2.x = p1.x + (p2.x - p1.x) * r4;
+      pc2.y = p1.y + (p2.y - p1.y) * r4;
+      pc2.z = p1.z + (p2.z - p1.z) * r4;
+      add_sphere_gear (mi, gear3, pc2);
+
+      /* center of shared edge, 2/3 in */
+      pc2.x = p1.x + (p2.x - p1.x) * r5;
+      pc2.y = p1.y + (p2.y - p1.y) * r5;
+      pc2.z = p1.z + (p2.z - p1.z) * r5;
+      add_sphere_gear (mi, gear3, pc2);
+    }
+
+  if (bp->ngears != 92) abort();
+}
+
+static void
+make_182 (ModeInfo *mi, const GLfloat *args)
+{
+  /* #### TODO: http://bugman123.com/Gears/182GearSpheres/ */
+  abort();
+}
+
+
+/* Window management, etc
+ */
+ENTRYPOINT void
+reshape_geodesic (ModeInfo *mi, int width, int height)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  GLfloat h = (GLfloat) height / (GLfloat) width;
+  int y = 0;
+
+  if (width > height * 5) {   /* tiny window: show middle */
+    height = width * 9/16;
+    y = -height/2;
+    h = height / (GLfloat) width;
+  }
+
+  glXMakeCurrent(MI_DISPLAY(mi), MI_WINDOW(mi), *(bp->glx_context));
+
+  glViewport (0, y, (GLint) width, (GLint) height);
+
+  glMatrixMode(GL_PROJECTION);
+  glLoadIdentity();
+  gluPerspective (30.0, 1/h, 1.0, 100.0);
+
+  glMatrixMode(GL_MODELVIEW);
+  glLoadIdentity();
+  gluLookAt( 0.0, 0.0, 30.0,
+             0.0, 0.0, 0.0,
+             0.0, 1.0, 0.0);
+
+# ifdef HAVE_MOBILE	/* Keep it the same relative size when rotated. */
+  {
+    int o = (int) current_device_rotation();
+    if (o != 0 && o != 180 && o != -180)
+      glScalef (1/h, 1/h, 1/h);
+  }
+# endif
+
+  glClear(GL_COLOR_BUFFER_BIT);
+}
+
+
+static void
+pick_shape (ModeInfo *mi, time_t last)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  int count = countof (gear_templates);
+
+  if (bp->colors)
+    free (bp->colors);
+
+  bp->ncolors = 1024;
+  bp->colors = (XColor *) calloc(bp->ncolors, sizeof(XColor));
+  make_smooth_colormap (0, 0, 0,
+                        bp->colors, &bp->ncolors,
+                        False, 0, False);
+
+  free_sphere_gears (mi);
+
+  if (last == 0)
+    {
+      bp->which = random() % count;
+    }
+  else if (bp->next < 0)
+    {
+      bp->which--;
+      if (bp->which < 0) bp->which = count-1;
+      bp->next = 0;
+    }
+  else if (bp->next > 0)
+    {
+      bp->which++;
+      if (bp->which >= count) bp->which = 0;
+      bp->next = 0;
+    }
+  else
+    {
+      int n = bp->which;
+      while (n == bp->which)
+        n = random() % count;
+      bp->which = n;
+    }
+
+  switch (gear_templates[bp->which].type) {
+  case PRISM: make_prism (mi); break;
+  case OCTO:  make_octo (mi); break;
+  case DECA:  make_deca (mi); break;
+  case G14:   make_14 (mi); break;
+  case G18:   make_18 (mi); break;
+  case G32:   make_32 (mi, gear_templates[bp->which].args); break;
+  case G92:   make_92 (mi, gear_templates[bp->which].args); break;
+  case G182:  make_182(mi, gear_templates[bp->which].args); break;
+  default: abort(); break;
+  }
+
+  sort_gears (mi);
+}
+
+
+
+ENTRYPOINT void 
+init_geodesic (ModeInfo *mi)
+{
+  geodesic_configuration *bp;
+  int wire = MI_IS_WIREFRAME(mi);
+
+  MI_INIT (mi, bps);
+
+  bp = &bps[MI_SCREEN(mi)];
+
+  bp->glx_context = init_GL(mi);
+
+  reshape_geodesic (mi, MI_WIDTH(mi), MI_HEIGHT(mi));
+
+  {
+    static GLfloat cspec[4] = {1.0, 1.0, 1.0, 1.0};
+    static const GLfloat shiny = 128.0;
+
+    static GLfloat pos[4] = {1.0, 1.0, 1.0, 0.0};
+    static GLfloat amb[4] = {0.0, 0.0, 0.0, 1.0};
+    static GLfloat dif[4] = {1.0, 1.0, 1.0, 1.0};
+    static GLfloat spc[4] = {0.0, 1.0, 1.0, 1.0};
+
+    glLightfv(GL_LIGHT0, GL_POSITION, pos);
+    glLightfv(GL_LIGHT0, GL_AMBIENT,  amb);
+    glLightfv(GL_LIGHT0, GL_DIFFUSE,  dif);
+    glLightfv(GL_LIGHT0, GL_SPECULAR, spc);
+
+    glMaterialfv (GL_FRONT, GL_SPECULAR,  cspec);
+    glMateriali  (GL_FRONT, GL_SHININESS, shiny);
+  }
+
+  if (! wire)
+    {
+      glEnable (GL_DEPTH_TEST);
+      glEnable (GL_BLEND);
+      glBlendFunc (GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
+      glEnable (GL_LIGHTING);
+      glEnable (GL_LIGHT0);
+    }
+
+  if (! bp->rot)
+  {
+    double spin_speed   = 0.25 * speed;
+    double wander_speed = 0.01 * speed;
+    double spin_accel   = 0.2;
+
+    bp->rot = make_rotator (do_spin ? spin_speed : 0,
+                            do_spin ? spin_speed : 0,
+                            do_spin ? spin_speed : 0,
+                            spin_accel,
+                            do_wander ? wander_speed : 0,
+                            True);
+    bp->trackball = gltrackball_init (True);
+  }
+
+  bp->font = load_texture_font (MI_DISPLAY(mi), "font");
+
+  pick_shape (mi, 0);
+}
+
+
+ENTRYPOINT Bool
+geodesic_handle_event (ModeInfo *mi, XEvent *event)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+
+  if (gltrackball_event_handler (event, bp->trackball,
+                                 MI_WIDTH (mi), MI_HEIGHT (mi),
+                                 &bp->button_down_p))
+    return True;
+  else
+    {
+      if (event->xany.type == KeyPress)
+        {
+          KeySym keysym;
+          char c = 0;
+          XLookupString (&event->xkey, &c, 1, &keysym, 0);
+          if (c == '<' || c == ',' || c == '-' || c == '_' ||
+              keysym == XK_Left || keysym == XK_Up || keysym == XK_Prior)
+            {
+              bp->next = -1;
+              goto SWITCH;
+            }
+          else if (c == '>' || c == '.' || c == '=' || c == '+' ||
+                   keysym == XK_Right || keysym == XK_Down ||
+                   keysym == XK_Next)
+            {
+              bp->next = 1;
+              goto SWITCH;
+            }
+        }
+
+      if (screenhack_event_helper (MI_DISPLAY(mi), MI_WINDOW(mi), event))
+        {
+        SWITCH:
+          bp->mode = 1;
+          bp->mode_tick = 4;
+          return True;
+        }
+    }
+
+  return False;
+}
+
+
+ENTRYPOINT void
+draw_geodesic (ModeInfo *mi)
+{
+  time_t now = time ((time_t *) 0);
+  int wire = MI_IS_WIREFRAME(mi);
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  Display *dpy = MI_DISPLAY(mi);
+  Window window = MI_WINDOW(mi);
+
+  if (!bp->glx_context)
+    return;
+
+  glXMakeCurrent(MI_DISPLAY(mi), MI_WINDOW(mi), *(bp->glx_context));
+
+
+  if (bp->draw_time == 0)
+    {
+      pick_shape (mi, bp->draw_time);
+      bp->draw_time = now;
+    }
+  else if (bp->mode == 0)
+    {
+      if (bp->draw_tick++ > 10)
+        {
+          if (bp->draw_time == 0) bp->draw_time = now;
+          bp->draw_tick = 0;
+
+          if (!bp->button_down_p &&
+              bp->draw_time + timeout <= now)
+            {
+              /* randomize every -timeout seconds */
+              bp->mode = 1;    /* go out */
+              bp->mode_tick = 10 / speed;
+              bp->draw_time = now;
+            }
+        }
+    }
+  else if (bp->mode == 1)   /* out */
+    {
+      if (--bp->mode_tick <= 0)
+        {
+          bp->mode_tick = 10 / speed;
+          bp->mode = 2;  /* go in */
+          pick_shape (mi, bp->draw_time);
+          bp->draw_time = now;
+        }
+    }
+  else if (bp->mode == 2)   /* in */
+    {
+      if (--bp->mode_tick <= 0)
+        bp->mode = 0;  /* normal */
+    }
+  else
+    abort();
+
+
+  if (! wire)
+    glShadeModel(GL_SMOOTH);
+
+  glEnable(GL_DEPTH_TEST);
+  glEnable(GL_NORMALIZE);
+  glEnable(GL_CULL_FACE);
+
+  glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
+
+  glPushMatrix ();
+
+  {
+    double x, y, z;
+    get_position (bp->rot, &x, &y, &z, !bp->button_down_p);
+    glTranslatef((x - 0.5) * 8,
+                 (y - 0.5) * 8,
+                 (z - 0.5) * 17);
+
+    gltrackball_rotate (bp->trackball);
+
+    get_rotation (bp->rot, &x, &y, &z, !bp->button_down_p);
+    glRotatef (x * 360, 1.0, 0.0, 0.0);
+    glRotatef (y * 360, 0.0, 1.0, 0.0);
+    glRotatef (z * 360, 0.0, 0.0, 1.0);
+  }
+
+  mi->polygon_count = 0;
+
+  glScalef (6, 6, 6);
+
+  if (bp->ngears < 14)
+    glScalef (0.8, 0.8, 0.8);  /* make these a little easier to see */
+
+  if (bp->mode != 0)
+    {
+      GLfloat s = (bp->mode == 1
+                   ? bp->mode_tick / (10 / speed)
+                   : ((10 / speed) - bp->mode_tick + 1) / (10 / speed));
+      glScalef (s, s, s);
+    }
+
+
+  {
+    int i;
+    for (i = 0; i < bp->ngears; i++)
+      {
+        const sphere_gear *s = &bp->gears[i];
+        const gear *g = s->g;
+
+        XYZ axis;
+        XYZ from = { 0, 1, 0 };
+        XYZ to = s->axis;
+        GLfloat angle;
+        GLfloat off = s->offset;
+
+        /* If an even number of teeth, offset by 1/2 tooth width. */
+        if (s->direction > 0 && !(g->nteeth & 1))
+          off += 360 / g->nteeth / 2;
+
+        axis  = cross_product (from, to);
+        angle = acos (dot_product (from, to));
+
+        glPushMatrix();
+        glTranslatef (to.x, to.y, to.z);
+        glRotatef (angle / M_PI * 180, axis.x, axis.y, axis.z);
+        glRotatef (-90, 1, 0, 0);
+        glRotatef(180, 0, 0, 1);
+        glRotatef ((bp->th - off) * g->ratio * s->direction,
+                   0, 0, 1);
+
+        glCallList (g->dlist);
+        mi->polygon_count += g->polygons;
+        glPopMatrix();
+
+#if 0
+        {				/* Draw tooth vectors */
+          GLfloat r = 1 - g->z;
+          XYZ pc;
+          int pt = parent_tooth (s, &pc);
+          int t;
+          glDisable(GL_LIGHTING);
+          glLineWidth (8);
+          for (t = 0; t < g->nteeth; t++)
+            {
+              XYZ p = tooth_coords (s, t);
+              XYZ p2;
+              p2.x = (r * s->axis.x + p.x) / 2;
+              p2.y = (r * s->axis.y + p.y) / 2;
+              p2.z = (r * s->axis.z + p.z) / 2;
+
+              if (t == pt)
+                glColor3f(1,0,1);
+              else
+                glColor3f(0,1,1);
+              glBegin(GL_LINES);
+              glVertex3f (p.x, p.y, p.z);
+              glVertex3f (p2.x, p2.y, p2.z);
+              glEnd();
+            }
+          if (!wire) glEnable(GL_LIGHTING);
+          glLineWidth (1);
+        }
+#endif
+
+#if 0
+        {				/* Draw the parent/child DAG */
+          GLfloat s1 = 1.1;
+          GLfloat s2 = s->parent ? s1 : 1.5;
+          GLfloat s3 = 1.0;
+          XYZ p1 = s->axis;
+          XYZ p2 = s->parent ? s->parent->axis : p1;
+          glDisable(GL_LIGHTING);
+          glColor3f(0,0,1);
+          glBegin(GL_LINES);
+          glVertex3f (s1 * p1.x, s1 * p1.y, s1 * p1.z);
+          glVertex3f (s2 * p2.x, s2 * p2.y, s2 * p2.z);
+          glVertex3f (s1 * p1.x, s1 * p1.y, s1 * p1.z);
+          glVertex3f (s3 * p1.x, s3 * p1.y, s3 * p1.z);
+          glEnd();
+          if (!wire) glEnable(GL_LIGHTING);
+        }
+#endif
+      }
+
+    /* We need to draw the fonts in a second pass in order to make
+       transparency (as a result of anti-aliasing) work properly.
+      */
+    if (do_numbers && bp->mode == 0)
+      for (i = 0; i < bp->ngears; i++)
+        {
+          const sphere_gear *s = &bp->gears[i];
+          const gear *g = s->g;
+
+          XYZ axis;
+          XYZ from = { 0, 1, 0 };
+          XYZ to = s->axis;
+          GLfloat angle;
+          GLfloat off = s->offset;
+
+          int w, h, j;
+          char buf[100];
+          XCharStruct e;
+
+          /* If an even number of teeth, offset by 1/2 tooth width. */
+          if (s->direction > 0 /* && !(g->nteeth & 1) */)
+            off += 360 / g->nteeth / 2;
+
+          axis  = cross_product (from, to);
+          angle = acos (dot_product (from, to));
+
+          glPushMatrix();
+          glTranslatef(to.x, to.y, to.z);
+          glRotatef (angle / M_PI * 180, axis.x, axis.y, axis.z);
+          glRotatef (-90, 1, 0, 0);
+          glRotatef(180, 0, 0, 1);
+          glRotatef ((bp->th - off) * g->ratio * s->direction,
+                     0, 0, 1);
+
+          glDisable (GL_LIGHTING);
+          glColor3f(1, 1, 0);
+          glPushMatrix();
+          glScalef(0.005, 0.005, 0.005);
+          sprintf (buf, "%d", i);
+          texture_string_metrics (bp->font, buf, &e, 0, 0);
+          w = e.width;
+          h = e.ascent + e.descent;
+          glTranslatef (-w/2, -h/2, 0);
+          print_texture_string (bp->font, buf);
+          glPopMatrix();
+
+# if 1
+          for (j = 0; j < g->nteeth; j++)          /* Number the teeth */
+            {
+              GLfloat ss = 0.08 * g->r / g->nteeth;
+              GLfloat r = g->r * 0.88;
+              GLfloat th = M_PI - (j * M_PI * 2 / g->nteeth + M_PI/2);
+
+
+              glPushMatrix();
+              glTranslatef (r * cos(th), r * sin(th), -g->z + 0.01);
+              glScalef(ss, ss, ss);
+              sprintf (buf, "%d", j + 1);
+              texture_string_metrics (bp->font, buf, &e, 0, 0);
+              w = e.width;
+              h = e.ascent + e.descent;
+              glTranslatef (-w/2, -h/2, 0);
+              print_texture_string (bp->font, buf);
+              glPopMatrix();
+            }
+# endif
+          glPopMatrix();
+          if (!wire) glEnable(GL_LIGHTING);
+        }
+
+    bp->th += 0.7 * speed;    /* Don't mod this to 360 - causes glitches. */
+  }
+
+  if (do_labels && bp->mode == 0)
+    {
+      glColor3f (1, 1, 0);
+      print_texture_label (mi->dpy, bp->font,
+                           mi->xgwa.width, mi->xgwa.height,
+                           1, bp->desc);
+    }
+
+  glPopMatrix ();
+
+  if (mi->fps_p) do_fps (mi);
+  glFinish();
+
+  glXSwapBuffers(dpy, window);
+}
+
+ENTRYPOINT void
+free_geodesic (ModeInfo *mi)
+{
+  geodesic_configuration *bp = &bps[MI_SCREEN(mi)];
+  if (!bp->glx_context)
+    return;
+  glXMakeCurrent(MI_DISPLAY(mi), MI_WINDOW(mi), *(bp->glx_context));
+  free_texture_font (bp->font);
+  free (bp->colors);
+  free_sphere_gears (mi);
+  if (bp->desc) free (bp->desc);
+}
+
+
+XSCREENSAVER_MODULE_2 ("GeodesicGears", geodesicgears, geodesic)
+
+#endif /* USE_GL */