--- /dev/null
+/* -*- Mode: C; tab-width: 4 -*- */
+/* apollonian --- Apollonian Circles */
+
+#if !defined( lint ) && !defined( SABER )
+static const char sccsid[] = "@(#)apollonian.c 5.02 2001/07/01 xlockmore";
+#endif
+
+/*-
+ * Copyright (c) 2000, 2001 by Allan R. Wilks <allan@research.att.com>.
+ *
+ * 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.
+ *
+ * radius r = 1 / c (curvature)
+ *
+ * Descartes Circle Theorem: (a, b, c, d are curvatures of tangential circles)
+ * Let a, b, c, d be the curvatures of for mutually (externally) tangent
+ * circles in the plane. Then
+ * a^2 + b^2 + c^2 + d^2 = (a + b + c + d)^2 / 2
+ *
+ * Complex Descartes Theorem: If the oriented curvatues and (complex) centers
+ * of an oriented Descrates configuration in the plane are a, b, c, d and
+ * w, x, y, z respectively, then
+ * a^2*w^2 + b^2*x^2 + c^2*y^2 + d^2*z^2 = (aw + bx + cy + dz)^2 / 2
+ * In addition these quantities satisfy
+ * a^2*w + b^2*x + c^2*y + d^2*z = (aw + bx + cy + dz)(a + b + c + d) / 2
+ *
+ * Enumerate root integer Descartes quadruples (a,b,c,d) satisfying the
+ * Descartes condition:
+ * 2(a^2+b^2+c^2+d^2) = (a+b+c+d)^2
+ * i.e., quadruples for which no application of the "pollinate" operator
+ * z <- 2(a+b+c+d) - 3*z,
+ * where z is in {a,b,c,d}, gives a quad of strictly smaller sum. This
+ * is equivalent to the condition:
+ * sum(a,b,c,d) >= 2*max(a,b,c,d)
+ * which, because of the Descartes condition, is equivalent to
+ * sum(a^2,b^2,c^2,d^2) >= 2*max(a,b,c,d)^2
+ *
+ *
+ * Todo:
+ * Add a small font
+ *
+ * Revision History:
+ * 25-Jun-2001: Converted from C and Postscript code by David Bagley
+ * Original code by Allan R. Wilks <allan@research.att.com>.
+ *
+ * From Circle Math Science News April 21, 2001 VOL. 254-255
+ * http://www.sciencenews.org/20010421/toc.asp
+ * Apollonian Circle Packings Assorted papers from Ronald L Graham,
+ * Jeffrey Lagarias, Colin Mallows, Allan Wilks, Catherine Yan
+ * http://front.math.ucdavis.edu/math.NT/0009113
+ * http://front.math.ucdavis.edu/math.MG/0101066
+ * http://front.math.ucdavis.edu/math.MG/0010298
+ * http://front.math.ucdavis.edu/math.MG/0010302
+ * http://front.math.ucdavis.edu/math.MG/0010324
+ */
+
+#ifdef STANDALONE
+#define MODE_apollonian
+#define PROGCLASS "Apollonian"
+#define HACK_INIT init_apollonian
+#define HACK_DRAW draw_apollonian
+#define apollonian_opts xlockmore_opts
+#define DEFAULTS "*delay: 1000000 \n" \
+ "*count: 64 \n" \
+ "*cycles: 20 \n" \
+ "*ncolors: 64 \n"
+#include "xlockmore.h" /* in xscreensaver distribution */
+#include "erase.h"
+#else /* STANDALONE */
+#include "xlock.h" /* in xlockmore distribution */
+#endif /* STANDALONE */
+
+#ifdef MODE_apollonian
+
+#define DEF_ALTGEOM "True"
+#define DEF_LABEL "True"
+
+static Bool altgeom;
+static Bool label;
+
+static XrmOptionDescRec opts[] =
+{
+ {(char *) "-altgeom", (char *) ".apollonian.altgeom", XrmoptionNoArg, (caddr_t) "on"},
+ {(char *) "+altgeom", (char *) ".apollonian.altgeom", XrmoptionNoArg, (caddr_t) "off"},
+ {(char *) "-label", (char *) ".apollonian.label", XrmoptionNoArg, (caddr_t) "on"},
+ {(char *) "+label", (char *) ".apollonian.label", XrmoptionNoArg, (caddr_t) "off"},
+};
+static argtype vars[] =
+{
+ {(caddr_t *) & altgeom, (char *) "altgeom", (char *) "AltGeom", (char *) DEF_ALTGEOM, t_Bool},
+ {(caddr_t *) & label, (char *) "label", (char *) "Label", (char *) DEF_LABEL, t_Bool},
+};
+static OptionStruct desc[] =
+{
+ {(char *) "-/+altgeom", (char *) "turn on/off alternate geometries (off euclidean space, on includes spherical and hyperbolic)"},
+ {(char *) "-/+label", (char *) "turn on/off alternate space and number labeling"},
+};
+
+ModeSpecOpt apollonian_opts =
+{sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, desc};
+
+#ifdef DOFONT
+extern XFontStruct *getFont(Display * display);
+#endif
+
+#ifdef USE_MODULES
+ModStruct apollonian_description =
+{"apollonian", "init_apollonian", "draw_apollonian", "release_apollonian",
+ "init_apollonian", "init_apollonian", (char *) NULL, &apollonian_opts,
+ 1000000, 64, 20, 1, 64, 1.0, "",
+ "Shows Apollonian Circles", 0, NULL};
+
+#endif
+
+typedef struct {
+ int a, b, c, d;
+} apollonian_quadruple;
+
+typedef struct {
+ double e; /* euclidean bend */
+ double s; /* spherical bend */
+ double h; /* hyperbolic bend */
+ double x, y; /* euclidean bend times euclidean position */
+} circle;
+enum space {
+ euclidean = 0, spherical, hyperbolic
+};
+
+const char * space_string[] = {
+ "euclidean",
+ "spherical",
+ "hyperbolic"
+};
+
+/*
+Generate Apollonian packing starting with a quadruple of circles.
+The four input lines each contain the 5-tuple (e,s,h,x,y) representing
+the circle with radius 1/e and center (x/e,y/e). The s and h is propagated
+like e, x and y, but can differ from e so as to represent different
+geometries, spherical and hyperbolic, respectively. The "standard" picture,
+for example (-1, 2, 2, 3), can be labeled for the three geometries.
+Origins of circles z1, z2, z3, z4
+a * z1 = 0
+b * z2 = (a+b)/a
+c * z3 = (q123 + a * i)^2/(a*(a+b)) where q123 = sqrt(a*b+a*c+b*c)
+d * z4 = (q124 + a * i)^2/(a*(a+b)) where q124 = q123 - a - b
+If (e,x,y) represents the Euclidean circle (1/e,x/e,y/e) (so that e is
+the label in the standard picture) then the "spherical label" is
+(e^2+x^2+y^2-1)/(2*e) (an integer!) and the "hyperbolic label", is
+calulated by h + s = e.
+*/
+circle examples[][4] = {
+{ /* double semi-bounded */
+ { 0, 0, 0, 0, 1},
+ { 0, 0, 0, 0, -1},
+ { 1, 1, 1, -1, 0},
+ { 1, 1, 1, 1, 0}
+},
+#if 0
+{ /* standard */
+ {-1, 0, -1, 0, 0},
+ { 2, 1, 1, 1, 0},
+ { 2, 1, 1, -1, 0},
+ { 3, 2, 1, 0, 2}
+},
+{ /* next simplest */
+ {-2, -1, -1, 0.0, 0},
+ { 3, 2, 1, 0.5, 0},
+ { 6, 3, 3, -2.0, 0},
+ { 7, 4, 3, -1.5, 2}
+},
+{ /* */
+ {-3, -2, -1, 0.0, 0},
+ { 4, 3, 1, 1.0 / 3.0, 0},
+ {12, 7, 5, -3.0, 0},
+ {13, 8, 5, -8.0 / 3.0, 2}
+},
+{ /* Mickey */
+ {-3, -2, -1, 0.0, 0},
+ { 5, 4, 1, 2.0 / 3.0, 0},
+ { 8, 5, 3, -4.0 / 3.0, -1},
+ { 8, 5, 3, -4.0 / 3.0, 1}
+},
+{ /* */
+ {-4, -3, -1, 0.00, 0},
+ { 5, 4, 1, 0.25, 0},
+ {20, 13, 7, -4.00, 0},
+ {21, 14, 7, -3.75, 2}
+},
+{ /* Mickey2 */
+ {-4, -2, -2, 0.0, 0},
+ { 8, 4, 4, 1.0, 0},
+ { 9, 5, 4, -0.75, -1},
+ { 9, 5, 4, -0.75, 1}
+},
+{ /* Mickey3 */
+ {-5, -4, -1, 0.0, 0},
+ { 7, 6, 1, 0.4, 0},
+ {18, 13, 5, -2.4, -1},
+ {18, 13, 5, -2.4, 1}
+},
+{ /* */
+ {-6, -5, -1, 0.0, 0},
+ { 7, 6, 1, 1.0 / 6.0, 0},
+ {42, 31, 11, -6.0, 0},
+ {43, 32, 11, -35.0 / 6.0, 2}
+},
+{ /* */
+ {-6, -3, -3, 0.0, 0},
+ {10, 5, 5, 2.0 / 3.0, 0},
+ {15, 8, 7, -1.5, 0},
+ {19, 10, 9, -5.0 / 6.0, 2}
+},
+{ /* asymmetric */
+ {-6, -5, -1, 0.0, 0.0},
+ {11, 10, 1, 5.0 / 6.0, 0.0},
+ {14, 11, 3, -16.0 / 15.0, -0.8},
+ {15, 12, 3, -0.9, 1.2}
+},
+#endif
+/* Non integer stuff */
+#define DELTA 2.154700538 /* ((3+2*sqrt(3))/3) */
+{ /* 3 fold symmetric bounded (x, y calculated later) */
+ { -1, -1, -1, 0.0, 0.0},
+ {DELTA, DELTA, DELTA, 1.0, 0.0},
+ {DELTA, DELTA, DELTA, 1.0, -1.0},
+ {DELTA, DELTA, DELTA, -1.0, 1.0}
+},
+{ /* semi-bounded (x, y calculated later) */
+#define ALPHA 2.618033989 /* ((3+sqrt(5))/2) */
+ { 1.0, 1.0, 1.0, 0, 0},
+ { 0.0, 0.0, 0.0, 0, -1},
+ {1.0/(ALPHA*ALPHA), 1.0/(ALPHA*ALPHA), 1.0/(ALPHA*ALPHA), -1, 0},
+ { 1.0/ALPHA, 1.0/ALPHA, 1.0/ALPHA, -1, 0}
+},
+{ /* unbounded (x, y calculated later) */
+/* #define PHI 1.618033989 *//* ((1+sqrt(5))/2) */
+#define BETA 2.890053638 /* (PHI+sqrt(PHI)) */
+ { 1.0, 1.0, 1.0, 0, 0},
+ {1.0/(BETA*BETA*BETA), 1.0/(BETA*BETA*BETA), 1.0/(BETA*BETA*BETA), 1, 0},
+ { 1.0/(BETA*BETA), 1.0/(BETA*BETA), 1.0/(BETA*BETA), 1, 0},
+ { 1.0/BETA, 1.0/BETA, 1.0/BETA, 1, 0}
+}
+};
+
+#define PREDEF_CIRCLE_GAMES (sizeof (examples) / (4 * sizeof (circle)))
+
+#if 0
+Euclidean
+0, 0, 1, 1
+-1, 2, 2, 3
+-2, 3, 6, 7
+-3, 5, 8, 8
+-4, 8, 9, 9
+-3, 4, 12, 13
+-6, 11, 14, 15
+ -5, 7, 18, 18
+ -6, 10, 15, 19
+ -7, 12, 17, 20
+ -4, 5, 20, 21
+ -9, 18, 19, 22
+ -8, 13, 21, 24
+Spherical
+0, 1, 1, 2
+ -1, 2, 3, 4
+ -2, 4, 5, 5
+ -2, 3, 7, 8
+Hyperbolic
+-1, 1, 1, 1
+ 0, 0, 1, 3
+ -2, 3, 5, 6
+ -3, 6, 6, 7
+#endif
+
+typedef struct {
+ int size;
+ XPoint offset;
+ int geometry;
+ circle c1, c2, c3, c4;
+ int color_offset;
+ int count;
+ Bool label, altgeom;
+ apollonian_quadruple *quad;
+#ifdef DOFONT
+ XFontStruct *font;
+#endif
+ int time;
+ int game;
+} apollonianstruct;
+
+static apollonianstruct *apollonians = (apollonianstruct *) NULL;
+
+#define FONT_HEIGHT 19
+#define FONT_WIDTH 15
+#define FONT_LENGTH 20
+#define MAX_CHAR 10
+#define K 2.15470053837925152902 /* 1+2/sqrt(3) */
+#define MAXBEND 100 /* Do not want configurable by user since it will take too
+ much time if increased. */
+
+static int
+gcd(int a, int b)
+{
+ int r;
+
+ while (b) {
+ r = a % b;
+ a = b;
+ b = r;
+ }
+ return a;
+}
+
+static int
+isqrt(int n)
+{
+ int y;
+
+ if (n < 0)
+ return -1;
+ y = (int) (sqrt((double) n) + 0.5);
+ return ((n == y*y) ? y : -1);
+}
+
+static void
+dquad(int n, apollonian_quadruple *quad)
+{
+ int a, b, c, d;
+ int counter = 0, B, C;
+
+ for (a = 0; a < MAXBEND; a++) {
+ B = (int) (K * a);
+ for (b = a + 1; b <= B; b++) {
+ C = (int) (((a + b) * (a + b)) / (4.0 * (b - a)));
+ for (c = b; c <= C; c++) {
+ d = isqrt(b*c-a*(b+c));
+ if (d >= 0 && (gcd(a,gcd(b,c)) <= 1)) {
+ quad[counter].a = -a;
+ quad[counter].b = b;
+ quad[counter].c = c;
+ quad[counter].d = -a+b+c-2*d;
+ if (++counter >= n) {
+ return;
+ }
+ }
+ }
+ }
+ }
+ (void) printf("found only %d below maximum bend of %d\n",
+ counter, MAXBEND);
+ for (; counter < n; counter++) {
+ quad[counter].a = -1;
+ quad[counter].b = 2;
+ quad[counter].c = 2;
+ quad[counter].d = 3;
+ }
+ return;
+}
+
+/*
+ * Given a Descartes quadruple of bends (a,b,c,d), with a<0, find a
+ * quadruple of circles, represented by (bend,bend*x,bend*y), such
+ * that the circles have the given bends and the bends times the
+ * centers are integers.
+ *
+ * This just performs an exaustive search, assuming that the outer
+ * circle has center in the unit square.
+ *
+ * It is always sufficient to look in {(x,y):0<=y<=x<=1/2} for the
+ * center of the outer circle, but this may not lead to a packing
+ * that can be labelled with integer spherical and hyperbolic labels.
+ * To effect the smaller search, replace FOR(a) with
+ *
+ * for (pa = ea/2; pa <= 0; pa++) for (qa = pa; qa <= 0; qa++)
+ */
+
+#define For(v,l,h) for (v = l; v <= h; v++)
+#define FOR(z) For(p##z,lop##z,hip##z) For(q##z,loq##z,hiq##z)
+#define H(z) ((e##z*e##z+p##z*p##z+q##z*q##z)%2)
+#define UNIT(z) ((abs(e##z)-1)*(abs(e##z)-1) >= p##z*p##z+q##z*q##z)
+#define T(z,w) is_tangent(e##z,p##z,q##z,e##w,p##w,q##w)
+#define LO(r,z) lo##r##z = iceil(e##z*(r##a+1),ea)-1
+#define HI(r,z) hi##r##z = iflor(e##z*(r##a-1),ea)-1
+#define B(z) LO(p,z); HI(p,z); LO(q,z); HI(q,z)
+
+static int
+is_quad(int a, int b, int c, int d)
+{
+ int s;
+
+ s = a+b+c+d;
+ return 2*(a*a+b*b+c*c+d*d) == s*s;
+}
+
+static Bool
+is_tangent(int e1, int p1, int q1, int e2, int p2, int q2)
+{
+ int dx, dy, s;
+
+ dx = p1*e2 - p2*e1;
+ dy = q1*e2 - q2*e1;
+ s = e1 + e2;
+ return dx*dx + dy*dy == s*s;
+}
+
+static int
+iflor(int a, int b)
+{
+ int q;
+
+ if (b == 0) {
+ (void) printf("iflor: b = 0\n");
+ return 0;
+ }
+ if (a%b == 0)
+ return a/b;
+ q = abs(a)/abs(b);
+ return ((a<0)^(b<0)) ? -q-1 : q;
+}
+
+static int
+iceil(int a, int b)
+{
+ int q;
+
+ if (b == 0) {
+ (void) printf("iceil: b = 0\n");
+ return 0;
+ }
+ if (a%b == 0)
+ return a/b;
+ q = abs(a)/abs(b);
+ return ((a<0)^(b<0)) ? -q : 1+q;
+}
+
+static double
+geom(int geometry, int e, int p, int q)
+{
+ int g = (geometry == spherical) ? -1 :
+ (geometry == hyperbolic) ? 1 : 0;
+
+ if (g)
+ return (e*e + (1.0 - p*p - q*q) * g) / (2.0*e);
+ (void) printf("geom: g = 0\n");
+ return e;
+}
+
+static void
+cquad(circle *c1, circle *c2, circle *c3, circle *c4)
+{
+ int ea, eb, ec, ed;
+ int pa, pb, pc, pd;
+ int qa, qb, qc, qd;
+ int lopa, lopb, lopc, lopd;
+ int hipa, hipb, hipc, hipd;
+ int loqa, loqb, loqc, loqd;
+ int hiqa, hiqb, hiqc, hiqd;
+
+ ea = (int) c1->e;
+ eb = (int) c2->e;
+ ec = (int) c3->e;
+ ed = (int) c4->e;
+ if (ea >= 0)
+ (void) printf("ea = %d\n", ea);
+ if (!is_quad(ea,eb,ec,ed))
+ (void) printf("Error not quad %d %d %d %d\n", ea, eb, ec, ed);
+ lopa = loqa = ea;
+ hipa = hiqa = 0;
+ FOR(a) {
+ B(b); B(c); B(d);
+ if (H(a) && UNIT(a)) FOR(b) {
+ if (H(b) && T(a,b)) FOR(c) {
+ if (H(c) && T(a,c) && T(b,c)) FOR(d) {
+ if (H(d) && T(a,d) && T(b,d) && T(c,d)) {
+ c1->s = geom(spherical, ea, pa, qa);
+ c1->h = geom(hyperbolic, ea, pa, qa);
+ c2->s = geom(spherical, eb, pb, qb);
+ c2->h = geom(hyperbolic, eb, pb, qb);
+ c3->s = geom(spherical, ec, pc, qc);
+ c3->h = geom(hyperbolic, ec, pc, qc);
+ c4->s = geom(spherical, ed, pd, qd);
+ c4->h = geom(hyperbolic, ed, pd, qd);
+ }
+ }
+ }
+ }
+ }
+}
+
+static void
+p(ModeInfo *mi, circle c)
+{
+ apollonianstruct *cp = &apollonians[MI_SCREEN(mi)];
+ char string[10];
+ double g, e;
+ int g_width;
+
+#ifdef DEBUG
+ (void) printf("c.e=%g c.s=%g c.h=%g c.x=%g c.y=%g\n",
+ c.e, c.s, c.h, c.x, c.y);
+#endif
+ g = (cp->geometry == spherical) ? c.s : (cp->geometry == hyperbolic) ?
+ c.h : c.e;
+ if (c.e < 0.0) {
+ if (g < 0.0)
+ g = -g;
+ if (MI_NPIXELS(mi) <= 2)
+ XSetForeground(MI_DISPLAY(mi), MI_GC(mi),
+ MI_WHITE_PIXEL(mi));
+ else
+ XSetForeground(MI_DISPLAY(mi), MI_GC(mi),
+ MI_PIXEL(mi, ((int) ((g + cp->color_offset) *
+ g)) % MI_NPIXELS(mi)));
+ XDrawArc(MI_DISPLAY(mi), MI_WINDOW(mi), MI_GC(mi),
+ ((int) (cp->size * (-cp->c1.e) * (c.x - 1.0) /
+ (-2.0 * c.e) + cp->size / 2.0 + cp->offset.x)),
+ ((int) (cp->size * (-cp->c1.e) * (c.y - 1.0) /
+ (-2.0 * c.e) + cp->size / 2.0 + cp->offset.y)),
+ (int) (cp->c1.e * cp->size / c.e),
+ (int) (cp->c1.e * cp->size / c.e), 0, 23040);
+ if (!cp->label) {
+#ifdef DEBUG
+ (void) printf("%g\n", -g);
+#endif
+ return;
+ }
+ (void) sprintf(string, "%g", (g == 0.0) ? 0 : -g);
+ if (cp->size >= 10 * FONT_WIDTH) {
+ /* hard code these to corners */
+ XDrawString(MI_DISPLAY(mi), MI_WINDOW(mi), MI_GC(mi),
+ ((int) (cp->size * c.x / (2.0 * c.e))) + cp->offset.x,
+ ((int) (cp->size * c.y / (2.0 * c.e))) + FONT_HEIGHT,
+ string, (g == 0.0) ? 1 : ((g < 10.0) ? 2 :
+ ((g < 100.0) ? 3 : 4)));
+ }
+ if (cp->altgeom && MI_HEIGHT(mi) >= 30 * FONT_WIDTH) {
+ XDrawString(MI_DISPLAY(mi), MI_WINDOW(mi), MI_GC(mi),
+ ((int) (cp->size * c.x / (2.0 * c.e) + cp->offset.x)),
+ ((int) (cp->size * c.y / (2.0 * c.e) + MI_HEIGHT(mi) -
+ FONT_HEIGHT / 2)), space_string[cp->geometry],
+ strlen(space_string[cp->geometry]));
+ }
+ return;
+ }
+ if (MI_NPIXELS(mi) <= 2)
+ XSetForeground(MI_DISPLAY(mi), MI_GC(mi), MI_WHITE_PIXEL(mi));
+ else
+ XSetForeground(MI_DISPLAY(mi), MI_GC(mi),
+ MI_PIXEL(mi, ((int) ((g + cp->color_offset) * g)) %
+ MI_NPIXELS(mi)));
+ if (c.e == 0.0) {
+ if (c.x == 0.0 && c.y != 0.0) {
+ XDrawLine(MI_DISPLAY(mi), MI_WINDOW(mi), MI_GC(mi),
+ 0, (int) ((c.y + 1.0) * cp->size / 2.0 + cp->offset.y),
+ MI_WIDTH(mi),
+ (int) ((c.y + 1.0) * cp->size / 2.0 + cp->offset.y));
+ } else if (c.y == 0.0 && c.x != 0.0) {
+ XDrawLine(MI_DISPLAY(mi), MI_WINDOW(mi), MI_GC(mi),
+ (int) ((c.x + 1.0) * cp->size / 2.0 + cp->offset.x), 0,
+ (int) ((c.x + 1.0) * cp->size / 2.0 + cp->offset.x),
+ MI_HEIGHT(mi));
+ }
+ return;
+ }
+ e = (cp->c1.e >= 0.0) ? 1.0 : -cp->c1.e;
+ XFillArc(MI_DISPLAY(mi), MI_WINDOW(mi), MI_GC(mi),
+ ((int) (cp->size * e * (c.x - 1.0) / (2.0 * c.e) +
+ cp->size / 2.0 + cp->offset.x)),
+ ((int) (cp->size * e * (c.y - 1.0) / (2.0 * c.e) +
+ cp->size / 2.0 + cp->offset.y)),
+ (int) (e * cp->size / c.e), (int) (e * cp->size / c.e),
+ 0, 23040);
+ if (!cp->label) {
+#ifdef DEBUG
+ (void) printf("%g\n", g);
+#endif
+ return;
+ }
+ if (MI_NPIXELS(mi) <= 2)
+ XSetForeground(MI_DISPLAY(mi), MI_GC(mi), MI_BLACK_PIXEL(mi));
+ else
+ XSetForeground(MI_DISPLAY(mi), MI_GC(mi),
+ MI_PIXEL(mi, ((int) ((g + cp->color_offset) * g) +
+ MI_NPIXELS(mi) / 2) % MI_NPIXELS(mi)));
+ g_width = (g < 10.0) ? 1: ((g < 100.0) ? 2 : 3);
+ if (c.e < e * cp->size / (FONT_LENGTH + 5 * g_width) && g < 1000.0) {
+ (void) sprintf(string, "%g", g);
+ XDrawString(MI_DISPLAY(mi), MI_WINDOW(mi), MI_GC(mi),
+ ((int) (cp->size * e * c.x / (2.0 * c.e) +
+ cp->size / 2.0 + cp->offset.x)) -
+ g_width * FONT_WIDTH / 2,
+ ((int) (cp->size * e * c.y / (2.0 * c.e) +
+ cp->size / 2.0 + cp->offset.y)) +
+ FONT_HEIGHT / 2,
+ string, g_width);
+ }
+}
+
+#define BIG 7
+static void
+f(ModeInfo *mi, circle c1, circle c2, circle c3, circle c4)
+{
+ apollonianstruct *cp = &apollonians[MI_SCREEN(mi)];
+ int e = (int) ((cp->c1.e >= 0.0) ? 1.0 : -cp->c1.e);
+ circle c;
+
+ c.e = 2*(c1.e+c2.e+c3.e) - c4.e;
+ c.s = 2*(c1.s+c2.s+c3.s) - c4.s;
+ c.h = 2*(c1.h+c2.h+c3.h) - c4.h;
+ c.x = 2*(c1.x+c2.x+c3.x) - c4.x;
+ c.y = 2*(c1.y+c2.y+c3.y) - c4.y;
+ if (c.e > cp->size * e || c.x / c.e > BIG || c.y / c.e > BIG ||
+ c.x / c.e < -BIG || c.y / c.e < -BIG)
+ return;
+ p(mi, c);
+ f(mi, c2, c3, c, c1);
+ f(mi, c1, c3, c, c2);
+ f(mi, c1, c2, c, c3);
+}
+
+static void
+free_apollonian(Display *display, apollonianstruct *cp)
+{
+ if (cp->quad != NULL) {
+ (void) free((void *) cp->quad);
+ cp->quad = (apollonian_quadruple *) NULL;
+ }
+#ifdef DOFONT
+ if (cp->gc != None) {
+ XFreeGC(display, cp->gc);
+ cp->gc = None;
+ }
+ if (cp->font != None) {
+ XFreeFont(display, cp->font);
+ cp->font = None;
+ }
+#endif
+}
+
+#ifndef DEBUG
+void
+randomize_c(int randomize, circle * c)
+{
+ if (randomize / 2) {
+ double temp;
+
+ temp = c->x;
+ c->x = c->y;
+ c->y = temp;
+ }
+ if (randomize % 2) {
+ c->x = -c->x;
+ c->y = -c->y;
+ }
+}
+#endif
+
+void
+init_apollonian(ModeInfo * mi)
+{
+ apollonianstruct *cp;
+ int i;
+
+ if (apollonians == NULL) {
+ if ((apollonians = (apollonianstruct *) calloc(MI_NUM_SCREENS(mi),
+ sizeof (apollonianstruct))) == NULL)
+ return;
+ }
+ cp = &apollonians[MI_SCREEN(mi)];
+
+ cp->size = MAX(MIN(MI_WIDTH(mi), MI_HEIGHT(mi)) - 1, 1);
+ cp->offset.x = (MI_WIDTH(mi) - cp->size) / 2;
+ cp->offset.y = (MI_HEIGHT(mi) - cp->size) / 2;
+ cp->color_offset = NRAND(MI_NPIXELS(mi));
+
+#ifdef DOFONT
+ if (cp->font == None) {
+ if ((cp->font = getFont(MI_DISPLAY(mi))) == None)
+ return False;
+ }
+#endif
+ cp->label = label;
+ cp->altgeom = cp->label && altgeom;
+
+ if (cp->quad == NULL) {
+ cp->count = ABS(MI_COUNT(mi));
+ if ((cp->quad = (apollonian_quadruple *) malloc(cp->count *
+ sizeof (apollonian_quadruple))) == NULL) {
+ return;
+ }
+ dquad(cp->count, cp->quad);
+ }
+ cp->game = NRAND(PREDEF_CIRCLE_GAMES + cp->count);
+ cp->geometry = (cp->game && cp->altgeom) ? NRAND(3) : 0;
+
+ if (cp->game < PREDEF_CIRCLE_GAMES) {
+ cp->c1 = examples[cp->game][0];
+ cp->c2 = examples[cp->game][1];
+ cp->c3 = examples[cp->game][2];
+ cp->c4 = examples[cp->game][3];
+ /* do not label non int */
+ cp->label = cp->label && (cp->c4.e == (int) cp->c4.e);
+ } else { /* uses results of dquad, all int */
+ i = cp->game - PREDEF_CIRCLE_GAMES;
+ cp->c1.e = cp->quad[i].a;
+ cp->c2.e = cp->quad[i].b;
+ cp->c3.e = cp->quad[i].c;
+ cp->c4.e = cp->quad[i].d;
+ if (cp->geometry)
+ cquad(&(cp->c1), &(cp->c2), &(cp->c3), &(cp->c4));
+ }
+ cp->time = 0;
+ MI_CLEARWINDOW(mi);
+ if (cp->game != 0) {
+ double q123;
+
+ if (cp->c1.e == 0.0 || cp->c1.e == -cp->c2.e)
+ return;
+ cp->c1.x = 0.0;
+ cp->c1.y = 0.0;
+ cp->c2.x = -(cp->c1.e + cp->c2.e) / cp->c1.e;
+ cp->c2.y = 0;
+ q123 = sqrt(cp->c1.e * cp->c2.e + cp->c1.e * cp->c3.e +
+ cp->c2.e * cp->c3.e);
+#ifdef DEBUG
+ (void) printf("q123 = %g, ", q123);
+#endif
+ cp->c3.x = (cp->c1.e * cp->c1.e - q123 * q123) / (cp->c1.e *
+ (cp->c1.e + cp->c2.e));
+ cp->c3.y = -2.0 * q123 / (cp->c1.e + cp->c2.e);
+ q123 = -cp->c1.e - cp->c2.e + q123;
+ cp->c4.x = (cp->c1.e * cp->c1.e - q123 * q123) / (cp->c1.e *
+ (cp->c1.e + cp->c2.e));
+ cp->c4.y = -2.0 * q123 / (cp->c1.e + cp->c2.e);
+#ifdef DEBUG
+ (void) printf("q124 = %g\n", q123);
+ (void) printf("%g %g %g %g %g %g %g %g\n",
+ cp->c1.x, cp->c1.y, cp->c2.x, cp->c2.y,
+ cp->c3.x, cp->c3.y, cp->c4.x, cp->c4.y);
+#endif
+ }
+#ifndef DEBUG
+ if (LRAND() & 1) {
+ cp->c3.y = -cp->c3.y;
+ cp->c4.y = -cp->c4.y;
+ }
+ i = NRAND(4);
+ randomize_c(i, &(cp->c1));
+ randomize_c(i, &(cp->c2));
+ randomize_c(i, &(cp->c3));
+ randomize_c(i, &(cp->c4));
+#endif
+}
+
+void
+draw_apollonian(ModeInfo * mi)
+{
+ apollonianstruct *cp;
+
+ if (apollonians == NULL)
+ return;
+ cp = &apollonians[MI_SCREEN(mi)];
+
+
+ MI_IS_DRAWN(mi) = True;
+
+ if (cp->time < 5) {
+ switch (cp->time) {
+ case 0:
+ p(mi, cp->c1);
+ p(mi, cp->c2);
+ p(mi, cp->c3);
+ p(mi, cp->c4);
+ break;
+ case 1:
+ f(mi, cp->c1, cp->c2, cp->c3, cp->c4);
+ break;
+ case 2:
+ f(mi, cp->c1, cp->c2, cp->c4, cp->c3);
+ break;
+ case 3:
+ f(mi, cp->c1, cp->c3, cp->c4, cp->c2);
+ break;
+ case 4:
+ f(mi, cp->c2, cp->c3, cp->c4, cp->c1);
+ }
+ }
+ if (++cp->time > MI_CYCLES(mi))
+ {
+#ifdef STANDALONE
+ erase_full_window(MI_DISPLAY(mi), MI_WINDOW(mi));
+#endif /* STANDALONE */
+ init_apollonian(mi);
+ }
+}
+
+void
+release_apollonian(ModeInfo * mi)
+{
+ if (apollonians != NULL) {
+ int screen;
+
+ for (screen = 0; screen < MI_NUM_SCREENS(mi); screen++)
+ free_apollonian(MI_DISPLAY(mi), &apollonians[screen]);
+ (void) free((void *) apollonians);
+ apollonians = (apollonianstruct *) NULL;
+ }
+}
+
+#endif /* MODE_apollonian */
projects / xscreensaver / blobdiff