/* -*- Mode: C; tab-width: 4 -*- */ /* apollonian --- Apollonian Circles */ #if 0 static const char sccsid[] = "@(#)apollonian.c 5.02 2001/07/01 xlockmore"; #endif /*- * Copyright (c) 2000, 2001 by Allan R. Wilks . * * 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 . * * 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 DEFAULTS "*delay: 1000000 \n" \ "*count: 64 \n" \ "*cycles: 20 \n" \ "*ncolors: 64 \n" \ "*font: fixed" "\n" \ "*fpsTop: true \n" \ "*fpsSolid: true \n" \ "*ignoreRotation: True" \ # define release_apollonian 0 # define reshape_apollonian 0 # define apollonian_handle_event 0 # include "xlockmore.h" /* in xscreensaver distribution */ #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[] = { {"-altgeom", ".apollonian.altgeom", XrmoptionNoArg, "on"}, {"+altgeom", ".apollonian.altgeom", XrmoptionNoArg, "off"}, {"-label", ".apollonian.label", XrmoptionNoArg, "on"}, {"+label", ".apollonian.label", XrmoptionNoArg, "off"}, }; static argtype vars[] = { {&altgeom, "altgeom", "AltGeom", DEF_ALTGEOM, t_Bool}, {&label, "label", "Label", DEF_LABEL, t_Bool}, }; static OptionStruct desc[] = { {"-/+altgeom", "turn on/off alternate geometries (off euclidean space, on includes spherical and hyperbolic)"}, {"-/+label", "turn on/off alternate space and number labeling"}, }; ENTRYPOINT 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", (char *) NULL, "init_apollonian", "init_apollonian", "free_apollonian", &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 }; static 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. */ static 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[15]; 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)), (char *) 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, int depth) { apollonianstruct *cp = &apollonians[MI_SCREEN(mi)]; int e = (int) ((cp->c1.e >= 0.0) ? 1.0 : -cp->c1.e); circle c; if (depth > mi->recursion_depth) mi->recursion_depth = depth; 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 == 0 || 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, depth+1); f(mi, c1, c3, c, c2, depth+1); f(mi, c1, c2, c, c3, depth+1); } ENTRYPOINT void free_apollonian (ModeInfo * mi) { apollonianstruct *cp = &apollonians[MI_SCREEN(mi)]; 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 static 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 ENTRYPOINT void init_apollonian (ModeInfo * mi) { apollonianstruct *cp; int i; MI_INIT (mi, apollonians); 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 mi->recursion_depth = -1; } ENTRYPOINT 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, 0); break; case 2: f(mi, cp->c1, cp->c2, cp->c4, cp->c3, 0); break; case 3: f(mi, cp->c1, cp->c3, cp->c4, cp->c2, 0); break; case 4: f(mi, cp->c2, cp->c3, cp->c4, cp->c1, 0); } } if (++cp->time > MI_CYCLES(mi)) init_apollonian(mi); } XSCREENSAVER_MODULE ("Apollonian", apollonian) #endif /* MODE_apollonian */