/* -*- 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 <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
*
*
* 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 DEFAULTS "*delay: 1000000 \n" \
"*count: 64 \n" \
"*cycles: 20 \n" \
"*ncolors: 64 \n" \
"*font: sans-serif bold 10\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 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;
XftFont *font;
XftColor xft_fg;
XftDraw *xftdraw;
int time;
int game;
} apollonianstruct;
static apollonianstruct *apollonians = (apollonianstruct *) NULL;
#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
set_xft_color (ModeInfo *mi, XftColor *c, unsigned long pixel)
{
XColor xc;
xc.pixel = pixel;
XQueryColor (MI_DISPLAY(mi), MI_COLORMAP(mi), &xc);
c->pixel = pixel;
c->color.red = xc.red;
c->color.green = xc.green;
c->color.blue = xc.blue;
c->color.alpha = 0xFFFF;
}
static void
p(ModeInfo *mi, circle c)
{
apollonianstruct *cp = &apollonians[MI_SCREEN(mi)];
char string[15];
double g, e;
int g_width;
unsigned long pix;
#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)
pix = MI_WHITE_PIXEL(mi);
else
pix = MI_PIXEL(mi, ((int) ((g + cp->color_offset) * g))
% MI_NPIXELS(mi));
XSetForeground(MI_DISPLAY(mi), MI_GC(mi), pix);
set_xft_color (mi, &cp->xft_fg, pix);
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;
}
sprintf(string, "%g", (g == 0.0) ? 0 : -g);
XftDrawStringUtf8 (cp->xftdraw, &cp->xft_fg, cp->font,
((int) (cp->size * c.x / (2.0 * c.e))) +
cp->offset.x + cp->font->ascent * 2,
((int) (cp->size * c.y / (2.0 * c.e))) +
cp->font->ascent * 4,
(FcChar8 *) string,
(g == 0 ? 1 :
g < 10 ? 2 :
g < 100 ? 3 : 4));
XftDrawStringUtf8 (cp->xftdraw, &cp->xft_fg, cp->font,
((int) (cp->size * c.x / (2.0 * c.e) +
cp->offset.x)) + cp->font->ascent * 2,
((int) (cp->size * c.y / (2.0 * c.e) +
MI_HEIGHT(mi) - cp->font->ascent * 4)),
(FcChar8 *) 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)
pix = MI_BLACK_PIXEL(mi);
else
pix = 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 / ((cp->font->ascent + cp->font->descent) * 2) &&
g < 1000.0) {
XGlyphInfo overall;
XSetForeground(MI_DISPLAY(mi), MI_GC(mi), pix);
set_xft_color (mi, &cp->xft_fg, pix);
sprintf(string, "%g", g);
XftTextExtentsUtf8 (MI_DISPLAY(mi), cp->font,
(FcChar8 *) string, g_width, &overall);
XftDrawStringUtf8 (cp->xftdraw, &cp->xft_fg, cp->font,
((int) (cp->size * e * c.x / (2.0 * c.e) +
cp->size / 2.0 + cp->offset.x)) -
overall.width / 2,
((int) (cp->size * e * c.y / (2.0 * c.e) +
cp->size / 2.0 + cp->offset.y)) +
cp->font->ascent / 2,
(FcChar8 *) 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;
}
XftFontClose (MI_DISPLAY(mi), cp->font);
XftDrawDestroy (cp->xftdraw);
}
#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;
char *s;
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));
cp->font = load_xft_font_retry (MI_DISPLAY(mi), MI_SCREEN(mi),
get_string_resource (MI_DISPLAY(mi),
"font", "Font"));
cp->xftdraw = XftDrawCreate (MI_DISPLAY(mi), MI_WINDOW(mi),
MI_VISUAL(mi), MI_COLORMAP(mi));
s = get_string_resource (MI_DISPLAY(mi), "foreground", "Foreground");
XftColorAllocName (MI_DISPLAY(mi), MI_VISUAL(mi), MI_COLORMAP(mi), s,
&cp->xft_fg);
free(s);
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 */
