--- /dev/null
+/* epicycle --- The motion of a body with epicycles, as in the pre-Copernican
+ * cosmologies.
+ *
+ * Copyright (c) 1998 James Youngman <jay@gnu.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.
+ */
+
+/* Standard C headers; screenhack.h assumes that these have already
+ * been included if required -- for example, it defines M_PI if not
+ * already defined.
+ */
+#include <float.h>
+#include <math.h>
+
+
+#include "screenhack.h"
+#include "erase.h"
+
+/* MIT-SHM headers omitted; this screenhack doesn't use it */
+
+
+
+/*********************************************************/
+/******************** MAGIC CONSTANTS ********************/
+/*********************************************************/
+#define MIN_RADIUS (5) /* smallest allowable circle radius */
+#define FILL_PROPORTION (0.9) /* proportion of screen to fill by scaling. */
+/*********************************************************/
+/***************** END OF MAGIC CONSTANTS ****************/
+/*********************************************************/
+
+
+
+#define FULLCIRCLE (2.0 * M_PI) /* radians in a circle. */
+
+
+/* Name of the Screensaver hack */
+char *progclass="Epicycle";
+
+/* Some of these resource values here are hand-tuned to give a
+ * pleasing variety of interesting shapes. These are not the only
+ * good settings, but you may find you need to change some as a group
+ * to get pleasing figures.
+ */
+char *defaults [] = {
+ ".background: black",
+ ".foreground: white",
+ "*colors: 100",
+ "*color0: red",
+ "*delay: 1000",
+ "*holdtime: 2",
+ "*lineWidth: 4",
+ "*minCircles: 2",
+ "*maxCircles: 10",
+ "*minSpeed: 0.003",
+ "*maxSpeed: 0.005",
+ "*harmonics: 8",
+ "*timestep: 1.0",
+ "*timestepCoarseFactor: 1.0", /* no option for this resource. */
+ "*divisorPoisson: 0.4",
+ "*sizeFactorMin: 1.05",
+ "*sizeFactorMax: 2.05",
+ 0
+};
+
+/* options passed to this program */
+XrmOptionDescRec options [] = {
+ { "-color0", ".color0", XrmoptionSepArg, 0 },
+ { "-colors", ".colors", XrmoptionSepArg, 0 },
+ { "-colours", ".colors", XrmoptionSepArg, 0 },
+ { "-foreground", ".foreground", XrmoptionSepArg, 0 },
+ { "-delay", ".delay", XrmoptionSepArg, 0 },
+ { "-holdtime", ".holdtime", XrmoptionSepArg, 0 },
+ { "-linewidth", ".lineWidth", XrmoptionSepArg, 0 },
+ { "-min_circles", ".minCircles", XrmoptionSepArg, 0 },
+ { "-max_circles", ".maxCircles", XrmoptionSepArg, 0 },
+ { "-min_speed", ".minSpeed", XrmoptionSepArg, 0 },
+ { "-max_speed", ".maxSpeed", XrmoptionSepArg, 0 },
+ { "-harmonics", ".harmonics", XrmoptionSepArg, 0 },
+ { "-timestep", ".timestep", XrmoptionSepArg, 0 },
+ { "-divisor_poisson",".divisorPoisson",XrmoptionSepArg, 0 },
+ { "-size_factor_min", ".sizeFactorMin", XrmoptionSepArg, 0 },
+ { "-size_factor_max", ".sizeFactorMax", XrmoptionSepArg, 0 },
+ { 0, 0, 0, 0 }
+};
+
+
+static Display *dpy;
+static Window window;
+static GC color0;
+static int width, height;
+static int x_offset, y_offset;
+static int unit_pixels;
+static unsigned long bg;
+static Colormap cmap;
+static int restart = 0;
+static int stop = 0;
+static double wdot_max;
+static XColor *colors = NULL;
+static int ncolors = 2;
+static int color_shift_pos=0; /* how far we are towards that. */
+static double colour_cycle_rate = 1.0;
+static int harmonics = 8;
+static double divisorPoisson = 0.4;
+static double sizeFactorMin = 1.05;
+static double sizeFactorMax = 2.05;
+static int minCircles;
+static int maxCircles;
+
+/* Each circle is centred on a point on the rim of another circle.
+ */
+struct tagCircle
+{
+ long radius; /* in pixels */
+ double w; /* position (radians ccw from x-axis) */
+ double initial_w; /* starting position */
+ double wdot; /* rotation rate (change in w per iteration) */
+ int divisor;
+
+ struct tagCircle *pchild;
+};
+typedef struct tagCircle Circle;
+
+
+struct tagBody /* a body that moves on a system of circles. */
+{
+ int x_origin, y_origin;
+ int x, y;
+ int old_x, old_y;
+ int current_color; /* pixel index into colors[] */
+ Circle *epicycles; /* system of circles on which it moves. */
+ struct tagBody *next; /* next in list. */
+};
+typedef struct tagBody Body;
+
+
+/* Determine the GCD of two numbers using Euclid's method. The other
+ * possible algorighm is Stein's method, but it's probably only going
+ * to be much faster on machines with no divide instruction, like the
+ * ARM and the Z80. The former is very fast anyway and the latter
+ * probably won't run X clients; in any case, this calculation is not
+ * the bulk of the computational expense of the program. I originally
+ * tried using Stein's method, but I wanted to remove the gotos. Not
+ * wanting to introduce possible bugs, I plumped for Euclid's method
+ * instead. Lastly, Euclid's algorithm is preferred to the
+ * generalisation for N inputs.
+ *
+ * See Knuth, section 4.5.2.
+ */
+static int
+gcd(int u, int v) /* Euclid's Method */
+{
+ /* If either operand of % is negative, the sign of the result is
+ * implementation-defined. See section 6.3.5 "Multiplicative
+ * Operators" of the ANSI C Standard (page 46 [LEFT HAND PAGE!] of
+ * "Annotated C Standard", Osborne, ISBN 0-07-881952-0).
+ */
+ if (u < 0) u = -u;
+ if (v < 0) v = -v;
+
+ while (0 != v)
+ {
+ int r;
+ r = u % v;
+ u = v;
+ v = r;
+ }
+ return u;
+}
+
+/* Determine the Lowest Common Multiple of two integers, using
+ * Euclid's Proposition 34, as explained in Knuth's The Art of
+ * Computer Programming, Vol 2, section 4.5.2.
+ */
+static int
+lcm(int u, int v)
+{
+ return u / gcd(u,v) * v;
+}
+
+static long
+random_radius(double scale)
+{
+ long r;
+
+ r = frand(scale) * unit_pixels/2; /* for frand() see utils/yarandom.h */
+ if (r < MIN_RADIUS)
+ r = MIN_RADIUS;
+ return r;
+}
+
+
+static long
+random_divisor(void)
+{
+ int divisor = 1;
+ int sign;
+
+ while (frand(1.0) < divisorPoisson && divisor <= harmonics)
+ {
+ ++divisor;
+ }
+ sign = (frand(1.0) < 0.5) ? +1 : -1;
+ return sign * divisor;
+}
+
+
+static void
+oom(void)
+{
+ fprintf(stderr, "Failed to allocate memory!\n");
+ exit(-1);
+}
+
+
+/* Construct a circle or die.
+ */
+Circle *
+new_circle(double scale)
+{
+ Circle *p = malloc(sizeof(Circle));
+
+ p->radius = random_radius(scale);
+ p->w = p->initial_w = 0.0;
+ p->divisor = random_divisor();
+ p->wdot = wdot_max / p->divisor;
+ p->pchild = NULL;
+
+ return p;
+}
+
+static void delete_circle(Circle *p)
+{
+ free(p);
+}
+
+static void
+delete_circle_chain(Circle *p)
+{
+ while (p)
+ {
+ Circle *q = p->pchild;
+ delete_circle(p);
+ p = q;
+ }
+}
+
+Circle *
+new_circle_chain(void)
+{
+ Circle *head;
+ double scale = 1.0, factor;
+ int n;
+
+ /* Parent circles are larger than their children by a factor of at
+ * least FACTOR_MIN and at most FACTOR_MAX.
+ */
+ factor = sizeFactorMin + frand(sizeFactorMax - sizeFactorMin);
+
+ /* There are between minCircles and maxCircles in each figure.
+ */
+ n = minCircles + rand() % (maxCircles - minCircles);
+
+ head = NULL;
+ while (n--)
+ {
+ Circle *p = new_circle(scale);
+ p->pchild = head;
+ head = p;
+
+ scale /= factor;
+ }
+ return head;
+}
+
+static void
+assign_random_common_w(Circle *p)
+{
+ double w_common = frand(FULLCIRCLE); /* anywhere on the circle */
+ while (p)
+ {
+ p->initial_w = w_common;
+ p = p->pchild;
+ }
+}
+
+static Body *
+new_body(void)
+{
+ Body *p = malloc(sizeof(Body));
+ if (NULL == p)
+ oom();
+ p->epicycles = new_circle_chain();
+ p->current_color = 0; /* ?? start them all on different colors? */
+ p->next = NULL;
+ p->x = p->y = 0;
+ p->old_x = p->old_y = 0;
+ p->x_origin = p->y_origin = 0;
+
+ /* Start all the epicycles at the same w value to make it easier to
+ * figure out at what T value the cycle is closed. We don't just fix
+ * the initial W value because that makes all the patterns tend to
+ * be symmetrical about the X axis.
+ */
+ assign_random_common_w(p->epicycles);
+ return p;
+}
+
+static void
+delete_body(Body *p)
+{
+ delete_circle_chain(p->epicycles);
+ free(p);
+}
+
+
+static void
+draw_body(Body *pb, GC gc)
+{
+ XDrawLine(dpy, window, gc, pb->old_x, pb->old_y, pb->x, pb->y);
+}
+
+static long
+compute_divisor_lcm(Circle *p)
+{
+ long l = 1;
+
+ while (p)
+ {
+ l = lcm(l, p->divisor);
+ p = p->pchild;
+ }
+ return l;
+}
+
+
+/* move_body()
+ *
+ * Calculate the position for the body at time T. We work in double
+ * rather than int to avoid the cumulative errors that would be caused
+ * by the rounding implicit in an assignment to int.
+ */
+static void
+move_body(Body *pb, double t)
+{
+ Circle *p;
+ double x, y;
+
+ pb->old_x = pb->x;
+ pb->old_y = pb->y;
+
+ x = pb->x_origin;
+ y = pb->y_origin;
+
+ for (p=pb->epicycles; NULL != p; p=p->pchild)
+ {
+ /* angular pos = initial_pos + time * angular speed */
+ /* but this is an angular position, so modulo FULLCIRCLE. */
+ p->w = fmod(p->initial_w + (t * p->wdot), FULLCIRCLE);
+
+ x += (p->radius * cos(p->w));
+ y += (p->radius * sin(p->w));
+ }
+
+ pb->x = (int)x;
+ pb->y = (int)y;
+}
+
+static int
+colour_init(XWindowAttributes *pxgwa)
+{
+ XGCValues gcv;
+
+#if 0
+ int H = random() % 360; /* colour choice from attraction.c. */
+ double S1 = 0.25;
+ double S2 = 1.00;
+ double V = frand(0.25) + 0.75;
+ int line_width = 0;
+#endif
+
+ int retval = 1;
+ unsigned long valuemask = 0L;
+ unsigned long fg;
+
+ /* Free any already allocated colors...
+ */
+ if (colors)
+ {
+ free_colors(dpy, cmap, colors, ncolors);
+ colors = 0;
+ ncolors = 0;
+ }
+
+ ncolors = get_integer_resource ("colors", "Colors");
+ if (0 == ncolors) /* English spelling? */
+ ncolors = get_integer_resource ("colours", "Colors");
+
+ if (ncolors < 2)
+ ncolors = 2;
+ if (ncolors <= 2)
+ mono_p = True;
+ colors = 0;
+
+ if (!mono_p)
+ {
+ colors = (XColor *) malloc(sizeof(*colors) * (ncolors+1));
+ if (!colors)
+ oom();
+
+ make_smooth_colormap (dpy, pxgwa->visual, cmap, colors, &ncolors,
+ True, /* allocate */
+ False, /* not writable */
+ True); /* verbose (complain about failure) */
+ if (ncolors <= 2)
+ {
+ if (colors)
+ free (colors);
+ colors = 0;
+ mono_p = True;
+ }
+ }
+
+
+ bg = get_pixel_resource ("background", "Background", dpy, cmap);
+
+ /* Set the line width
+ */
+ gcv.line_width = get_integer_resource ("lineWidth", "Integer");
+ if (gcv.line_width)
+ {
+ valuemask |= GCLineWidth;
+
+ gcv.join_style = JoinRound;
+ gcv.cap_style = CapRound;
+
+ valuemask |= (GCCapStyle | GCJoinStyle);
+ }
+
+
+ /* Set the drawing function.
+ */
+ gcv.function = GXcopy;
+ valuemask |= GCFunction;
+
+ /* Set the foreground.
+ */
+ if (mono_p)
+ fg = get_pixel_resource ("foreground", "Foreground", dpy, cmap);
+ else
+ fg = bg ^ get_pixel_resource (("color0"), "Foreground", dpy, cmap);
+ gcv.foreground = fg;
+ valuemask |= GCForeground;
+
+ /* Actually create the GC.
+ */
+ color0 = XCreateGC (dpy, window, valuemask, &gcv);
+
+ return retval;
+}
+
+
+/* check_events(); originally from XScreensaver: hacks/maze.c,
+ * but now quite heavily modified.
+ *
+ * Reaction to events:-
+ *
+ * Mouse 1 -- new figure }
+ * 2 -- new figure }-- ignored when running on root window.
+ * 3 -- exit }
+ *
+ * Window resized or exposed -- new figure.
+ * Window iconised -- wait until it's re-mapped, then start a new figure.
+ */
+static int
+check_events (void) /* X event handler [ rhess ] */
+{
+ XEvent e;
+ int unmapped = 0;
+
+ while (unmapped || XPending(dpy))
+ {
+ XNextEvent(dpy, &e);
+
+ switch (e.type)
+ {
+ case ButtonPress:
+ switch (e.xbutton.button)
+ {
+ case 3:
+ exit (0);
+ break;
+
+ case 2:
+ case 1:
+ default:
+ restart = 1 ;
+ stop = 0 ;
+ break;
+ }
+ break;
+
+ case ConfigureNotify:
+ restart = 1;
+ break;
+
+ case UnmapNotify:
+ printf("unmapped!\n");
+ unmapped = 1;
+ restart = 1; /* restart with new fig. when re-mapped. */
+ break;
+
+ case Expose:
+ if (0 == e.xexpose.count)
+ {
+ /* We can get several expose events in the queue.
+ * Only the last one has a zero count. We eat
+ * events in this function so as to avoid restarting
+ * the screensaver many times in quick succession.
+ */
+ restart = 1;
+ }
+ /* If we had been unmapped and are now waiting to be re-mapped,
+ * indicate that we condition we are waiting for is now met.
+ */
+ if (unmapped)
+ printf("re-mapped!\n");
+ unmapped = 0;
+ break;
+
+ default:
+ screenhack_handle_event(dpy, &e);
+ break;
+ }
+
+ /* If we're unmapped, don't return to the caller. This
+ * prevents us wasting CPU, calculating new positions for
+ * things that will never be plotted. This is a real CPU
+ * saver.
+ */
+ if (!unmapped)
+ return 1;
+ }
+ return 0;
+}
+
+
+static void
+setup(void)
+{
+ XWindowAttributes xgwa;
+ int root;
+
+ XGetWindowAttributes (dpy, window, &xgwa);
+ cmap = xgwa.colormap;
+
+ width = xgwa.width;
+ height = xgwa.height;
+ x_offset = width / 2;
+ y_offset = height / 2;
+ unit_pixels = width < height ? width : height;
+
+ {
+ static Bool done = False;
+ if (!done)
+ {
+ colour_init(&xgwa);
+ done = True;
+ }
+ }
+
+ root = get_boolean_resource("root", "Boolean");
+
+ if (root)
+ {
+ XSelectInput(dpy, window, ExposureMask);
+ }
+ else
+ {
+ XWindowAttributes xgwa;
+ XGetWindowAttributes (dpy, window, &xgwa);
+ XSelectInput (dpy, window,
+ xgwa.your_event_mask | ExposureMask |
+ ButtonPressMask |StructureNotifyMask);
+ }
+
+}
+static void
+color_step(Body *pb, double frac)
+{
+ if (!mono_p)
+ {
+ int newshift = ncolors * fmod(frac * colour_cycle_rate, 1.0);
+ if (newshift != color_shift_pos)
+ {
+ pb->current_color = newshift;
+ XSetForeground (dpy, color0, colors[pb->current_color].pixel);
+ color_shift_pos = newshift;
+ }
+ }
+}
+
+
+long
+distance(long x1, long y1, long x2, long y2)
+{
+ long dx, dy;
+
+ dx = x2 - x1;
+ dy = y2 - y1;
+ return dx*dx + dy*dy;
+}
+
+#if 0
+static int poisson_irand(double p)
+{
+ int r = 1;
+ while (fabs(frand(1.0)) < p)
+ ++r;
+ return r < 1 ? 1 : r;
+}
+#endif
+
+static void
+precalculate_figure(Body *pb,
+ double xtime, double step,
+ int *x_max, int *y_max,
+ int *x_min, int *y_min)
+{
+ double t;
+
+ move_body(pb, 0.0); /* move once to avoid initial line from origin */
+ *x_min = *x_max = pb->x;
+ *y_min = *y_max = pb->y;
+
+ for (t=0.0; t<xtime; t += step)
+ {
+ move_body(pb, t); /* move once to avoid initial line from origin */
+ if (pb->x > *x_max)
+ *x_max = pb->x;
+ if (pb->x < *x_min)
+ *x_min = pb->x;
+ if (pb->y > *y_max)
+ *y_max = pb->y;
+ if (pb->y < *y_min)
+ *y_min = pb->y;
+ }
+}
+
+static int i_max(int a, int b)
+{
+ return (a>b) ? a : b;
+}
+
+static void rescale_circles(Body *pb,
+ int x_max, int y_max,
+ int x_min, int y_min)
+{
+ double xscale, yscale, scale;
+ double xm, ym;
+
+ x_max -= x_offset;
+ x_min -= x_offset;
+ y_max -= y_offset;
+ y_min -= y_offset;
+
+ x_max = i_max(x_max, -x_min);
+ y_max = i_max(y_max, -y_min);
+
+
+ xm = width / 2.0;
+ ym = height / 2.0;
+ if (x_max > xm)
+ xscale = xm / x_max;
+ else
+ xscale = 1.0;
+ if (y_max > ym)
+ yscale = ym / y_max;
+ else
+ yscale = 1.0;
+
+ if (xscale < yscale) /* wider than tall */
+ scale = xscale; /* ensure width fits onscreen */
+ else
+ scale = yscale; /* ensure height fits onscreen */
+
+
+ scale *= FILL_PROPORTION; /* only fill FILL_PROPORTION of screen */
+ if (scale < 1.0) /* only reduce, don't enlarge. */
+ {
+ Circle *p;
+ for (p=pb->epicycles; p; p=p->pchild)
+ {
+ p->radius *= scale;
+ }
+ }
+ else
+ {
+ printf("enlarge by x%.2f skipped...\n", scale);
+ }
+}
+
+
+/* angular speeds of the circles are harmonics of a fundamental
+ * value. That should please the Pythagoreans among you... :-)
+ */
+static double
+random_wdot_max(void)
+{
+ /* Maximum and minimum values for the choice of wdot_max. Possible
+ * epicycle speeds vary from wdot_max to (wdot_max * harmonics).
+ */
+ double minspeed, maxspeed;
+ minspeed = get_float_resource("minSpeed", "Double");
+ maxspeed = get_float_resource("maxSpeed", "Double");
+ return harmonics * (minspeed + FULLCIRCLE * frand(maxspeed-minspeed));
+}
+
+/* this is the function called for your screensaver */
+/*GLOBAL*/ void
+screenhack(Display *disp, Window win)
+{
+ Body *pb = NULL;
+ long l;
+ double t, timestep, circle, xtime, timestep_coarse;
+ int delay;
+ int uncleared = 1;
+ int xmax, xmin, ymax, ymin;
+ int holdtime = get_integer_resource ("holdtime", "Integer");
+
+ dpy = disp;
+ window = win;
+
+ circle = FULLCIRCLE;
+
+ XClearWindow(dpy, window);
+ uncleared = 0;
+
+ delay = get_integer_resource ("delay", "Integer");
+ harmonics = get_integer_resource("harmonics", "Integer");
+ divisorPoisson = get_float_resource("divisorPoisson", "Double");
+
+ timestep = get_float_resource("timestep", "Double");
+ timestep_coarse = timestep *
+ get_float_resource("timestepCoarseFactor", "Double");
+
+ sizeFactorMin = get_float_resource("sizeFactorMin", "Double");
+ sizeFactorMax = get_float_resource("sizeFactorMax", "Double");
+
+ minCircles = get_integer_resource ("minCircles", "Integer");
+ maxCircles = get_integer_resource ("maxCircles", "Integer");
+
+ xtime = 0; /* is this right? */
+ while (0 == stop)
+ {
+ setup(); /* do this inside the loop to cope with any window resizing */
+ restart = 0;
+
+ /* Flush any outstanding events; this has the side effect of
+ * reducing the number of "false restarts"; resdtarts caused by
+ * one event (e.g. ConfigureNotify) followed by another
+ * (e.g. Expose).
+ */
+ XSync(dpy, True);
+
+ wdot_max = random_wdot_max();
+
+ if (pb)
+ {
+ delete_body(pb);
+ pb = NULL;
+ }
+ pb = new_body();
+ pb->x_origin = pb->x = x_offset;
+ pb->y_origin = pb->y = y_offset;
+
+
+ if (uncleared)
+ {
+ erase_full_window(dpy, window);
+ uncleared = 0;
+ }
+
+ fflush(stdout);
+ precalculate_figure(pb, xtime, timestep_coarse,
+ &xmax, &ymax, &xmin, &ymin);
+
+ rescale_circles(pb, xmax, ymax, xmin, ymin);
+
+ move_body(pb, 0.0); /* move once to avoid initial line from origin */
+ move_body(pb, 0.0); /* move once to avoid initial line from origin */
+
+
+ t = 0.0; /* start at time zero. */
+
+ l = compute_divisor_lcm(pb->epicycles);
+
+ colour_cycle_rate = fabs(l);
+
+ xtime = fabs(l * circle / wdot_max);
+
+ if (colors) /* (colors==NULL) if mono_p */
+ XSetForeground (dpy, color0, colors[pb->current_color].pixel);
+
+ while (0 == restart)
+ {
+ color_step(pb, t/xtime );
+ draw_body(pb, color0);
+ uncleared = 1;
+
+
+ /* Check if the figure is complete...*/
+ if (t > xtime)
+ {
+ XSync (dpy, False);
+
+ check_events();
+ if (holdtime)
+ sleep(holdtime); /* show complete figure for a bit. */
+
+ restart = 1; /* begin new figure. */
+ }
+
+
+ check_events();
+ if (delay)
+ usleep (delay);
+
+ t += timestep;
+ move_body(pb, t);
+ check_events();
+ }
+ }
+}
+
projects / xscreensaver / blobdiff