/* epicycle --- The motion of a body with epicycles, as in the pre-Copernican * cosmologies. * * Copyright (c) 1998 James Youngman * * 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 #include #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. */ if (maxCircles == minCircles) n = minCircles; /* Avoid division by zero. */ else n = minCircles + random() % (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 { 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; tx > *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(); } } }