X-Git-Url: http://git.hungrycats.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=hacks%2Fflow.c;h=64347332f7b55d2a1df40ddb57b1180b94e8c93c;hb=c1b9b55ad8d59dc05ef55e316aebf5863e7dfa56;hp=20554824b700bf692d626ada548a2a5d1204f566;hpb=df053bcb240bd8d82e3bebf48a9766a8728bca4b;p=xscreensaver diff --git a/hacks/flow.c b/hacks/flow.c index 20554824..64347332 100644 --- a/hacks/flow.c +++ b/hacks/flow.c @@ -1,13 +1,18 @@ -/* -*- Mode: C; tab-width: 4 -*- */ +/* -*- Mode: C; tab-width: 4; c-basic-offset: 4 -*- */ /* flow --- flow of strange bees */ +#if 0 #if !defined( lint ) && !defined( SABER ) -static const char sccsid[] = "@(#)flow.c 4.10 98/04/24 xlockmore"; - +static const char sccsid[] = "@(#)flow.c 5.00 2000/11/01 xlockmore"; +#endif #endif /*- - * Copyright (c) 1996 by Tim Auckland + * Copyright (c) 1996 by Tim Auckland + * Incorporating some code from Stephen Davies Copyright (c) 2000 + * + * Search code based on techniques described in "Strange Attractors: + * Creating Patterns in Chaos" by Julien C. Sprott * * Permission to use, copy, modify, and distribute this software and its * documentation for any purpose and without fee is hereby granted, @@ -23,409 +28,1198 @@ static const char sccsid[] = "@(#)flow.c 4.10 98/04/24 xlockmore"; * * "flow" shows a variety of continuous phase-space flows around strange * attractors. It includes the well-known Lorentz mask (the "Butterfly" - * of chaos fame), two forms of Rossler's "Folded Band" and a Poincare' - * section of the "Bagel". + * of chaos fame), two forms of Rossler's "Folded Band" and Poincare' + * sections of the "Birkhoff Bagel" and Duffing's forced occilator. "flow" + * can now discover new attractors. * * Revision History: - * 09-Apr-97: Ported to xlockmore-4 - * 18-Jul-96: Adapted from swarm.c Copyright (c) 1991 by Patrick J. Naughton. - * 31-Aug-90: Adapted from xswarm by Jeff Butterworth. (butterwo@ncsc.org) + * + * 29-Oct-2004: [TDA] Discover Attractors unknown to science. + * Replace 2D rendering of Periodic Attractors with a 3D + * 'interrupted' rendering. Replace "-/+allow2d" with "-/+periodic" + * Replace all ODE formulae with completely generic forms. + * Add '-search' option to perform background high-speed discovery + * for completely new attractors without impacting rendering + * performance. + * Use gaussian distribution for initial point positions and for + * parameter search. + * Add "+dbuf" option to allow Double-Buffering to be turned off on + * slow X servers. + * Remove redundant '-zoom' option. Now automatically zooms if both + * rotation and riding are permitted. + * Replace dynamic bounding box with static one pre-calculated + * during discovery phase. + * Simplify and fix bounding box clipping code. Should now be safe + * to run without double buffer on all XFree86 servers if desired. + * 12-Oct-2004: [TDA] Merge Xscreensaver and Xlockmore branches + * Added Chalky's orbital camera, but made the zooming work by + * flying the camera rather than interpolating the view transforms. + * Added Chalky's Bounding Box, but time-averaged the boundaries to + * let the lost bees escape. + * Added Chalky's 'view-frustrum' clipping, but only applying it to + * the Bounding Box. Trails make clipping less useful. + * Added Chalky's "-slow" and "-freeze" options for compatibility, + * but haven't implemented the features, since the results are ugly + * and make no mathematical contribution. + * Added Double-Buffering as a work-around for a persistent XFree86 + * bug that left debris on the screen. + * 21-Mar-2003: [TDA] Trails added (XLockmore branch) + * 01-Nov-2000: [TDA] Allocation checks (XLockmore branch) + * 21-Feb-2000: [Chalky] Major hackage (Stephen Davies, chalky@null.net) + * (Xscreensaver branch) + * Forced perspective mode, added 3d box around attractor which + * involved coding 3d-planar-clipping against the view-frustrum + * thingy. Also made view alternate between piggybacking on a 'bee' + * to zooming around outside the attractor. Most bees slow down and + * stop, to make the structure of the attractor more obvious. +* 28-Jan-1999: [TDA] Catch 'lost' bees in flow.c and disable them. + * (XLockmore branch) + * I chose to disable them rather than reinitialise them because + * reinitialising can produce fake attractors. + * This has allowed me to relax some of the parameters and initial + * conditions slightly to catch some of the more extreme cases. As a + * result you may see some bees fly away at the start - these are the ones + * that 'missed' the attractor. If the bee with the camera should fly + * away the mode will restart :-) + * 31-Nov-1998: [TDA] Added Duffing (what a strange day that was :) DAB) + * Duffing's forced oscillator has been added to the formula list and + * the parameters section has been updated to display it in Poincare' + * section. + * 30-Nov-1998: [TDA] Added travelling perspective option + * A more exciting point-of-view has been added to all autonomous flows. + * This views the flow as seen by a particle moving with the flow. In the + * metaphor of the original code, I've attached a camera to one of the + * trained bees! + * 30-Nov-1998: [TDA] Much code cleanup. + * 09-Apr-1997: [TDA] Ported to xlockmore-4 + * 18-Jul-1996: Adapted from swarm.c Copyright (c) 1991 by Patrick J. Naughton. + * 31-Aug-1990: Adapted from xswarm by Jeff Butterworth. (butterwo@ncsc.org). */ #ifdef STANDALONE -# define PROGCLASS "Flow" -# define HACK_INIT init_flow -# define HACK_DRAW draw_flow -# define flow_opts xlockmore_opts -# define DEFAULTS "*delay: 1000 \n" \ - "*count: 1024 \n" \ - "*cycles: 3000 \n" \ - "*ncolors: 200 \n" -# define SMOOTH_COLORS -# include "xlockmore.h" /* in xscreensaver distribution */ -# include "erase.h" +# define MODE_flow +# define DEFAULTS "*delay: 10000 \n" \ + "*count: 3000 \n" \ + "*size: -10 \n" \ + "*cycles: 10000 \n" \ + "*ncolors: 200 \n" +# define reshape_flow 0 +# define flow_handle_event 0 +# include "xlockmore.h" /* in xscreensaver distribution */ #else /* STANDALONE */ # include "xlock.h" /* in xlockmore distribution */ #endif /* STANDALONE */ -ModeSpecOpt flow_opts = -{0, NULL, 0, NULL, NULL}; +#ifdef MODE_flow + +#define DEF_ROTATE "TRUE" +#define DEF_RIDE "TRUE" +#define DEF_BOX "TRUE" +#define DEF_PERIODIC "TRUE" +#define DEF_SEARCH "TRUE" +#define DEF_DBUF "TRUE" + +static Bool rotatep; +static Bool ridep; +static Bool boxp; +static Bool periodicp; +static Bool searchp; +static Bool dbufp; + +static XrmOptionDescRec opts[] = { + {"-rotate", ".flow.rotate", XrmoptionNoArg, "on"}, + {"+rotate", ".flow.rotate", XrmoptionNoArg, "off"}, + {"-ride", ".flow.ride", XrmoptionNoArg, "on"}, + {"+ride", ".flow.ride", XrmoptionNoArg, "off"}, + {"-box", ".flow.box", XrmoptionNoArg, "on"}, + {"+box", ".flow.box", XrmoptionNoArg, "off"}, + {"-periodic", ".flow.periodic", XrmoptionNoArg, "on"}, + {"+periodic", ".flow.periodic", XrmoptionNoArg, "off"}, + {"-search", ".flow.search", XrmoptionNoArg, "on"}, + {"+search", ".flow.search", XrmoptionNoArg, "off"}, + {"-dbuf", ".flow.dbuf", XrmoptionNoArg, "on"}, + {"+dbuf", ".flow.dbuf", XrmoptionNoArg, "off"}, +}; + +static argtype vars[] = { + {&rotatep, "rotate", "Rotate", DEF_ROTATE, t_Bool}, + {&ridep, "ride", "Ride", DEF_RIDE, t_Bool}, + {&boxp, "box", "Box", DEF_BOX, t_Bool}, + {&periodicp, "periodic", "Periodic", DEF_PERIODIC, t_Bool}, + {&searchp, "search", "Search", DEF_SEARCH, t_Bool}, + {&dbufp, "dbuf", "Dbuf", DEF_DBUF, t_Bool}, +}; + +static OptionStruct desc[] = { + {"-/+rotate", "turn on/off rotating around attractor."}, + {"-/+ride", "turn on/off ride in the flow."}, + {"-/+box", "turn on/off bounding box."}, + {"-/+periodic", "turn on/off periodic attractors."}, + {"-/+search", "turn on/off search for new attractors."}, + {"-/+dbuf", "turn on/off double buffering."}, +}; + +ENTRYPOINT ModeSpecOpt flow_opts = +{sizeof opts / sizeof opts[0], opts, + sizeof vars / sizeof vars[0], vars, desc}; #ifdef USE_MODULES -ModStruct flow_description = -{"flow", "init_flow", "draw_flow", "release_flow", - "refresh_flow", "init_flow", NULL, &flow_opts, - 1000, 1024, 3000, 1, 64, 1.0, "", - "Shows dynamic strange attractors", 0, NULL}; +ModStruct flow_description = { + "flow", "init_flow", "draw_flow", "release_flow", + "refresh_flow", "init_flow", NULL, &flow_opts, + 1000, 1024, 10000, -10, 200, 1.0, "", + "Shows dynamic strange attractors", 0, NULL +}; #endif -#define TIMES 2 /* number of time positions recorded */ +typedef struct { double x, y, z; } dvector; -typedef struct { - double x; - double y; - double z; -} dvector; +#define N_PARS 20 /* Enough for Full Cubic or Periodic Cubic */ +typedef dvector Par[N_PARS]; +enum { /* Name the parameter indices to make it easier to write + standard examples */ + C, + X,XX,XXX,XXY,XXZ,XY,XYY,XYZ,XZ,XZZ, + Y,YY,YYY,YYZ,YZ,YZZ, + Z,ZZ,ZZZ, + SINY = XY /* OK to overlap in this case */ +}; -typedef struct { - double a, b, c; -} Par; +/* Camera target [TDA] */ +typedef enum { + ORBIT = 0, + BEE = 1 +} Chaseto; /* Macros */ -#define X(t,b) (sp->p[(t)*sp->beecount+(b)].x) -#define Y(t,b) (sp->p[(t)*sp->beecount+(b)].y) -#define Z(t,b) (sp->p[(t)*sp->beecount+(b)].z) -#define balance_rand(v) ((LRAND()/MAXRAND*(v))-((v)/2)) /* random number around 0 */ +#define IX(C) ((C) * segindex + sp->cnsegs[(C)]) +#define B(t,b) (sp->p + (t) + (b) * sp->taillen) +#define X(t,b) (B((t),(b))->x) +#define Y(t,b) (B((t),(b))->y) +#define Z(t,b) (B((t),(b))->z) +#define balance_rand(v) ((LRAND()/MAXRAND*(v))-((v)/2)) /* random around 0 */ +#define LOST_IN_SPACE 2000.0 +#define INITIALSTEP 0.04 +#define EYEHEIGHT 0.005 +#define MINTRAIL 2 +#define BOX_L 36 -typedef struct { - int pix; - int width; - int height; - int count; - double size; +/* Points that make up the box (normalized coordinates) */ +static const double box[][3] = { + {1,1,1}, /* 0 */ + {1,1,-1}, /* 1 */ + {1,-1,-1}, /* 2 */ + {1,-1,1}, /* 3 */ + {-1,1,1}, /* 4 */ + {-1,1,-1}, /* 5 */ + {-1,-1,-1},/* 6 */ + {-1,-1,1}, /* 7 */ + {1, .8, .8}, + {1, .8,-.8}, + {1,-.8,-.8}, + {1,-.8, .8}, + { .8,1, .8}, + { .8,1,-.8}, + {-.8,1,-.8}, + {-.8,1, .8}, + { .8, .8,1}, + { .8,-.8,1}, + {-.8,-.8,1}, + {-.8, .8,1}, + {-1, .8, .8}, + {-1, .8,-.8}, + {-1,-.8,-.8}, + {-1,-.8, .8}, + { .8,-1, .8}, + { .8,-1,-.8}, + {-.8,-1,-.8}, + {-.8,-1, .8}, + { .8, .8,-1}, + { .8,-.8,-1}, + {-.8,-.8,-1}, + {-.8, .8,-1} +}; + +/* Lines connecting the box dots */ +static const double lines[][2] = { + {0,1}, {1,2}, {2,3}, {3,0}, /* box */ + {4,5}, {5,6}, {6,7}, {7,4}, + {0,4}, {1,5}, {2,6}, {3,7}, + {4+4,5+4}, {5+4,6+4}, {6+4,7+4}, {7+4,4+4}, + {4+8,5+8}, {5+8,6+8}, {6+8,7+8}, {7+8,4+8}, + {4+12,5+12}, {5+12,6+12}, {6+12,7+12}, {7+12,4+12}, + {4+16,5+16}, {5+16,6+16}, {6+16,7+16}, {7+16,4+16}, + {4+20,5+20}, {5+20,6+20}, {6+20,7+20}, {7+20,4+20}, + {4+24,5+24}, {5+24,6+24}, {6+24,7+24}, {7+24,4+24}, +}; +typedef struct { + /* Variables used in rendering */ + dvector cam[3]; /* camera flight path */ + int chasetime; + Chaseto chaseto; + Pixmap buffer; /* Double Buffer */ + dvector circle[2]; /* POV that circles around the scene */ + dvector centre; /* centre */ int beecount; /* number of bees */ - XSegment *csegs; /* bee lines */ + XSegment *csegs; /* bee lines */ int *cnsegs; XSegment *old_segs; /* old bee lines */ - double step; - dvector c; /* centre */ - dvector *p; /* bee positions x[time][bee#] */ - double *t; - double theta; - double dtheta; - double phi; - double dphi; - void (*ODE) (Par par, - double *dx, double *dy, double *dz, - double x, double y, double z, - double t); + int nold_segs; + int taillen; + + /* Variables common to iterators */ + dvector (*ODE) (Par par, double x, double y, double z); + dvector range; /* Initial conditions */ + double yperiod; /* ODE's where Y is periodic. */ + + /* Variables used in iterating main flow */ Par par; + dvector *p; /* bee positions x[time][bee#] */ + int count; + double lyap; + double size; + dvector mid; /* Effective bounding box */ + double step; + + /* second set of variables, used for parallel search */ + Par par2; + dvector p2[2]; + int count2; + double lyap2; + double size2; + dvector mid2; + double step2; + } flowstruct; -static flowstruct *flows = NULL; +static flowstruct *flows = (flowstruct *) NULL; -static void -Lorentz(Par par, - double *dx, double *dy, double *dz, - double x, double y, double z, - double t) +/* + * Private functions + */ + + +/* ODE functions */ + +/* Generic 3D Cubic Polynomial. Includes all the Quadratics (Lorentz, + Rossler) and much more! */ + +/* I considered offering a seperate 'Quadratic' option, since Cubic is + clearly overkill for the standard examples, but the performance + difference is too small to measure. The compute time is entirely + dominated by the XDrawSegments calls anyway. [TDA] */ +static dvector +Cubic(Par a, double x, double y, double z) { - *dx = par.a * (y - x); - *dy = x * (par.b - z) - y; - *dz = x * y - par.c * z; + dvector d; + d.x = a[C].x + a[X].x*x + a[XX].x*x*x + a[XXX].x*x*x*x + a[XXY].x*x*x*y + + a[XXZ].x*x*x*z + a[XY].x*x*y + a[XYY].x*x*y*y + a[XYZ].x*x*y*z + + a[XZ].x*x*z + a[XZZ].x*x*z*z + a[Y].x*y + a[YY].x*y*y + + a[YYY].x*y*y*y + a[YYZ].x*y*y*z + a[YZ].x*y*z + a[YZZ].x*y*z*z + + a[Z].x*z + a[ZZ].x*z*z + a[ZZZ].x*z*z*z; + + d.y = a[C].y + a[X].y*x + a[XX].y*x*x + a[XXX].y*x*x*x + a[XXY].y*x*x*y + + a[XXZ].y*x*x*z + a[XY].y*x*y + a[XYY].y*x*y*y + a[XYZ].y*x*y*z + + a[XZ].y*x*z + a[XZZ].y*x*z*z + a[Y].y*y + a[YY].y*y*y + + a[YYY].y*y*y*y + a[YYZ].y*y*y*z + a[YZ].y*y*z + a[YZZ].y*y*z*z + + a[Z].y*z + a[ZZ].y*z*z + a[ZZZ].y*z*z*z; + + d.z = a[C].z + a[X].z*x + a[XX].z*x*x + a[XXX].z*x*x*x + a[XXY].z*x*x*y + + a[XXZ].z*x*x*z + a[XY].z*x*y + a[XYY].z*x*y*y + a[XYZ].z*x*y*z + + a[XZ].z*x*z + a[XZZ].z*x*z*z + a[Y].z*y + a[YY].z*y*y + + a[YYY].z*y*y*y + a[YYZ].z*y*y*z + a[YZ].z*y*z + a[YZZ].z*y*z*z + + a[Z].z*z + a[ZZ].z*z*z + a[ZZZ].z*z*z*z; + + return d; } -static void -Rossler(Par par, - double *dx, double *dy, double *dz, - double x, double y, double z, - double t) +/* 3D Cubic in (x,z) with periodic sinusoidal forcing term in x. y is + the independent periodic (time) axis. This includes Birkhoff's + Bagel and Duffing's Attractor */ +static dvector +Periodic(Par a, double x, double y, double z) { - *dx = -(y + par.a * z); - *dy = x + y * par.b; - *dz = par.c + z * (x - 5.7); + dvector d; + + d.x = a[C].x + a[X].x*x + a[XX].x*x*x + a[XXX].x*x*x*x + + a[XXZ].x*x*x*z + a[XZ].x*x*z + a[XZZ].x*x*z*z + a[Z].x*z + + a[ZZ].x*z*z + a[ZZZ].x*z*z*z + a[SINY].x*sin(y); + + d.y = a[C].y; + + d.z = a[C].z + a[X].z*x + a[XX].z*x*x + a[XXX].z*x*x*x + + a[XXZ].z*x*x*z + a[XZ].z*x*z + a[XZZ].z*x*z*z + a[Z].z*z + + a[ZZ].z*z*z + a[ZZZ].z*z*z*z; + + return d; } +/* Numerical integration of the ODE using 2nd order Runge Kutta. + Returns length^2 of the update, so that we can detect if the step + size needs reducing. */ +static double +Iterate(dvector *p, dvector(*ODE)(Par par, double x, double y, double z), + Par par, double step) +{ + dvector k1, k2, k3; + + k1 = ODE(par, p->x, p->y, p->z); + k1.x *= step; + k1.y *= step; + k1.z *= step; + k2 = ODE(par, p->x + k1.x, p->y + k1.y, p->z + k1.z); + k2.x *= step; + k2.y *= step; + k2.z *= step; + k3.x = (k1.x + k2.x) / 2.0; + k3.y = (k1.y + k2.y) / 2.0; + k3.z = (k1.z + k2.z) / 2.0; + + p->x += k3.x; + p->y += k3.y; + p->z += k3.z; + + return k3.x*k3.x + k3.y*k3.y + k3.z*k3.z; +} + +/* Memory functions */ + +#define deallocate(p,t) if (p!=NULL) {free(p); p=(t*)NULL; } +#define allocate(p,t,s) if ((p=(t*)malloc(sizeof(t)*s))==NULL)\ +{free_flow(sp);return;} + static void -RosslerCone(Par par, - double *dx, double *dy, double *dz, - double x, double y, double z, - double t) +free_flow(flowstruct *sp) { - *dx = -(y + par.a * z); - *dy = x + y * par.b - z * z * par.c; - *dz = 0.2 + z * (x - 5.7); + deallocate(sp->csegs, XSegment); + deallocate(sp->cnsegs, int); + deallocate(sp->old_segs, XSegment); + deallocate(sp->p, dvector); } -static void -Bagel(Par par, - double *dx, double *dy, double *dz, - double x, double y, double z, - double t) +/* Generate Gaussian random number: mean 0, "amplitude" A (actually + A is 3*standard deviation). */ + +/* Note this generates a pair of gaussian variables, so it saves one + to give out next time it's called */ +static double +Gauss_Rand(double A) { - *dx = -y + par.b * sin(par.c * t); - *dy = 0.7 * x + par.a * y * (0.1 - x * x); - *dz = 0; + static double d; + static Bool ready = 0; + if(ready) { + ready = 0; + return A/3 * d; + } else { + double x, y, w; + do { + x = 2.0 * (double)LRAND() / MAXRAND - 1.0; + y = 2.0 * (double)LRAND() / MAXRAND - 1.0; + w = x*x + y*y; + } while(w >= 1.0); + + w = sqrt((-2 * log(w))/w); + ready = 1; + d = x * w; + return A/3 * y * w; + } +} + +/* Attempt to discover new atractors by sending a pair of bees on a + fast trip through the new flow and computing their Lyapunov + exponent. Returns False if the bees fly away. + + If the bees stay bounded, the new bounds and the Lyapunov exponent + are stored in sp and the function returns True. + + Repeat invocations continue the flow and improve the accuracy of + the bounds and the Lyapunov exponent. Set sp->count2 to zero to + start a new test. + + Acts on alternate variable set, so that it can be run in parallel + with the main flow */ + +static Bool +discover(ModeInfo * mi) +{ + flowstruct *sp; + double l = 0; + dvector dl; + dvector max, min; + double dl2, df, rs, lsum = 0, s, maxv2 = 0, v2; + + int N, i, nl = 0; + + if (flows == NULL) + return 0; + sp = &flows[MI_SCREEN(mi)]; + + if(sp->count2 == 0) { + /* initial conditions */ + sp->p2[0].x = Gauss_Rand(sp->range.x); + sp->p2[0].y = (sp->yperiod > 0)? + balance_rand(sp->range.y) : Gauss_Rand(sp->range.y); + sp->p2[0].z = Gauss_Rand(sp->range.z); + + /* 1000 steps to find an attractor */ + /* Most cases explode out here */ + for(N=0; N < 1000; N++){ + Iterate(sp->p2, sp->ODE, sp->par2, sp->step2); + if(sp->yperiod > 0 && sp->p2[0].y > sp->yperiod) + sp->p2[0].y -= sp->yperiod; + if(fabs(sp->p2[0].x) > LOST_IN_SPACE || + fabs(sp->p2[0].y) > LOST_IN_SPACE || + fabs(sp->p2[0].z) > LOST_IN_SPACE) { + return 0; + } + sp->count2++; + } + /* Small perturbation */ + sp->p2[1].x = sp->p2[0].x + 0.000001; + sp->p2[1].y = sp->p2[0].y; + sp->p2[1].z = sp->p2[0].z; + } + + /* Reset bounding box */ + max.x = min.x = sp->p2[0].x; + max.y = min.y = sp->p2[0].y; + max.z = min.z = sp->p2[0].z; + + /* Compute Lyapunov Exponent */ + + /* (Technically, we're only estimating the largest Lyapunov + Exponent, but that's all we need to know to determine if we + have a strange attractor.) [TDA] */ + + /* Fly two bees close together */ + for(N=0; N < 5000; N++){ + for(i=0; i< 2; i++) { + v2 = Iterate(sp->p2+i, sp->ODE, sp->par2, sp->step2); + if(sp->yperiod > 0 && sp->p2[i].y > sp->yperiod) + sp->p2[i].y -= sp->yperiod; + + if(fabs(sp->p2[i].x) > LOST_IN_SPACE || + fabs(sp->p2[i].y) > LOST_IN_SPACE || + fabs(sp->p2[i].z) > LOST_IN_SPACE) { + return 0; + } + if(v2 > maxv2) maxv2 = v2; /* Track max v^2 */ + } + + /* find bounding box */ + if ( sp->p2[0].x < min.x ) min.x = sp->p2[0].x; + else if ( sp->p2[0].x > max.x ) max.x = sp->p2[0].x; + if ( sp->p2[0].y < min.y ) min.y = sp->p2[0].y; + else if ( sp->p2[0].y > max.y ) max.y = sp->p2[0].y; + if ( sp->p2[0].z < min.z ) min.z = sp->p2[0].z; + else if ( sp->p2[0].z > max.z ) max.z = sp->p2[0].z; + + /* Measure how much we have to pull the two bees to prevent + them diverging. */ + dl.x = sp->p2[1].x - sp->p2[0].x; + dl.y = sp->p2[1].y - sp->p2[0].y; + dl.z = sp->p2[1].z - sp->p2[0].z; + + dl2 = dl.x*dl.x + dl.y*dl.y + dl.z*dl.z; + if(dl2 > 0) { + df = 1e12 * dl2; + rs = 1/sqrt(df); + sp->p2[1].x = sp->p2[0].x + rs * dl.x; + sp->p2[1].y = sp->p2[0].y + rs * dl.y; + sp->p2[1].z = sp->p2[0].z + rs * dl.z; + lsum = lsum + log(df); + nl = nl + 1; + l = M_LOG2E / 2 * lsum / nl / sp->step2; + } + sp->count2++; + } + /* Anything that didn't explode has a finite attractor */ + /* If Lyapunov is negative then it probably hit a fixed point or a + * limit cycle. Positive Lyapunov indicates a strange attractor. */ + + sp->lyap2 = l; + + sp->size2 = max.x - min.x; + s = max.y - min.y; + if(s > sp->size2) sp->size2 = s; + s = max.z - min.z; + if(s > sp->size2) sp->size2 = s; + + sp->mid2.x = (max.x + min.x) / 2; + sp->mid2.y = (max.y + min.y) / 2; + sp->mid2.z = (max.z + min.z) / 2; + + if(sqrt(maxv2) > sp->size2 * 0.2) { + /* Flowing too fast, reduce step size. This + helps to eliminate high-speed limit cycles, + which can show +ve Lyapunov due to integration + inaccuracy. */ + sp->step2 /= 2; + } + return 1; } -void -init_flow(ModeInfo * mi) +/* Sets up initial conditions for a flow without all the extra baggage + that goes with init_flow */ +static void +restart_flow(ModeInfo * mi) { flowstruct *sp; int b; - dvector range; + if (flows == NULL) + return; + sp = &flows[MI_SCREEN(mi)]; + sp->count = 0; + + /* Re-Initialize point positions, velocities, etc. */ + for (b = 0; b < sp->beecount; b++) { + X(0, b) = Gauss_Rand(sp->range.x); + Y(0, b) = (sp->yperiod > 0)? + balance_rand(sp->range.y) : Gauss_Rand(sp->range.y); + Z(0, b) = Gauss_Rand(sp->range.z); + } +} + +/* Returns true if line was behind a clip plane, or it clips the line */ +/* nx,ny,nz is the normal to the plane. d is the distance from the origin */ +/* s and e are the end points of the line to be clipped */ +static int +clip(double nx, double ny, double nz, double d, dvector *s, dvector *e) +{ + int front1, front2; + dvector w, p; + double t; + + front1 = (nx*s->x + ny*s->y + nz*s->z >= -d); + front2 = (nx*e->x + ny*e->y + nz*e->z >= -d); + if (!front1 && !front2) return 1; + if (front1 && front2) return 0; + w.x = e->x - s->x; + w.y = e->y - s->y; + w.z = e->z - s->z; + + /* Find t in line equation */ + t = ( -d - nx*s->x - ny*s->y - nz*s->z) / ( nx*w.x + ny*w.y + nz*w.z); + + p.x = s->x + w.x * t; + p.y = s->y + w.y * t; + p.z = s->z + w.z * t; + + /* Move clipped point to the intersection */ + if (front2) { + *s = p; + } else { + *e = p; + } + return 0; +} + +/* + * Public functions + */ + +ENTRYPOINT void +init_flow (ModeInfo * mi) +{ + flowstruct *sp; + char *name; + if (flows == NULL) { if ((flows = (flowstruct *) calloc(MI_NUM_SCREENS(mi), - sizeof (flowstruct))) == NULL) + sizeof (flowstruct))) == NULL) return; } sp = &flows[MI_SCREEN(mi)]; + sp->count2 = 0; + + sp->taillen = MI_SIZE(mi); + if (sp->taillen < -MINTRAIL) { + /* Change by sqrt so it seems more variable */ + sp->taillen = NRAND((int)sqrt((double) (-sp->taillen - MINTRAIL + 1))); + sp->taillen = sp->taillen * sp->taillen + MINTRAIL; + } else if (sp->taillen < MINTRAIL) { + sp->taillen = MINTRAIL; + } + + if(!rotatep && !ridep) rotatep = True; /* We need at least one viewpoint */ + + /* Start camera at Orbit or Bee */ + if(rotatep) { + sp->chaseto = ORBIT; + } else { + sp->chaseto = BEE; + } + sp->chasetime = 1; /* Go directly to target */ + + sp->lyap = 0; + sp->yperiod = 0; + sp->step2 = INITIALSTEP; + + /* Zero parameter set */ + memset(sp->par2, 0, N_PARS * sizeof(dvector)); + + /* Set up standard examples */ + switch (NRAND((periodicp) ? 5 : 3)) { + case 0: + /* + x' = a(y - x) + y' = x(b - z) - y + z' = xy - cz + */ + name = "Lorentz"; + sp->par2[Y].x = 10 + balance_rand(5*0); /* a */ + sp->par2[X].x = - sp->par2[Y].x; /* -a */ + sp->par2[X].y = 28 + balance_rand(5*0); /* b */ + sp->par2[XZ].y = -1; + sp->par2[Y].y = -1; + sp->par2[XY].z = 1; + sp->par2[Z].z = - 2 + balance_rand(1*0); /* -c */ + break; + case 1: + /* + x' = -(y + az) + y' = x + by + z' = c + z(x - 5.7) + */ + name = "Rossler"; + sp->par2[Y].x = -1; + sp->par2[Z].x = -2 + balance_rand(1); /* a */ + sp->par2[X].y = 1; + sp->par2[Y].y = 0.2 + balance_rand(0.1); /* b */ + sp->par2[C].z = 0.2 + balance_rand(0.1); /* c */ + sp->par2[XZ].z = 1; + sp->par2[Z].z = -5.7; + break; + case 2: + /* + x' = -(y + az) + y' = x + by - cz^2 + z' = 0.2 + z(x - 5.7) + */ + name = "RosslerCone"; + sp->par2[Y].x = -1; + sp->par2[Z].x = -2; /* a */ + sp->par2[X].y = 1; + sp->par2[Y].y = 0.2; /* b */ + sp->par2[ZZ].y = -0.331 + balance_rand(0.01); /* c */ + sp->par2[C].z = 0.2; + sp->par2[XZ].z = 1; + sp->par2[Z].z = -5.7; + break; + case 3: + /* + x' = -z + b sin(y) + y' = c + z' = 0.7x + az(0.1 - x^2) + */ + name = "Birkhoff"; + sp->par2[Z].x = -1; + sp->par2[SINY].x = 0.35 + balance_rand(0.25); /* b */ + sp->par2[C].y = 1.57; /* c */ + sp->par2[X].z = 0.7; + sp->par2[Z].z = 1 + balance_rand(0.5); /* a/10 */ + sp->par2[XXZ].z = -10 * sp->par2[Z].z; /* -a */ + sp->yperiod = 2 * M_PI; + break; + default: + /* + x' = -ax - z/2 - z^3/8 + b sin(y) + y' = c + z' = 2x + */ + name = "Duffing"; + sp->par2[X].x = -0.2 + balance_rand(0.1); /* a */ + sp->par2[Z].x = -0.5; + sp->par2[ZZZ].x = -0.125; + sp->par2[SINY].x = 27.0 + balance_rand(3.0); /* b */ + sp->par2[C].y = 1.33; /* c */ + sp->par2[X].z = 2; + sp->yperiod = 2 * M_PI; + break; + + } + + sp->range.x = 5; + sp->range.z = 5; + + if(sp->yperiod > 0) { + sp->ODE = Periodic; + /* periodic flows show either uniform distribution or a + snapshot on the 'time' axis */ + sp->range.y = NRAND(2)? sp->yperiod : 0; + } else { + sp->range.y = 5; + sp->ODE = Cubic; + } + + /* Run discoverer to set up bounding box, etc. Lyapunov will + probably be innaccurate, since we're only running it once, but + we're using known strange attractors so it should be ok. */ + discover(mi); + if(MI_IS_VERBOSE(mi)) + fprintf(stdout, + "flow: Lyapunov exponent: %g, step: %g, size: %g (%s)\n", + sp->lyap2, sp->step2, sp->size2, name); + /* Install new params */ + sp->lyap = sp->lyap2; + sp->size = sp->size2; + sp->mid = sp->mid2; + sp->step = sp->step2; + memcpy(sp->par, sp->par2, sizeof(sp->par2)); + + sp->count2 = 0; /* Reset search */ + + free_flow(sp); sp->beecount = MI_COUNT(mi); - if (sp->beecount < 0) { - /* if sp->beecount is random ... the size can change */ - if (sp->csegs != NULL) { - (void) free((void *) sp->csegs); - sp->csegs = NULL; - } - if (sp->cnsegs != NULL) { - (void) free((void *) sp->cnsegs); - sp->cnsegs = NULL; - } - if (sp->old_segs != NULL) { - (void) free((void *) sp->old_segs); - sp->old_segs = NULL; - } - if (sp->p != NULL) { - (void) free((void *) sp->p); - sp->p = NULL; - } - if (sp->t != NULL) { - (void) free((void *) sp->t); - sp->t = NULL; - } - sp->beecount = NRAND(-sp->beecount) + 1; /* Add 1 so its not too boring */ + if (sp->beecount < 0) { /* random variations */ + sp->beecount = NRAND(-sp->beecount) + 1; /* Minimum 1 */ } - sp->count = 0; - sp->width = MI_WIDTH(mi); - sp->height = MI_HEIGHT(mi); - - sp->theta = balance_rand(M_PI); - sp->phi = balance_rand(M_PI); - sp->dtheta = 0.002; - sp->dphi = 0.001; - switch (NRAND(4)) { - case 0: - sp->ODE = Lorentz; - sp->step = 0.02; - sp->size = 60; - sp->c.x = 0; - sp->c.y = 0; - sp->c.z = 24; - range.x = 5; - range.y = 5; - range.z = 1; - sp->par.a = 10 + balance_rand(5); - sp->par.b = 28 + balance_rand(5); - sp->par.c = 2 + balance_rand(1); - break; - case 1: - sp->ODE = Rossler; - sp->step = 0.05; - sp->size = 24; - sp->c.x = 0; - sp->c.y = 0; - sp->c.z = 3; - range.x = 4; - range.y = 4; - range.z = 7; - sp->par.a = 2 + balance_rand(1); - sp->par.b = 0.2 + balance_rand(0.1); - sp->par.c = 0.2 + balance_rand(0.1); - break; - case 2: - sp->ODE = RosslerCone; - sp->step = 0.05; - sp->size = 24; - sp->c.x = 0; - sp->c.y = 0; - sp->c.z = 3; - range.x = 4; - range.y = 4; - range.z = 4; - sp->par.a = 2; - sp->par.b = 0.2; - sp->par.c = 0.25 + balance_rand(0.09); - break; - case 3: - default: - sp->ODE = Bagel; - sp->step = 0.04; - sp->size = 2.6; - sp->c.x = 0 /*-1.0*/ ; - sp->c.y = 0; - sp->c.z = 0; - range.x = 3; - range.y = 4; - range.z = 0; - sp->par.a = 10 + balance_rand(5); - sp->par.b = 0.35 + balance_rand(0.25); - sp->par.c = 1.57; - sp->theta = 0; - sp->phi = 0; - sp->dtheta = 0 /*sp->par.c*sp->step */ ; - sp->dphi = 0; - break; +# ifdef HAVE_COCOA /* Don't second-guess Quartz's double-buffering */ + dbufp = False; +# endif + + if(dbufp) { /* Set up double buffer */ + if (sp->buffer != None) + XFreePixmap(MI_DISPLAY(mi), sp->buffer); + sp->buffer = XCreatePixmap(MI_DISPLAY(mi), MI_WINDOW(mi), + MI_WIDTH(mi), MI_HEIGHT(mi), MI_DEPTH(mi)); + } else { + sp->buffer = MI_WINDOW(mi); } + /* no "NoExpose" events from XCopyArea wanted */ + XSetGraphicsExposures(MI_DISPLAY(mi), MI_GC(mi), False); + + /* Make sure we're using 'thin' lines */ + XSetLineAttributes(MI_DISPLAY(mi), MI_GC(mi), 0, LineSolid, CapNotLast, + JoinMiter); - /* Clear the background. */ + /* Clear the background (may be slow depending on user prefs). */ MI_CLEARWINDOW(mi); /* Allocate memory. */ - - if (!sp->csegs) { - sp->csegs = (XSegment *) malloc(sizeof (XSegment) * sp->beecount - * MI_NPIXELS(mi)); - sp->cnsegs = (int *) malloc(sizeof (int) * MI_NPIXELS(mi)); - - sp->old_segs = (XSegment *) malloc(sizeof (XSegment) * sp->beecount); - sp->p = (dvector *) malloc(sizeof (dvector) * sp->beecount * TIMES); - sp->t = (double *) malloc(sizeof (double) * sp->beecount); + if (sp->csegs == NULL) { + allocate(sp->csegs, XSegment, + (sp->beecount + BOX_L) * MI_NPIXELS(mi) * sp->taillen); + allocate(sp->cnsegs, int, MI_NPIXELS(mi)); + allocate(sp->old_segs, XSegment, sp->beecount * sp->taillen); + allocate(sp->p, dvector, sp->beecount * sp->taillen); } + /* Initialize point positions, velocities, etc. */ + restart_flow(mi); - /* bees */ - for (b = 0; b < sp->beecount; b++) { - X(0, b) = balance_rand(range.x); - X(1, b) = X(0, b); - Y(0, b) = balance_rand(range.y); - Y(1, b) = Y(0, b); - Z(0, b) = balance_rand(range.z); - Z(1, b) = Z(0, b); - sp->t[b] = 0; - } + /* Set up camera tail */ + X(1, 0) = sp->cam[1].x = 0; + Y(1, 0) = sp->cam[1].y = 0; + Z(1, 0) = sp->cam[1].z = 0; } - -void -draw_flow(ModeInfo * mi) +ENTRYPOINT void +draw_flow (ModeInfo * mi) { - Display *display = MI_DISPLAY(mi); - Window window = MI_WINDOW(mi); - GC gc = MI_GC(mi); - flowstruct *sp = &flows[MI_SCREEN(mi)]; - int b, c; - int col, ix; - double sint, cost, sinp, cosp; - - sp->theta += sp->dtheta; - sp->phi += sp->dphi; - sint = sin(sp->theta); - cost = cos(sp->theta); - sinp = sin(sp->phi); - cosp = cos(sp->phi); + int b, i; + int col, begin, end; + double M[3][3]; /* transformation matrix */ + flowstruct *sp = NULL; + int swarm = 0; + int segindex; + + if (flows == NULL) + return; + sp = &flows[MI_SCREEN(mi)]; + if (sp->csegs == NULL) + return; + +#ifdef HAVE_COCOA /* Don't second-guess Quartz's double-buffering */ + XClearWindow (MI_DISPLAY(mi), MI_WINDOW(mi)); +#endif + + /* multiplier for indexing segment arrays. Used in IX macro, etc. */ + segindex = (sp->beecount + BOX_L) * sp->taillen; + + if(searchp){ + if(sp->count2 == 0) { /* start new search */ + sp->step2 = INITIALSTEP; + /* Pick random parameters. Actual range is irrelevant + since parameter scale determines flow speed but not + structure. */ + for(i=0; i< N_PARS; i++) { + sp->par2[i].x = Gauss_Rand(1.0); + sp->par2[i].y = Gauss_Rand(1.0); + sp->par2[i].z = Gauss_Rand(1.0); + } + } + if(!discover(mi)) { /* Flow exploded, reset. */ + sp->count2 = 0; + } else { + if(sp->lyap2 < 0) { + sp->count2 = 0; /* Attractor found, but it's not strange */ + }else if(sp->count2 > 1000000) { /* This one will do */ + sp->count2 = 0; /* Reset search */ + if(MI_IS_VERBOSE(mi)) + fprintf(stdout, + "flow: Lyapunov exponent: %g, step: %g, size: %g (unnamed)\n", + sp->lyap2, sp->step2, sp->size2); + /* Install new params */ + sp->lyap = sp->lyap2; + sp->size = sp->size2; + sp->mid = sp->mid2; + sp->step = sp->step2; + memcpy(sp->par, sp->par2, sizeof(sp->par2)); + + /* If we're allowed to zoom out, do so now, so that we + get a look at the new attractor. */ + if(sp->chaseto == BEE && rotatep) { + sp->chaseto = ORBIT; + sp->chasetime = 100; + } + /* Reset initial conditions, so we don't get + misleading artifacts in the particle density. */ + restart_flow(mi); + } + } + } + + /* Reset segment buffers */ for (col = 0; col < MI_NPIXELS(mi); col++) sp->cnsegs[col] = 0; + MI_IS_DRAWN(mi) = True; + + /* Calculate circling POV [Chalky]*/ + sp->circle[1] = sp->circle[0]; + sp->circle[0].x = sp->size * 2 * sin(sp->count / 100.0) * + (-0.6 + 0.4 *cos(sp->count / 500.0)) + sp->mid.x; + sp->circle[0].y = sp->size * 2 * cos(sp->count / 100.0) * + (0.6 + 0.4 *cos(sp->count / 500.0)) + sp->mid.y; + sp->circle[0].z = sp->size * 2 * sin(sp->count / 421.0) + sp->mid.z; + + /* Timed chase instead of Chalkie's Bistable oscillator [TDA] */ + if(rotatep && ridep) { + if(sp->chaseto == BEE && NRAND(1000) == 0){ + sp->chaseto = ORBIT; + sp->chasetime = 100; + }else if(NRAND(4000) == 0){ + sp->chaseto = BEE; + sp->chasetime = 100; + } + } + + /* Set up orientation matrix */ + { + double x[3], p[3], x2=0, xp=0; + int j; + + /* Chasetime is here to guarantee the camera makes it all the + way to the target in a finite number of steps. */ + if(sp->chasetime > 1) + sp->chasetime--; + + if(sp->chaseto == BEE){ + /* Camera Head targets bee 0 */ + sp->cam[0].x += (X(0, 0) - sp->cam[0].x)/sp->chasetime; + sp->cam[0].y += (Y(0, 0) - sp->cam[0].y)/sp->chasetime; + sp->cam[0].z += (Z(0, 0) - sp->cam[0].z)/sp->chasetime; + + /* Camera Tail targets previous position of bee 0 */ + sp->cam[1].x += (X(1, 0) - sp->cam[1].x)/sp->chasetime; + sp->cam[1].y += (Y(1, 0) - sp->cam[1].y)/sp->chasetime; + sp->cam[1].z += (Z(1, 0) - sp->cam[1].z)/sp->chasetime; + + /* Camera Wing targets bee 1 */ + sp->cam[2].x += (X(0, 1) - sp->cam[2].x)/sp->chasetime; + sp->cam[2].y += (Y(0, 1) - sp->cam[2].y)/sp->chasetime; + sp->cam[2].z += (Z(0, 1) - sp->cam[2].z)/sp->chasetime; + } else { + /* Camera Head targets Orbiter */ + sp->cam[0].x += (sp->circle[0].x - sp->cam[0].x)/sp->chasetime; + sp->cam[0].y += (sp->circle[0].y - sp->cam[0].y)/sp->chasetime; + sp->cam[0].z += (sp->circle[0].z - sp->cam[0].z)/sp->chasetime; + + /* Camera Tail targets diametrically opposite the middle + of the bounding box from the Orbiter */ + sp->cam[1].x += + (2*sp->circle[0].x - sp->mid.x - sp->cam[1].x)/sp->chasetime; + sp->cam[1].y += + (2*sp->circle[0].y - sp->mid.y - sp->cam[1].y)/sp->chasetime; + sp->cam[1].z += + (2*sp->circle[0].z - sp->mid.z - sp->cam[1].z)/sp->chasetime; + /* Camera Wing targets previous position of Orbiter */ + sp->cam[2].x += (sp->circle[1].x - sp->cam[2].x)/sp->chasetime; + sp->cam[2].y += (sp->circle[1].y - sp->cam[2].y)/sp->chasetime; + sp->cam[2].z += (sp->circle[1].z - sp->cam[2].z)/sp->chasetime; + } + + /* Viewpoint from Tail of camera */ + sp->centre.x=sp->cam[1].x; + sp->centre.y=sp->cam[1].y; + sp->centre.z=sp->cam[1].z; + + /* forward vector */ + x[0] = sp->cam[0].x - sp->cam[1].x; + x[1] = sp->cam[0].y - sp->cam[1].y; + x[2] = sp->cam[0].z - sp->cam[1].z; + + /* side */ + p[0] = sp->cam[2].x - sp->cam[1].x; + p[1] = sp->cam[2].y - sp->cam[1].y; + p[2] = sp->cam[2].z - sp->cam[1].z; + + + /* So long as X and P don't collide, these can be used to form + three mutually othogonal axes: X, (X x P) x X and X x P. + After being normalised to unit length, these form the + Orientation Matrix. */ + + for(i=0; i<3; i++){ + x2+= x[i]*x[i]; /* X . X */ + xp+= x[i]*p[i]; /* X . P */ + M[0][i] = x[i]; /* X */ + } + + for(i=0; i<3; i++) /* (X x P) x X */ + M[1][i] = x2*p[i] - xp*x[i]; /* == (X . X) P - (X . P) X */ + + M[2][0] = x[1]*p[2] - x[2]*p[1]; /* X x P */ + M[2][1] = -x[0]*p[2] + x[2]*p[0]; + M[2][2] = x[0]*p[1] - x[1]*p[0]; + + /* normalise axes */ + for(j=0; j<3; j++){ + double A=0; + for(i=0; i<3; i++) A+=M[j][i]*M[j][i]; /* sum squares */ + A=sqrt(A); + if(A>0) + for(i=0; i<3; i++) M[j][i]/=A; + } + + if(sp->chaseto == BEE) { + X(0, 1)=X(0, 0)+M[1][0]*sp->step; /* adjust neighbour */ + Y(0, 1)=Y(0, 0)+M[1][1]*sp->step; + Z(0, 1)=Z(0, 0)+M[1][2]*sp->step; + } + } + + /* <=- Bounding Box -=> */ + if(boxp) { + for (b = 0; b < BOX_L; b++) { + + /* Chalky's clipping code, Only used for the box */ + /* clipping trails is slow and of little benefit. [TDA] */ + int p1 = lines[b][0]; + int p2 = lines[b][1]; + dvector A1, A2; + double x1=box[p1][0]* sp->size/2 + sp->mid.x - sp->centre.x; + double y1=box[p1][1]* sp->size/2 + sp->mid.y - sp->centre.y; + double z1=box[p1][2]* sp->size/2 + sp->mid.z - sp->centre.z; + double x2=box[p2][0]* sp->size/2 + sp->mid.x - sp->centre.x; + double y2=box[p2][1]* sp->size/2 + sp->mid.y - sp->centre.y; + double z2=box[p2][2]* sp->size/2 + sp->mid.z - sp->centre.z; + + A1.x=M[0][0]*x1 + M[0][1]*y1 + M[0][2]*z1; + A1.y=M[1][0]*x1 + M[1][1]*y1 + M[1][2]*z1; + A1.z=M[2][0]*x1 + M[2][1]*y1 + M[2][2]*z1 + EYEHEIGHT * sp->size; + A2.x=M[0][0]*x2 + M[0][1]*y2 + M[0][2]*z2; + A2.y=M[1][0]*x2 + M[1][1]*y2 + M[1][2]*z2; + A2.z=M[2][0]*x2 + M[2][1]*y2 + M[2][2]*z2 + EYEHEIGHT * sp->size; + + /* Clip in 3D before projecting down to 2D. A 2D clip + after projection wouldn't be able to handle lines that + cross x=0 */ + if (clip(1, 0, 0,-1, &A1, &A2) || /* Screen */ + clip(1, 2, 0, 0, &A1, &A2) || /* Left */ + clip(1,-2, 0, 0, &A1, &A2) || /* Right */ + clip(1,0, 2.0*MI_WIDTH(mi)/MI_HEIGHT(mi), 0, &A1, &A2)||/*UP*/ + clip(1,0,-2.0*MI_WIDTH(mi)/MI_HEIGHT(mi), 0, &A1, &A2))/*Down*/ + continue; + + /* Colour according to bee */ + col = b % (MI_NPIXELS(mi) - 1); + + sp->csegs[IX(col)].x1 = MI_WIDTH(mi)/2 + MI_WIDTH(mi) * A1.y/A1.x; + sp->csegs[IX(col)].y1 = MI_HEIGHT(mi)/2 + MI_WIDTH(mi) * A1.z/A1.x; + sp->csegs[IX(col)].x2 = MI_WIDTH(mi)/2 + MI_WIDTH(mi) * A2.y/A2.x; + sp->csegs[IX(col)].y2 = MI_HEIGHT(mi)/2 + MI_WIDTH(mi) * A2.z/A2.x; + sp->cnsegs[col]++; + } + } + /* <=- Bees -=> */ for (b = 0; b < sp->beecount; b++) { - /* Age the arrays. */ - X(1, b) = X(0, b); - Y(1, b) = Y(0, b); - Z(1, b) = Z(0, b); - - /* 2nd order Kunge Kutta */ - { - double k1x, k1y, k1z; - double k2x, k2y, k2z; - - sp->t[b] += sp->step; /* tick */ - sp->ODE(sp->par, &k1x, &k1y, &k1z, - X(1, b), Y(1, b), Z(1, b), sp->t[b]); - k1x *= sp->step; - k1y *= sp->step; - k1z *= sp->step; - sp->ODE(sp->par, &k2x, &k2y, &k2z, - X(1, b) + k1x, Y(1, b) + k1y, Z(1, b) + k1z, sp->t[b]); - k2x *= sp->step; - k2y *= sp->step; - k2z *= sp->step; - X(0, b) = X(1, b) + (k1x + k2x) / 2.0; - Y(0, b) = Y(1, b) + (k1y + k2y) / 2.0; - Z(0, b) = Z(1, b) + (k1z + k2z) / 2.0; + if(fabs(X(0, b)) > LOST_IN_SPACE || + fabs(Y(0, b)) > LOST_IN_SPACE || + fabs(Z(0, b)) > LOST_IN_SPACE){ + if(sp->chaseto == BEE && b == 0){ + /* Lost camera bee. Need to replace it since + rerunning init_flow could lose us a hard-won new + attractor. Try moving it very close to a random + other bee. This way we have a good chance of being + close to the attractor and not forming a false + artifact. If we've lost many bees this may need to + be repeated. */ + /* Don't worry about camera wingbee. It stays close + to the main camera bee no matter what happens. */ + int newb = 1 + NRAND(sp->beecount - 1); + X(0, 0) = X(0, newb) + 0.001; + Y(0, 0) = Y(0, newb); + Z(0, 0) = Z(0, newb); + if(MI_IS_VERBOSE(mi)) + fprintf(stdout, + "flow: resetting lost camera near bee %d\n", + newb); + } + continue; } - /* Fill the segment lists. */ + /* Age the tail. It's critical this be fast since + beecount*taillen can be large. */ + memmove(B(1, b), B(0, b), (sp->taillen - 1) * sizeof(dvector)); + Iterate(B(0,b), sp->ODE, sp->par, sp->step); - /* Tumble */ -#define DISPLAYX(A) (sp->width/2+sp->width/sp->size* \ - ((X((A),b)-sp->c.x)*cost \ - -(Y((A),b)-sp->c.y)*sint*cosp \ - +(Z((A),b)-sp->c.z)*sint*sinp)) -#define DISPLAYY(A) (sp->height/2-sp->height/sp->size* \ - ((X((A),b)-sp->c.x)*sint \ - +(Y((A),b)-sp->c.y)*cost*cosp \ - -(Z((A),b)-sp->c.z)*cost*sinp)) + /* Don't show wingbee since he's not quite in the flow. */ + if(sp->chaseto == BEE && b == 1) continue; /* Colour according to bee */ col = b % (MI_NPIXELS(mi) - 1); - - ix = col * sp->beecount + sp->cnsegs[col]; - sp->csegs[ix].x1 = DISPLAYX(0); - sp->csegs[ix].y1 = DISPLAYY(0); - sp->csegs[ix].x2 = DISPLAYX(1); - sp->csegs[ix].y2 = DISPLAYY(1); - sp->cnsegs[col]++; + + /* Fill the segment lists. */ + + begin = 0; /* begin new trail */ + end = MIN(sp->taillen, sp->count); /* short trails at first */ + for(i=0; i < end; i++){ + double x = X(i,b)-sp->centre.x; + double y = Y(i,b)*(sp->yperiod < 0? (sp->size/sp->yperiod) :1) + -sp->centre.y; + double z = Z(i,b)-sp->centre.z; + double XM=M[0][0]*x + M[0][1]*y + M[0][2]*z; + double YM=M[1][0]*x + M[1][1]*y + M[1][2]*z; + double ZM=M[2][0]*x + M[2][1]*y + M[2][2]*z + EYEHEIGHT * sp->size; + short absx, absy; + + swarm++; /* count the remaining bees */ + if(sp->yperiod > 0 && Y(i,b) > sp->yperiod){ + int j; + Y(i,b) -= sp->yperiod; + /* hide tail to prevent streaks in Y. Streaks in X,Z + are ok, they help to outline the Poincare' + slice. */ + for(j = i; j < end; j++) Y(j,b) = Y(i,b); + begin = i + 1; + break; + } + + if(XM <= 0){ /* off screen - new trail */ + begin = i + 1; + continue; + } + absx = MI_WIDTH(mi)/2 + MI_WIDTH(mi) * YM/XM; + absy = MI_HEIGHT(mi)/2 + MI_WIDTH(mi) * ZM/XM; + /* Performance bottleneck */ + if(absx <= 0 || absx >= MI_WIDTH(mi) || + absy <= 0 || absy >= MI_HEIGHT(mi)) { + /* off screen - new trail */ + begin = i + 1; + continue; + } + if(i > begin) { /* complete previous segment */ + sp->csegs[IX(col)].x2 = absx; + sp->csegs[IX(col)].y2 = absy; + sp->cnsegs[col]++; + } + + if(i < end -1){ /* start new segment */ + sp->csegs[IX(col)].x1 = absx; + sp->csegs[IX(col)].y1 = absy; + } + } } - if (sp->count) { - XSetForeground(display, gc, MI_BLACK_PIXEL(mi)); - XDrawSegments(display, window, gc, sp->old_segs, sp->beecount); + + /* Erase */ + XSetForeground(MI_DISPLAY(mi), MI_GC(mi), MI_BLACK_PIXEL(mi)); + if (dbufp) { /* In Double Buffer case, prepare off-screen copy */ + /* For slow systems, this can be the single biggest bottleneck + in the program. These systems may be better of not using + the double buffer. */ + XFillRectangle(MI_DISPLAY(mi), sp->buffer, MI_GC(mi), 0, 0, + MI_WIDTH(mi), MI_HEIGHT(mi)); + } else { /* Otherwise, erase previous segment list directly */ + XDrawSegments(MI_DISPLAY(mi), sp->buffer, MI_GC(mi), + sp->old_segs, sp->nold_segs); } - XSetForeground(display, gc, MI_WHITE_PIXEL(mi)); - if (MI_NPIXELS(mi) > 2) { - for (col = 0; col < MI_NPIXELS(mi); col++) { + + /* Render */ + if (MI_NPIXELS(mi) > 2){ /* colour */ + int mn = 0; + for (col = 0; col < MI_NPIXELS(mi) - 1; col++) if (sp->cnsegs[col] > 0) { - XSetForeground(display, gc, MI_PIXEL(mi, col)); - XDrawSegments(display, window, gc, - sp->csegs + col * sp->beecount, - sp->cnsegs[col]); + if(sp->cnsegs[col] > mn) mn = sp->cnsegs[col]; + XSetForeground(MI_DISPLAY(mi), MI_GC(mi), MI_PIXEL(mi, col+1)); + /* This is usually the biggest bottleneck on most + systems. The maths load is insignificant compared + to this. */ + XDrawSegments(MI_DISPLAY(mi), sp->buffer, MI_GC(mi), + sp->csegs + col * segindex, sp->cnsegs[col]); } - } - } else { - /* mono */ - XSetForeground(display, gc, MI_PIXEL(mi, 1)); - XDrawSegments(display, window, gc, - sp->csegs + col * sp->beecount, - sp->cnsegs[col]); + } else { /* mono handled seperately since xlockmore uses '1' for + mono white! */ + XSetForeground(MI_DISPLAY(mi), MI_GC(mi), MI_WHITE_PIXEL(mi)); + XDrawSegments(MI_DISPLAY(mi), sp->buffer, MI_GC(mi), + sp->csegs, sp->cnsegs[0]); } - for (col = 0, c = 0; col < MI_NPIXELS(mi); col++) - for (b = 0; b < sp->cnsegs[col]; b++) { - XSegment s = (sp->csegs + col * sp->beecount)[b]; - - sp->old_segs[c].x1 = s.x1; - sp->old_segs[c].y1 = s.y1; - sp->old_segs[c].x2 = s.x2; - sp->old_segs[c].y2 = s.y2; - c++; + if (dbufp) { /* In Double Buffer case, this updates the screen */ + XCopyArea(MI_DISPLAY(mi), sp->buffer, MI_WINDOW(mi), MI_GC(mi), 0, 0, + MI_WIDTH(mi), MI_HEIGHT(mi), 0, 0); + } else { /* Otherwise, screen is already updated. Copy segments + to erase-list to be erased directly next time. */ + int c = 0; + for (col = 0; col < MI_NPIXELS(mi) - 1; col++) { + memcpy(sp->old_segs + c, sp->csegs + col * segindex, + sp->cnsegs[col] * sizeof(XSegment)); + c += sp->cnsegs[col]; } - if (++sp->count > MI_CYCLES(mi)) { + sp->nold_segs = c; + } + + if(sp->count > 1 && swarm == 0) { /* all gone */ + if(MI_IS_VERBOSE(mi)) + fprintf(stdout, "flow: all gone at %d\n", sp->count); + init_flow(mi); + } + + if(sp->count++ > MI_CYCLES(mi)){ /* Time's up. If we haven't + found anything new by now we + should pick a new standard + flow */ init_flow(mi); } } -void -release_flow(ModeInfo * mi) +ENTRYPOINT void +release_flow (ModeInfo * mi) { if (flows != NULL) { int screen; - for (screen = 0; screen < MI_NUM_SCREENS(mi); screen++) { - flowstruct *sp = &flows[screen]; - - if (sp->csegs != NULL) - (void) free((void *) sp->csegs); - if (sp->cnsegs != NULL) - (void) free((void *) sp->cnsegs); - if (sp->old_segs != NULL) - (void) free((void *) sp->old_segs); - if (sp->p != NULL) - (void) free((void *) sp->p); - if (sp->t != NULL) - (void) free((void *) sp->t); - } - (void) free((void *) flows); - flows = NULL; + for (screen = 0; screen < MI_NUM_SCREENS(mi); screen++) + free_flow(&flows[screen]); + free(flows); + flows = (flowstruct *) NULL; } } -void -refresh_flow(ModeInfo * mi) +ENTRYPOINT void +refresh_flow (ModeInfo * mi) { - MI_CLEARWINDOW(mi); + if(!dbufp) MI_CLEARWINDOW(mi); } + +XSCREENSAVER_MODULE ("Flow", flow) + +#endif /* MODE_flow */