/* This file contains two 3 dimensional orbit-type fractal generators - IFS and LORENZ3D, along with code to generate red/blue 3D images. Tim Wegner */ #include #include #include #include #include "fractint.h" #include "fractype.h" int realtime; extern int overflow; extern int soundflag; extern int basehertz; extern int solidguessing; extern int fractype; extern int glassestype; extern int whichimage; extern int init3d[]; extern char floatflag; extern VECTOR view; extern int xxadjust, yyadjust; extern int xxadjust1, yyadjust1; extern int xshift,yshift; extern int xshift1,yshift1; extern void (*plot)(); extern void (*standardplot)(); extern int debugflag; /* for debugging purposes */ extern int xdots, ydots; /* coordinates of dots on the screen */ extern int maxit; /* try this many iterations */ extern double param[]; extern double xxmin,xxmax,yymin,yymax,xx3rd,yy3rd; /* selected screen corners */ extern char far plasmamessage[]; extern int diskvideo; /* for disk-video klooges */ extern int bitshift; /* bit shift for fudge */ extern long fudge; /* fudge factor (2**n) */ extern int colors; /* maximum colors available */ extern int display3d; static int t; static long l_dx,l_dy,l_dz,l_dt,l_a,l_b,l_c,l_d; static long l_adt,l_bdt,l_cdt,l_xdt,l_ydt; static long l_initx,l_inity,l_initz; static long initorbitlong[3]; static double dx,dy,dz,dt,a,b,c,d; static double adt,bdt,cdt,xdt,ydt; static double initx,inity,initz; static double initorbit[3]; extern int inside; extern int alloc_resume(int,int); extern int start_resume(); extern void end_resume(); extern int put_resume(int len, ...); extern int get_resume(int len, ...); extern int calc_status, resuming; /* these are potential user parameters */ int connect = 1; /* flag to connect points with a line */ int waste = 100; /* waste this many points before plotting */ int projection = 2; /* projection plane - default is to plot x-y */ /******************************************************************/ /* zoom box conversion functions */ /******************************************************************/ double determinant(mat) /* determinant of 3x3 matrix */ double mat[3][3]; { /* calculate determinant of 3x3 matrix */ return(mat[0][0]*mat[1][1]*mat[2][2] + mat[0][2]*mat[1][0]*mat[2][1] + mat[0][1]*mat[1][2]*mat[2][0] - mat[2][0]*mat[1][1]*mat[0][2] - mat[1][0]*mat[0][1]*mat[2][2] - mat[0][0]*mat[1][2]*mat[2][1]); } solve3x3(mat,vec,ans) /* solve 3x3 inhomogeneous linear equations */ double mat[3][3], vec[3], ans[3]; { /* solve 3x3 linear equation [mat][ans] = [vec] */ double denom; double tmp[3][3]; int i; denom = determinant(mat); if(fabs(denom) < DBL_EPSILON) /* test if can solve */ return(-1); memcpy(tmp,mat,sizeof(double)*9); for(i=0;i<3;i++) { tmp[0][i] = vec[0]; tmp[1][i] = vec[1]; tmp[2][i] = vec[2]; ans[i] = determinant(tmp)/denom; tmp[0][i] = mat[0][i]; tmp[1][i] = mat[1][i]; tmp[2][i] = mat[2][i]; } return(0); } /* Conversion of complex plane to screen coordinates for rotating zoom box. Assume there is an affine transformation mapping complex zoom parallelogram to rectangular screen. We know this map must map parallelogram corners to screen corners, so we have following equations: a*xxmin+b*yymax+e == 0 (upper left) c*xxmin+d*yymax+f == 0 a*xx3rd+b*yy3rd+e == 0 (lower left) c*xx3rd+d*yy3rd+f == ydots-1 a*xxmax+b*yymin+e == xdots-1 (lower right) c*xxmax+d*yymin+f == ydots-1 First we must solve for a,b,c,d,e,f - (which we do once per image), then we just apply the transformation to each orbit value. */ struct affine { /* weird order so a,b,e and c,d,f are vectors */ double a; double b; double e; double c; double d; double f; }; setup_convert_to_screen(struct affine *scrn_cnvt) { /* we do this twice - rather than having six equations with six unknowns, everything partitions to two sets of three equations with three unknowns. Nice, because who wants to calculate a 6x6 determinant?? */ double mat[3][3]; double vec[3]; /* first these equations - solve for a,b,e a*xxmin+b*yymax+e == 0 (upper left) a*xx3rd+b*yy3rd+e == 0 (lower left) a*xxmax+b*yymin+e == xdots-1 (lower right) */ mat[0][0] = xxmin; mat[0][1] = yymax; mat[0][2] = 1.0; mat[1][0] = xx3rd; mat[1][1] = yy3rd; mat[1][2] = 1.0; mat[2][0] = xxmax; mat[2][1] = yymin; mat[2][2] = 1.0; vec[0] = 0.0; vec[1] = 0.0; vec[2] = (double)(xdots-1); if(solve3x3(mat,vec, &(scrn_cnvt->a))) return(-1); /* now solve these: c*xxmin+d*yymax+f == 0 c*xx3rd+d*yy3rd+f == ydots-1 c*xxmax+d*yymin+f == ydots-1 (mat[][] has not changed - only vec[]) */ vec[0] = 0.0; vec[1] = (double)(ydots-1); vec[2] = (double)(ydots-1); if(solve3x3(mat,vec, &scrn_cnvt->c)) return(-1); return(0); } /******************************************************************/ /* setup functions - put in fractalspecific[fractype].per_image */ /******************************************************************/ double orbit; long l_orbit; extern double sinx,cosx; long l_sinx,l_cosx; orbit3dlongsetup() { connect = 1; waste = 100; projection = 2; if(fractype==LHENON || fractype==KAM || fractype==KAM3D) connect=0; if(fractype==LROSSLER) waste = 500; if(fractype==LLORENZ) projection = 1; initorbitlong[0] = fudge; /* initial conditions */ initorbitlong[1] = fudge; initorbitlong[2] = fudge; if(fractype==LHENON) { l_a = param[0]*fudge; l_b = param[1]*fudge; l_c = param[2]*fudge; l_d = param[3]*fudge; } else if(fractype==KAM || fractype==KAM3D) { a = param[0]; /* angle */ if(param[1] <= 0.0) param[1] = .01; l_b = param[1]*fudge; /* stepsize */ l_c = param[2]*fudge; /* stop */ t = l_d = param[3]; /* points per orbit */ l_sinx = sin(a)*fudge; l_cosx = cos(a)*fudge; l_orbit = 0; initorbitlong[0] = initorbitlong[1] = initorbitlong[2] = 0; } else { l_dt = param[0]*fudge; l_a = param[1]*fudge; l_b = param[2]*fudge; l_c = param[3]*fudge; } /* precalculations for speed */ l_adt = multiply(l_a,l_dt,bitshift); l_bdt = multiply(l_b,l_dt,bitshift); l_cdt = multiply(l_c,l_dt,bitshift); solidguessing = 0; return(1); } orbit3dfloatsetup() { connect = 1; waste = 100; projection = 2; if(fractype==FPHENON || fractype==FPPICKOVER || fractype==FPGINGERBREAD || fractype == KAMFP || fractype == KAM3DFP) connect=0; if(fractype==FPROSSLER) waste = 500; if(fractype==FPLORENZ) projection = 1; /* plot x and z */ initorbit[0] = 1; /* initial conditions */ initorbit[1] = 1; initorbit[2] = 1; if(fractype==FPGINGERBREAD) { initorbit[0] = -.1; /* initial conditions */ initorbit[1] = 0; } if(fractype==FPHENON || fractype==FPPICKOVER) { a = param[0]; b = param[1]; c = param[2]; d = param[3]; } else if(fractype==KAMFP || fractype==KAM3DFP) { a = param[0]; /* angle */ if(param[1] <= 0.0) param[1] = .01; b = param[1]; /* stepsize */ c = param[2]; /* stop */ t = l_d = param[3]; /* points per orbit */ sinx = sin(a); cosx = cos(a); orbit = 0; initorbit[0] = initorbit[1] = initorbit[2] = 0; } else { dt = param[0]; a = param[1]; b = param[2]; c = param[3]; } /* precalculations for speed */ adt = a*dt; bdt = b*dt; cdt = c*dt; solidguessing = 0; return(1); } /******************************************************************/ /* orbit functions - put in fractalspecific[fractype].orbitcalc */ /******************************************************************/ lorenz3dlongorbit(long *l_x, long *l_y, long *l_z) { l_xdt = multiply(*l_x,l_dt,bitshift); l_ydt = multiply(*l_y,l_dt,bitshift); l_dx = -multiply(l_adt,*l_x,bitshift) + multiply(l_adt,*l_y,bitshift); l_dy = multiply(l_bdt,*l_x,bitshift) -l_ydt -multiply(*l_z,l_xdt,bitshift); l_dz = -multiply(l_cdt,*l_z,bitshift) + multiply(*l_x,l_ydt,bitshift); *l_x += l_dx; *l_y += l_dy; *l_z += l_dz; return(0); } lorenz3dfloatorbit(double *x, double *y, double *z) { xdt = (*x)*dt; ydt = (*y)*dt; dx = -adt*(*x) + adt*(*y); dy = bdt*(*x) - ydt - (*z)*xdt; dz = -cdt*(*z) + (*x)*ydt; *x += dx; *y += dy; *z += dz; return(0); } henonfloatorbit(double *x, double *y, double *z) { double newx,newy; newx = 1 + *y - a*(*x)*(*x); newy = b*(*x); *x = newx; *y = newy; return(0); } henonlongorbit(long *l_x, long *l_y, long *l_z) { long newx,newy; newx = multiply(*l_x,*l_x,bitshift); newx = multiply(newx,l_a,bitshift); newx = fudge + *l_y - newx; newy = multiply(l_b,*l_x,bitshift); *l_x = newx; *l_y = newy; return(0); } rosslerfloatorbit(double *x, double *y, double *z) { xdt = (*x)*dt; ydt = (*y)*dt; dx = -ydt - (*z)*dt; dy = xdt + (*y)*adt; dz = bdt + (*z)*xdt - (*z)*cdt; *x += dx; *y += dy; *z += dz; return(0); } pickoverfloatorbit(double *x, double *y, double *z) { double newx,newy,newz; newx = sin(a*(*y)) - (*z)*cos(b*(*x)); newy = (*z)*sin(c*(*x)) - cos(d*(*y)); newz = sin(*x); *x = newx; *y = newy; *z = newz; return(0); } /* page 149 "Science of Fractal Images" */ gingerbreadfloatorbit(double *x, double *y, double *z) { double newx; newx = 1 - (*y) + fabs(*x); *y = *x; *x = newx; return(0); } rosslerlongorbit(long *l_x, long *l_y, long *l_z) { l_xdt = multiply(*l_x,l_dt,bitshift); l_ydt = multiply(*l_y,l_dt,bitshift); l_dx = -l_ydt - multiply(*l_z,l_dt,bitshift); l_dy = l_xdt + multiply(*l_y,l_adt,bitshift); l_dz = l_bdt + multiply(*l_z,l_xdt,bitshift) - multiply(*l_z,l_cdt,bitshift); *l_x += l_dx; *l_y += l_dy; *l_z += l_dz; return(0); } /* OSTEP = Orbit Step (and inner orbit value) */ /* NTURNS = Outside Orbit */ /* TURN2 = Points per orbit */ /* a = Angle */ kamtorusfloatorbit(double *r, double *s, double *z) { double srr; if(t++ >= l_d) { orbit += b; (*r) = (*s) = orbit/3; t = 0; *z = orbit; if(orbit > c) return(1); } srr = (*s)-(*r)*(*r); (*s)=(*r)*sinx+srr*cosx; (*r)=(*r)*cosx-srr*sinx; return(0); } kamtoruslongorbit(long *r, long *s, long *z) { long srr; if(t++ >= l_d) { l_orbit += l_b; (*r) = (*s) = l_orbit/3; t = 0; *z = l_orbit; if(l_orbit > l_c) return(1); } srr = (*s)-multiply((*r),(*r),bitshift); (*s)=multiply((*r),l_sinx,bitshift)+multiply(srr,l_cosx,bitshift); (*r)=multiply((*r),l_cosx,bitshift)-multiply(srr,l_sinx,bitshift); return(0); } /**********************************************************************/ /* Main fractal engines - put in fractalspecific[fractype].calctype */ /**********************************************************************/ orbit2dfloat() { double *soundvar; double x,y,z; int color,col,row; int count; int oldrow, oldcol; double *p0,*p1,*p2; struct affine cvt; /* setup affine screen coord conversion */ setup_convert_to_screen(&cvt); /* set up projection scheme */ if(projection==0) { p0 = &z; p1 = &x; p2 = &y; } else if(projection==1) { p0 = &x; p1 = &z; p2 = &y; } else if(projection==2) { p0 = &x; p1 = &y; p2 = &z; } if(soundflag==1) soundvar = &x; else if(soundflag==2) soundvar = &y; else if(soundflag==3) soundvar = &z; count = 0; if(inside > 0) color = inside; if(color >= colors) color = 1; oldcol = oldrow = -1; x = initorbit[0]; y = initorbit[1]; z = initorbit[2]; if (resuming) { start_resume(); get_resume(sizeof(count),&count,sizeof(color),&color, sizeof(oldrow),&oldrow,sizeof(oldcol),&oldcol, sizeof(x),&x,sizeof(y),&y,sizeof(z),&z, sizeof(t),&t,sizeof(orbit),&orbit, 0); end_resume(); } while(1) { if(check_key()) { nosnd(); alloc_resume(100,1); put_resume(sizeof(count),&count,sizeof(color),&color, sizeof(oldrow),&oldrow,sizeof(oldcol),&oldcol, sizeof(x),&x,sizeof(y),&y,sizeof(z),&z, sizeof(t),&t,sizeof(orbit),&orbit, 0); return(-1); } if (++count > 1000) { /* time to switch colors? */ count = 0; if (++color >= colors) /* another color to switch to? */ color = 1; /* (don't use the background color) */ } col = cvt.a*x + cvt.b*y + cvt.e; row = cvt.c*x + cvt.d*y + cvt.f; if ( col >= 0 && col < xdots && row >= 0 && row < ydots ) { if (soundflag > 0) snd((int)(*soundvar*100+basehertz)); if(oldcol != -1 && connect) draw_line(col,row,oldcol,oldrow,color&(colors-1)); else (*plot)(col,row,color&(colors-1)); oldcol = col; oldrow = row; } else oldrow = oldcol = -1; if(fractalspecific[fractype].orbitcalc(p0, p1, p2)) break; } return(0); } orbit2dlong() { long a,b,c,d,e,f; long *soundvar; long x,y,z; int color,col,row; int count; int oldrow, oldcol; long *p0,*p1,*p2; struct affine cvt; /* setup affine screen coord conversion */ setup_convert_to_screen(&cvt); a = cvt.a*fudge; b = cvt.b*fudge; c = cvt.c*fudge; d = cvt.d*fudge; e = cvt.e*fudge; f = cvt.f*fudge; /* set up projection scheme */ if(projection==0) { p0 = &z; p1 = &x; p2 = &y; } else if(projection==1) { p0 = &x; p1 = &z; p2 = &y; } else if(projection==2) { p0 = &x; p1 = &y; p2 = &z; } if(soundflag==1) soundvar = &x; else if(soundflag==2) soundvar = &y; else if(soundflag==3) soundvar = &z; count = 0; if(inside > 0) color = inside; if(color >= colors) color = 1; oldcol = oldrow = -1; x = initorbitlong[0]; y = initorbitlong[1]; z = initorbitlong[2]; if (resuming) { start_resume(); get_resume(sizeof(count),&count,sizeof(color),&color, sizeof(oldrow),&oldrow,sizeof(oldcol),&oldcol, sizeof(x),&x,sizeof(y),&y,sizeof(z),&z, sizeof(t),&t,sizeof(l_orbit),&l_orbit, 0); end_resume(); } while(1) { if(check_key()) { nosnd(); alloc_resume(100,1); put_resume(sizeof(count),&count,sizeof(color),&color, sizeof(oldrow),&oldrow,sizeof(oldcol),&oldcol, sizeof(x),&x,sizeof(y),&y,sizeof(z),&z, sizeof(t),&t,sizeof(l_orbit),&l_orbit, 0); return(-1); } if (++count > 1000) { /* time to switch colors? */ count = 0; if (++color >= colors) /* another color to switch to? */ color = 1; /* (don't use the background color) */ } col = (multiply(a,x,bitshift) + multiply(b,y,bitshift) + e) >> bitshift; row = (multiply(c,x,bitshift) + multiply(d,y,bitshift) + f) >> bitshift; if ( col >= 0 && col < xdots && row >= 0 && row < ydots ) { if (soundflag > 0) { double yy; yy = *soundvar; yy = yy/fudge; snd((int)(yy*100+basehertz)); } if(oldcol != -1 && connect) draw_line(col,row,oldcol,oldrow,color&(colors-1)); else (*plot)(col,row,color&(colors-1)); oldcol = col; oldrow = row; } else oldrow = oldcol = -1; /* Calculate the next point */ if(fractalspecific[fractype].orbitcalc(p0, p1, p2)) break; } return(0); } orbit3dlongcalc() { long a,b,c,d,e,f; unsigned count; int oldcol,oldrow; int oldcol1,oldrow1; double tmpx, tmpy, tmpz; long iview[3]; /* perspective viewer's coordinates */ long tmp; long maxvals[3]; long minvals[3]; unsigned long maxct,ct; register int col; register int row; register int color; int i,j,k; /* 3D viewing stuff */ MATRIX doublemat; /* transformation matrix */ MATRIX doublemat1; /* transformation matrix */ long longmat[4][4]; /* long version of matrix */ long longmat1[4][4]; /* long version of matrix */ long orbit[3]; /* interated function orbit value */ long viewvect[3]; /* orbit transformed for viewing */ long viewvect1[3]; /* orbit transformed for viewing */ struct affine cvt; /* setup affine screen coord conversion */ setup_convert_to_screen(&cvt); a = cvt.a*fudge; b = cvt.b*fudge; c = cvt.c*fudge; d = cvt.d*fudge; e = cvt.e*fudge; f = cvt.f*fudge; oldcol1 = oldrow1 = oldcol = oldrow = -1; color = 2; if(color >= colors) color = 1; orbit[0] = initorbitlong[0]; orbit[1] = initorbitlong[1]; orbit[2] = initorbitlong[2]; for(i=0;i<3;i++) { minvals[i] = 1L << 30; maxvals[i] = -minvals[i]; } setupmatrix(doublemat); if(realtime) setupmatrix(doublemat1); /* copy xform matrix to long for for fixed point math */ for (i = 0; i < 4; i++) for (j = 0; j < 4; j++) { longmat[i][j] = doublemat[i][j] * fudge; if(realtime) longmat1[i][j] = doublemat1[i][j] * fudge; } if(diskvideo) /* this would KILL a disk drive! */ { setvideomode(3,0,0,0); buzzer(2); helpmessage(plasmamessage); return(-1); } /* make maxct a function of screen size */ maxct = maxit*40L; count = ct = 0L; while(ct++ < maxct) /* loop until keypress or maxit */ { /* calc goes here */ if (++count > 1000) { /* time to switch colors? */ count = 0; if (++color >= colors) /* another color to switch to? */ color = 1; /* (don't use the background color) */ } if(check_key()) { nosnd(); return(-1); } fractalspecific[fractype].orbitcalc(&orbit[0],&orbit[1],&orbit[2]); /* 3D VIEWING TRANSFORM */ longvmult(orbit,longmat,viewvect, bitshift); if(realtime) longvmult(orbit,longmat1,viewvect1, bitshift); if(ct <= waste) /* waste this many points to find minz and maxz */ { /* find minz and maxz */ for(i=0;i<3;i++) if ((tmp = viewvect[i]) < minvals[i]) minvals[i] = tmp; else if (tmp > maxvals[i]) maxvals[i] = tmp; if(ct == waste) { iview[0] = iview[1] = 0L; /* center viewer on origin */ /* z value of user's eye - should be more negative than extreme negative part of image */ iview[2] = (long)((minvals[2]-maxvals[2])*(double)ZVIEWER/100.0); /* center image on origin */ tmpx = (-minvals[0]-maxvals[0])/(2.0*fudge); /* center x */ tmpy = (-minvals[1]-maxvals[1])/(2.0*fudge); /* center y */ /* apply perspective shift */ tmpx += ((double)xshift*(xxmax-xxmin))/(xdots) ; tmpy += ((double)yshift*(yymax-yymin))/(ydots); tmpz = -((double)maxvals[2]); tmpz /= fudge; trans(tmpx,tmpy,tmpz,doublemat); if(realtime) { /* center image on origin */ tmpx = (-minvals[0]-maxvals[0])/(2.0*fudge); /* center x */ tmpy = (-minvals[1]-maxvals[1])/(2.0*fudge); /* center y */ tmpx += ((double)xshift1*(xxmax-xxmin))/(xdots); tmpy += ((double)yshift1*(yymax-yymin))/(ydots); tmpz = -((double)maxvals[2]); tmpz /= fudge; trans(tmpx,tmpy,tmpz,doublemat1); } for(i=0;i<3;i++) { view[i] = iview[i]; view[i] /= fudge; } /* copy xform matrix to long for for fixed point math */ for (i = 0; i < 4; i++) for (j = 0; j < 4; j++) { longmat[i][j] = doublemat[i][j] * fudge; if(realtime) longmat1[i][j] = doublemat1[i][j] * fudge; } } } if(ct > waste) { /* apply perspective if requested */ if(ZVIEWER) { if(debugflag==22 || ZVIEWER < 100) /* use float for small persp */ { /* use float perspective calc */ VECTOR tmpv; for(i=0;i<3;i++) { tmpv[i] = viewvect[i]; tmpv[i] /= fudge; } perspective(tmpv); for(i=0;i<3;i++) viewvect[i] = tmpv[i]*fudge; if(realtime) { for(i=0;i<3;i++) { tmpv[i] = viewvect1[i]; tmpv[i] /= fudge; } perspective(tmpv); for(i=0;i<3;i++) viewvect1[i] = tmpv[i]*fudge; } } else { longpersp(viewvect,iview,bitshift); if(realtime) longpersp(viewvect1,iview,bitshift); } } if(realtime) whichimage=1; /* plot if inside window */ col = (multiply(a,viewvect[0],bitshift)+ multiply(b,viewvect[1],bitshift)+e) >> bitshift; row = (multiply(c,viewvect[0],bitshift)+ multiply(d,viewvect[1],bitshift)+f) >> bitshift; col += xxadjust; row += yyadjust; if ( 0 <= col && col < xdots && 0 <= row && row < ydots) { if (soundflag > 0) { double yy; yy = viewvect[soundflag-1]; yy = yy/fudge; snd((int)(yy*100+basehertz)); } if(oldcol != -1 && connect) draw_line(col,row,oldcol,oldrow,color&(colors-1)); else (*plot)(col,row,color&(colors-1)); oldcol = col; oldrow = row; } else oldrow = oldcol = -1; if(realtime) { whichimage=2; /* plot if inside window */ col = (multiply(a,viewvect1[0],bitshift)+ multiply(b,viewvect1[1],bitshift)+e) >> bitshift; row = (multiply(c,viewvect1[0],bitshift)+ multiply(d,viewvect1[1],bitshift)+f) >> bitshift; col += xxadjust1; row += yyadjust1; if ( 0 <= col && col < xdots && 0 <= row && row < ydots) { if(oldcol1 != -1 && connect) draw_line(col,row,oldcol1,oldrow1,color&(colors-1)); else (*plot)(col,row,color&(colors-1)); oldcol1 = col; oldrow1 = row; } else oldrow1 = oldcol1 = -1; } } } return(0); } orbit3dfloatcalc() { unsigned count; int oldcol,oldrow; int oldcol1,oldrow1; double tmpx, tmpy, tmpz; extern VECTOR view; double tmp; double maxvals[3]; double minvals[3]; extern int init3d[]; unsigned long maxct,ct; register int col; register int row; register int color; int i,j,k; /* 3D viewing stuff */ MATRIX doublemat; /* transformation matrix */ MATRIX doublemat1; /* transformation matrix */ double orbit[3]; /* interated function orbit value */ double viewvect[3]; /* orbit transformed for viewing */ double viewvect1[3]; /* orbit transformed for viewing */ struct affine cvt; /* setup affine screen coord conversion */ setup_convert_to_screen(&cvt); oldcol = oldrow = -1; oldcol1 = oldrow1 = -1; color = 2; if(color >= colors) color = 1; orbit[0] = initorbit[0]; orbit[1] = initorbit[1]; orbit[2] = initorbit[2]; for(i=0;i<3;i++) { minvals[i] = 100000.0; /* impossible value */ maxvals[i] = -100000.0; } setupmatrix(doublemat); if(realtime) setupmatrix(doublemat1); if(diskvideo) /* this would KILL a disk drive! */ { setvideomode(3,0,0,0); buzzer(2); helpmessage(plasmamessage); return(-1); } maxct = maxit*40L; count = ct = 0L; while(ct++ < maxct) /* loop until keypress or maxit */ { /* calc goes here */ if (++count > 1000) { /* time to switch colors? */ count = 0; if (++color >= colors) /* another color to switch to? */ color = 1; /* (don't use the background color) */ } if(check_key()) { nosnd(); return(-1); } fractalspecific[fractype].orbitcalc(&orbit[0],&orbit[1],&orbit[2]); /* 3D VIEWING TRANSFORM */ vmult(orbit,doublemat,viewvect ); if(realtime) vmult(orbit,doublemat1,viewvect1); if(ct <= waste) /* waste this many points to find minz and maxz */ { /* find minz and maxz */ for(i=0;i<3;i++) if ((tmp = viewvect[i]) < minvals[i]) minvals[i] = tmp; else if (tmp > maxvals[i]) maxvals[i] = tmp; if(ct == waste) { view[0] = view[1] = 0; /* center on origin */ /* z value of user's eye - should be more negative than extreme negative part of image */ view[2] = (minvals[2]-maxvals[2])*(double)ZVIEWER/100.0; /* center image on origin */ tmpx = (-minvals[0]-maxvals[0])/(2.0); /* center x */ tmpy = (-minvals[1]-maxvals[1])/(2.0); /* center y */ /* apply perspective shift */ tmpx += ((double)xshift*(xxmax-xxmin))/(xdots) ; tmpy += ((double)yshift*(yymax-yymin))/(ydots); tmpz = -((double)maxvals[2]); trans(tmpx,tmpy,tmpz,doublemat); if(realtime) { /* center image on origin */ tmpx = (-minvals[0]-maxvals[0])/(2.0); /* center x */ tmpy = (-minvals[1]-maxvals[1])/(2.0); /* center y */ tmpx += ((double)xshift1*(xxmax-xxmin))/(xdots); tmpy += ((double)yshift1*(yymax-yymin))/(ydots); tmpz = -((double)maxvals[2]); trans(tmpx,tmpy,tmpz,doublemat1); } } } if(ct > waste) { /* apply perspective if requested */ if(ZVIEWER) { perspective(viewvect); if(realtime) perspective(viewvect1); } if(realtime) whichimage=1; /* plot if inside window */ col = cvt.a*viewvect[0] + cvt.b*viewvect[1] + cvt.e + xxadjust; row = cvt.c*viewvect[0] + cvt.d*viewvect[1] + cvt.f + yyadjust; if ( 0 <= col && col < xdots && 0 <= row && row < ydots) { if (soundflag > 0) snd((int)(viewvect[soundflag-1]*100+basehertz)); if(oldcol != -1 && connect) draw_line(col,row,oldcol,oldrow,color&(colors-1)); else (*plot)(col,row,color&(colors-1)); oldcol = col; oldrow = row; } else oldrow = oldcol = -1; if(realtime) { whichimage=2; /* plot if inside window */ col = cvt.a*viewvect1[0] + cvt.b*viewvect1[1] + cvt.e + xxadjust1; row = cvt.c*viewvect1[0] + cvt.d*viewvect1[1] + cvt.f + yyadjust1; if ( 0 <= col && col < xdots && 0 <= row && row < ydots) { if(oldcol1 != -1 && connect) draw_line(col,row,oldcol1,oldrow1,color&(colors-1)); else (*plot)(col,row,color&(colors-1)); oldcol1 = col; oldrow1 = row; } else oldrow1 = oldcol1 = -1; } } } return(0); } /* this function's only purpose is to manage funnyglasses related */ /* stuff so the code is not duplicated for ifs3d() and lorenz3d() */ funny_glasses_call(int (*calc)()) { int status; status = 0; if(glassestype) whichimage = 1; else whichimage = 0; plot_setup(); plot = standardplot; status = calc(); if(realtime && glassestype != 3) { realtime = 0; return(status); } if(glassestype && status == 0) { if(glassestype==3) /* photographer's mode */ { setfortext(); printf("First image (left eye) is ready - hit any key to see it\n"); printf("Then hit any key again to create second image\n"); getch(); setforgraphics(); getch(); /* is there a better way to clear the screen in graphics mode? */ setvideomode(videoentry.videomodeax, videoentry.videomodebx, videoentry.videomodecx, videoentry.videomodedx); } whichimage = 2; plot_setup(); plot = standardplot; /* is there a better way to clear the graphics screen ? */ if(status = calc()) return(status); if(glassestype==3) /* photographer's mode */ { setfortext(); printf("Second image (right eye) is ready - hit any key to see it\n"); getch(); setforgraphics(); } } return(status); } /* double version - mainly for testing */ ifs3dfloat() { double tmp; double tmpx; double tmpy; double tmpz; VECTOR minvals; VECTOR maxvals; unsigned long maxct,ct; register int col; register int row; register int color; double newx,newy,newz,r,sum; int i,k; /* 3D viewing stuff */ MATRIX doublemat; /* transformation matrix */ MATRIX doublemat1; /* transformation matrix */ VECTOR orbitvect; /* interated function orbit value */ VECTOR viewvect; /* orbit transformed for viewing */ VECTOR viewvect1; /* orbit transformed for viewing */ struct affine cvt; /* setup affine screen coord conversion */ setup_convert_to_screen(&cvt); srand(1); for(i=0;i<3;i++) { minvals[i] = 100000.0; /* impossible value */ maxvals[i] = -100000.0; } setupmatrix(doublemat); if(realtime) setupmatrix(doublemat1); if(diskvideo) /* this would KILL a disk drive! */ { setvideomode(3,0,0,0); buzzer(2); helpmessage(plasmamessage); return(-1); } orbitvect[0] = 0; orbitvect[1] = 0; orbitvect[2] = 0; maxct = maxit*40L; ct = 0L; while(ct++ < maxct) /* loop until keypress or maxit */ { if (ct & 127) /* reduce the number of keypress checks */ if( check_key() ) /* keypress bails out */ return(-1); r = rand(); /* generate fudged random number between 0 and 1 */ r /= 32767; /* pick which iterated function to execute, weighted by probability */ sum = initifs3d[0][12]; k = 0; while ( sum < r) { k++; sum += initifs3d[k][12]; if (initifs3d[k+1][12] == 0) break; /* for safety */ } /* calculate image of last point under selected iterated function */ newx = initifs3d[k][0] * orbitvect[0] + initifs3d[k][1] * orbitvect[1] + initifs3d[k][2] * orbitvect[2] + initifs3d[k][9]; newy = initifs3d[k][3] * orbitvect[0] + initifs3d[k][4] * orbitvect[1] + initifs3d[k][5] * orbitvect[2] + initifs3d[k][10]; newz = initifs3d[k][6] * orbitvect[0] + initifs3d[k][7] * orbitvect[1] + initifs3d[k][8] * orbitvect[2] + initifs3d[k][11]; orbitvect[0] = newx; orbitvect[1] = newy; orbitvect[2] = newz; /* 3D VIEWING TRANSFORM */ vmult(orbitvect,doublemat,viewvect); if(realtime) vmult(orbitvect,doublemat1,viewvect1); /* find minz and maxz */ if(ct <= waste) /* waste this many points to find minz and maxz */ { for(i=0;i<3;i++) if ((tmp = viewvect[i]) < minvals[i]) minvals[i] = tmp; else if (tmp > maxvals[i]) maxvals[i] = tmp; if(ct == waste) { /* center viewer position on object */ view[0] = view[1] = 0; /* center on origin */ /* z value of user's eye - should be more negative than extreme negative part of image */ view[2] = (minvals[2]-maxvals[2])*(double)ZVIEWER/100.0; /* center image on origin */ tmpx = (-minvals[0]-maxvals[0])/(2.0); /* center x */ tmpy = (-minvals[1]-maxvals[1])/(2.0); /* center y */ /* apply perspective shift */ tmpx += ((double)xshift*(xxmax-xxmin))/(xdots) ; tmpy += ((double)yshift*(yymax-yymin))/(ydots); tmpz = -((double)maxvals[2]); trans(tmpx,tmpy,tmpz,doublemat); if(realtime) { /* center image on origin */ tmpx = (-minvals[0]-maxvals[0])/(2.0); /* center x */ tmpy = (-minvals[1]-maxvals[1])/(2.0); /* center y */ tmpx += ((double)xshift1*(xxmax-xxmin))/(xdots); tmpy += ((double)yshift1*(yymax-yymin))/(ydots); tmpz = -((double)maxvals[2]); trans(tmpx,tmpy,tmpz,doublemat1); } } } if(ct > waste) { /* apply perspective if requested */ if(ZVIEWER) { perspective(viewvect); if(realtime) perspective(viewvect1); } if(realtime) whichimage=1; /* plot if inside window */ col = cvt.a*viewvect[0] + cvt.b*viewvect[1] + cvt.e + xxadjust; row = cvt.c*viewvect[0] + cvt.d*viewvect[1] + cvt.f + yyadjust; if ( 0 <= col && col < xdots && 0 <= row && row < ydots) { color = getcolor(col,row)+1; if( color < colors ) /* color sticks on last value */ (*plot)(col,row,color); } if(realtime) { whichimage=2; /* plot if inside window */ col = cvt.a*viewvect1[0] + cvt.b*viewvect1[1] + cvt.e + xxadjust1; row = cvt.c*viewvect1[0] + cvt.d*viewvect1[1] + cvt.f + yyadjust1; if ( 0 <= col && col < xdots && 0 <= row && row < ydots) { color = getcolor(col,row)+1; if( color < colors ) /* color sticks on last value */ (*plot)(col,row,color); } } } } /* end while */ return(0); } ifs() /* IFS logic shamelessly converted to integer math */ { long a,b,c,d,e,f; long *lifsptr; unsigned long maxct,ct; register int col; register int row; register int color; long localifs[NUMIFS][7]; /* local IFS values */ long x,y,newx,newy,r,sum, tempr; int i,j,k; struct affine cvt; /* setup affine screen coord conversion */ setup_convert_to_screen(&cvt); a = cvt.a*fudge; b = cvt.b*fudge; c = cvt.c*fudge; d = cvt.d*fudge; e = cvt.e*fudge; f = cvt.f*fudge; srand(1); if(diskvideo) { /* this would KILL a disk drive! */ setvideomode(3,0,0,0); buzzer(2); helpmessage(plasmamessage); return(-1); } for (i = 0; i < NUMIFS; i++) /* fill in the local IFS array */ for (j = 0; j < IFSPARM; j++) localifs[i][j] = initifs[i][j] * fudge; tempr = fudge / 32767; /* find the proper rand() fudge */ /* make maxct a function of screen size */ /* 1k times maxit at EGA resolution seems about right */ maxct = (float)maxit*(1024.0*xdots*ydots)/(640.0*350.0); ct = 0L; x = y = 0; while(ct++ < maxct) /* loop until keypress or maxit */ { if (ct & 127) /* reduce the number of keypress checks */ if( check_key() ) /* keypress bails out */ return(-1); r = rand(); /* generate fudged random number between 0 and 1 */ r *= tempr; /* pick which iterated function to execute, weighted by probability */ sum = localifs[0][6]; k = 0; while ( sum < r) { k++; sum += localifs[k][6]; if (localifs[k+1][6] == 0) break; /* for safety */ } /* calculate image of last point under selected iterated function */ newx = multiply(localifs[k][0], x, bitshift) + multiply(localifs[k][1], y, bitshift) + localifs[k][4]; newy = multiply(localifs[k][2], x, bitshift) + multiply(localifs[k][3], y, bitshift) + localifs[k][5]; x = newx; y = newy; /* plot if inside window */ col = (multiply(a,x,bitshift) + multiply(b,y,bitshift) + e) >> bitshift; row = (multiply(c,x,bitshift) + multiply(d,y,bitshift) + f) >> bitshift; if ( col >= 0 && col < xdots && row >= 0 && row < ydots ) { /* color is count of hits on this pixel */ color = getcolor(col,row)+1; if( color < colors ) /* color sticks on last value */ (*plot)(col,row,color); } } return(0); } ifs3dlong() { long a,b,c,d,e,f; double tmpx, tmpy, tmpz; extern VECTOR view; long iview[3]; /* perspective viewer's coordinates */ long tmp; long maxvals[3]; long minvals[3]; extern int init3d[]; unsigned long maxct,ct; register int col; register int row; register int color; long localifs[NUMIFS][IFS3DPARM]; /* local IFS values */ long newx,newy,newz,r,sum, tempr; int i,j,k; /* 3D viewing stuff */ MATRIX doublemat; /* transformation matrix */ MATRIX doublemat1; /* transformation matrix */ long longmat[4][4]; /* long version of matrix */ long longmat1[4][4]; /* long version of matrix */ long orbitvect[3]; /* interated function orbit value */ long viewvect[3]; /* orbit transformed for viewing */ long viewvect1[3]; /* orbit transformed for viewing */ struct affine cvt; srand(1); /* setup affine screen coord conversion */ setup_convert_to_screen(&cvt); a = cvt.a*fudge; b = cvt.b*fudge; c = cvt.c*fudge; d = cvt.d*fudge; e = cvt.e*fudge; f = cvt.f*fudge; for(i=0;i<3;i++) { minvals[i] = 1L << 30; maxvals[i] = -minvals[i]; } setupmatrix(doublemat); if(realtime) setupmatrix(doublemat1); /* copy xform matrix to long for for fixed point math */ for (i = 0; i < 4; i++) for (j = 0; j < 4; j++) { longmat[i][j] = doublemat[i][j] * fudge; if(realtime) longmat1[i][j] = doublemat1[i][j] * fudge; } if(diskvideo) /* this would KILL a disk drive! */ { setvideomode(3,0,0,0); buzzer(2); helpmessage(plasmamessage); return(-1); } for (i = 0; i < NUMIFS; i++) /* fill in the local IFS array */ for (j = 0; j < IFS3DPARM; j++) localifs[i][j] = initifs3d[i][j] * fudge; tempr = fudge / 32767; /* find the proper rand() fudge */ orbitvect[0] = 0; orbitvect[1] = 0; orbitvect[2] = 0; maxct = maxit*40L; ct = 0L; while(ct++ < maxct) /* loop until keypress or maxit */ { if (ct & 127) /* reduce the number of keypress checks */ if( check_key() ) /* keypress bails out */ return(-1); r = rand(); /* generate fudged random number between 0 and 1 */ r *= tempr; /* pick which iterated function to execute, weighted by probability */ sum = localifs[0][12]; k = 0; while ( sum < r) { k++; sum += localifs[k][12]; if (localifs[k+1][12] == 0) break; /* for safety */ } /* calculate image of last point under selected iterated function */ newx = multiply(localifs[k][0], orbitvect[0], bitshift) + multiply(localifs[k][1], orbitvect[1], bitshift) + multiply(localifs[k][2], orbitvect[2], bitshift) + localifs[k][9]; newy = multiply(localifs[k][3], orbitvect[0], bitshift) + multiply(localifs[k][4], orbitvect[1], bitshift) + multiply(localifs[k][5], orbitvect[2], bitshift) + localifs[k][10]; newz = multiply(localifs[k][6], orbitvect[0], bitshift) + multiply(localifs[k][7], orbitvect[1], bitshift) + multiply(localifs[k][8], orbitvect[2], bitshift) + localifs[k][11]; orbitvect[0] = newx; orbitvect[1] = newy; orbitvect[2] = newz; /* 3D VIEWING TRANSFORM */ longvmult(orbitvect,longmat,viewvect, bitshift); if(realtime) longvmult(orbitvect,longmat1,viewvect1, bitshift); if(ct <= waste) /* waste this many points to find minz and maxz */ { /* find minz and maxz */ for(i=0;i<3;i++) if ((tmp = viewvect[i]) < minvals[i]) minvals[i] = tmp; else if (tmp > maxvals[i]) maxvals[i] = tmp; if(ct == waste) { iview[0] = iview[1] = 0L; /* center viewer on origin */ /* z value of user's eye - should be more negative than extreme negative part of image */ iview[2] = (long)((minvals[2]-maxvals[2])*(double)ZVIEWER/100.0); /* center image on origin */ tmpx = (-minvals[0]-maxvals[0])/(2.0*fudge); /* center x */ tmpy = (-minvals[1]-maxvals[1])/(2.0*fudge); /* center y */ /* apply perspective shift */ tmpx += ((double)xshift*(xxmax-xxmin))/(xdots) ; tmpy += ((double)yshift*(yymax-yymin))/(ydots); tmpz = -((double)maxvals[2]); tmpz /= fudge; trans(tmpx,tmpy,tmpz,doublemat); if(realtime) { /* center image on origin */ tmpx = (-minvals[0]-maxvals[0])/(2.0*fudge); /* center x */ tmpy = (-minvals[1]-maxvals[1])/(2.0*fudge); /* center y */ tmpx += ((double)xshift1*(xxmax-xxmin))/(xdots); tmpy += ((double)yshift1*(yymax-yymin))/(ydots); tmpz = -((double)maxvals[2]); tmpz /= fudge; trans(tmpx,tmpy,tmpz,doublemat1); } for(i=0;i<3;i++) { view[i] = iview[i]; view[i] /= fudge; } /* copy xform matrix to long for for fixed point math */ for (i = 0; i < 4; i++) for (j = 0; j < 4; j++) { longmat[i][j] = doublemat[i][j] * fudge; if(realtime) longmat1[i][j] = doublemat1[i][j] * fudge; } } } if(ct > waste) { /* apply perspective if requested */ if(ZVIEWER && ct > waste) { if(debugflag==22 || ZVIEWER < 100) /* use float for small persp */ { /* use float perspective calc */ VECTOR tmpv; for(i=0;i<3;i++) { tmpv[i] = viewvect[i]; tmpv[i] /= fudge; } perspective(tmpv); for(i=0;i<3;i++) viewvect[i] = tmpv[i]*fudge; if(realtime) { for(i=0;i<3;i++) { tmpv[i] = viewvect1[i]; tmpv[i] /= fudge; } perspective(tmpv); for(i=0;i<3;i++) viewvect1[i] = tmpv[i]*fudge; } } else { longpersp(viewvect,iview,bitshift); if(realtime) longpersp(viewvect1,iview,bitshift); } } if(realtime) whichimage=1; /* plot if inside window */ col = (multiply(a,viewvect[0],bitshift)+ multiply(b,viewvect[1],bitshift)+e) >> bitshift; row = (multiply(c,viewvect[0],bitshift)+ multiply(d,viewvect[1],bitshift)+f) >> bitshift; col += xxadjust; row += yyadjust; if ( 0 <= col && col < xdots && 0 <= row && row < ydots) { color = getcolor(col,row)+1; if( color < colors ) /* color sticks on last value */ (*plot)(col,row,color); } if(realtime) { whichimage=2; /* plot if inside window */ col = (multiply(a,viewvect1[0],bitshift)+ multiply(b,viewvect1[1],bitshift)+e) >> bitshift; row = (multiply(c,viewvect1[0],bitshift)+ multiply(d,viewvect1[1],bitshift)+f) >> bitshift; col += xxadjust1; row += yyadjust1; if ( 0 <= col && col < xdots && 0 <= row && row < ydots) { color = getcolor(col,row)+1; if( color < colors ) /* color sticks on last value */ (*plot)(col,row,color); } } } } return(0); } setupmatrix(MATRIX doublemat) { /* build transformation matrix */ identity (doublemat); /* apply rotations - uses the same rotation variables as line3d.c */ xrot ((double)XROT / 57.29577,doublemat); yrot ((double)YROT / 57.29577,doublemat); zrot ((double)ZROT / 57.29577,doublemat); /* apply scale */ /* scale((double)XSCALE/100.0,(double)YSCALE/100.0,(double)ROUGH/100.0,doublemat);*/ } orbit3dfloat() { display3d = -1; if(0 < glassestype && glassestype < 3) realtime = 1; else realtime = 0; return(funny_glasses_call(orbit3dfloatcalc)); } orbit3dlong() { display3d = -1; if(0 < glassestype && glassestype < 3) realtime = 1; else realtime = 0; return(funny_glasses_call(orbit3dlongcalc)); } ifs3d() { display3d = -1; if(0 < glassestype && glassestype < 3) realtime = 1; else realtime = 0; if(floatflag) return(funny_glasses_call(ifs3dfloat)); /* double version of ifs3d */ else return(funny_glasses_call(ifs3dlong)); /* long version of ifs3d */ }