/* * soi.c -- SOI * * Simultaneous Orbit Iteration Image Generation Method. Computes * rectangular regions by tracking the orbits of only a few key points. * * Copyright (c) 1994-1997 Michael R. Ganss. All Rights Reserved. * * This file is distributed under the same conditions as * AlmondBread. For further information see * . * */ #include #include #include #include "port.h" #include "prototyp.h" #define DBLS LDBL #define FABS(x) fabsl(x) /* the following needs to be changed back to frexpl once the portability issue has been addressed JCO */ #ifndef XFRACT #define FREXP(x,y) frexpl(x,y) #else #define FREXP(x,y) frexp(x,y) #endif #define TRUE 1 #define FALSE 0 #define EVERY 15 #define BASIN_COLOR 0 int rhombus_stack[10]; int rhombus_depth; int max_rhombus_depth; int minstackavail; /* int minstack=1700; */ /* need this much stack to recurse */ int minstack=2200; /* and this much stack to not crash when is pressed */ static DBLS twidth; static DBLS equal; static char baxinxx = FALSE; long iteration(register DBLS cr, register DBLS ci, register DBLS re, register DBLS im, long start) { register long iter,offset=0; int k,n; register DBLS ren,imn,sre,sim; #ifdef INTEL register float mag; register unsigned long bail=0x41800000,magi; /* bail=16.0 */ register unsigned long eq=*(unsigned long *)&equal; #else register DBLS mag; #endif DBLS d; int exponent; if(baxinxx) { sre=re; sim=im; ren=re*re; imn=im*im; if(start!=0) { offset=maxit-start+7; iter=offset>>3; offset&=7; offset=(8-offset); } else iter=maxit>>3; k=n=8; do { im=im*re; re=ren-imn; im+=im; re+=cr; im+=ci; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; #ifdef INTEL mag=FABS(sre-re); magi=*(unsigned long *)&mag; if(magi>3; offset&=7; offset=(8-offset); } else iter=maxit>>3; do { im=im*re; re=ren-imn; im+=im; re+=cr; im+=ci; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*re; ren=re+im; re=re-im; imn+=imn; re=ren*re; im=imn+ci; re+=cr; imn=im*im; ren=re*re; mag=ren+imn; #ifdef INTEL magi=*(unsigned long *)&mag; #endif } #ifdef INTEL while (magi>3])); } } static void puthline(int x1,int y1,int x2,int color) { int x; for(x=x1;x<=x2;x++) (*plot)(x,y1,color); } static void putbox(int x1, int y1, int x2, int y2, int color) { for(; y1<=y2; y1++) puthline(x1,y1,x2,color); } /* maximum side length beyond which we start regular scanning instead of subdividing */ #define SCAN 16 /* pixel interleave used in scanning */ #define INTERLEAVE 4 /* compute the value of the interpolation polynomial at (x,y) */ #define GET_REAL(x,y) \ interpolate(cim1,midi,cim2,\ interpolate(cre1,midr,cre2,zre1,zre5,zre2,x),\ interpolate(cre1,midr,cre2,zre6,zre9,zre7,x),\ interpolate(cre1,midr,cre2,zre3,zre8,zre4,x),y) #define GET_IMAG(x,y) \ interpolate(cre1,midr,cre2,\ interpolate(cim1,midi,cim2,zim1,zim6,zim3,y),\ interpolate(cim1,midi,cim2,zim5,zim9,zim8,y),\ interpolate(cim1,midi,cim2,zim2,zim7,zim4,y),x) /* compute the value of the interpolation polynomial at (x,y) from saved values before interpolation failed to stay within tolerance */ #define GET_SAVED_REAL(x,y) \ interpolate(cim1,midi,cim2,\ interpolate(cre1,midr,cre2,sr1,sr5,sr2,x),\ interpolate(cre1,midr,cre2,sr6,sr9,sr7,x),\ interpolate(cre1,midr,cre2,sr3,sr8,sr4,x),y) #define GET_SAVED_IMAG(x,y) \ interpolate(cre1,midr,cre2,\ interpolate(cim1,midi,cim2,si1,si6,si3,y),\ interpolate(cim1,midi,cim2,si5,si9,si8,y),\ interpolate(cim1,midi,cim2,si2,si7,si4,y),x) /* compute the value of the interpolation polynomial at (x,y) during scanning. Here, key values do not change, so we can precompute coefficients in one direction and simply evaluate the polynomial during scanning. */ #define GET_SCAN_REAL(x,y) \ interpolate(cim1,midi,cim2,\ EVALUATE(cre1,midr,br10,br11,br12,x),\ EVALUATE(cre1,midr,br20,br21,br22,x),\ EVALUATE(cre1,midr,br30,br31,br32,x),y) #define GET_SCAN_IMAG(x,y) \ interpolate(cre1,midr,cre2,\ EVALUATE(cim1,midi,bi10,bi11,bi12,y),\ EVALUATE(cim1,midi,bi20,bi21,bi22,y),\ EVALUATE(cim1,midi,bi30,bi31,bi32,y),x) /* compute coefficients of Newton polynomial (b0,..,b2) from (x0,w0),..,(x2,w2). */ #define INTERPOLATE(x0,x1,x2,w0,w1,w2,b0,b1,b2) \ b0=w0;\ b1=(w1-w0)/(LDBL)(x1-x0);\ b2=((w2-w1)/(LDBL)(x2-x1)-b1)/(x2-x0) /* evaluate Newton polynomial given by (x0,b0),(x1,b1) at x:=t */ #define EVALUATE(x0,x1,b0,b1,b2,t) \ ((b2*(t-x1)+b1)*(t-x0)+b0) /* Newton Interpolation. It computes the value of the interpolation polynomial given by (x0,w0)..(x2,w2) at x:=t */ static DBLS interpolate(DBLS x0, DBLS x1, DBLS x2, DBLS w0, DBLS w1, DBLS w2, DBLS t) { register DBLS b0=w0,b1=w1,b2=w2,b; /*b0=(r0*b1-r1*b0)/(x1-x0); b1=(r1*b2-r2*b1)/(x2-x1); b0=(r0*b1-r2*b0)/(x2-x0); return (DBLS)b0;*/ b=(b1-b0)/(x1-x0); return (DBLS)((((b2-b1)/(x2-x1)-b)/(x2-x0))*(t-x1)+b)*(t-x0)+b0; /* if(t= 700) #pragma code_seg ("soi2_text") /* place following in an overlay */ #endif /* SOICompute - Perform simultaneous orbit iteration for a given rectangle Input: cre1..cim2 : values defining the four corners of the rectangle x1..y2 : corresponding pixel values zre1..zim9 : intermediate iterated values of the key points (key values) (cre1,cim1) (cre2,cim1) (zre1,zim1) (zre5,zim5) (zre2,zim2) +------------+------------+ | | | | | | (zre6,zim6) (zre9,zim9) (zre7,zim7) | | | | | | +------------+------------+ (zre3,zim3) (zre8,zim8) (zre4,zim4) (cre1,cim2) (cre2,cim2) iter : current number of iterations */ static DBLS zre1, zim1, zre2, zim2, zre3, zim3, zre4, zim4, zre5, zim5, zre6, zim6, zre7, zim7, zre8, zim8, zre9, zim9; /* The purpose of this macro is to reduce the number of parameters of the function rhombus(), since this is a recursive function, and stack space under DOS is extremely limited. */ #define RHOMBUS(CRE1,CRE2,CIM1,CIM2,X1,X2,Y1,Y2,ZRE1,ZIM1,ZRE2,ZIM2,ZRE3,ZIM3,\ ZRE4, ZIM4, ZRE5, ZIM5,ZRE6, ZIM6, ZRE7, ZIM7, ZRE8, ZIM8, ZRE9, ZIM9,ITER) \ zre1=(ZRE1);zim1=(ZIM1);\ zre2=(ZRE2);zim2=(ZIM2);\ zre3=(ZRE3);zim3=(ZIM3);\ zre4=(ZRE4);zim4=(ZIM4);\ zre5=(ZRE5);zim5=(ZIM5);\ zre6=(ZRE6);zim6=(ZIM6);\ zre7=(ZRE7);zim7=(ZIM7);\ zre8=(ZRE8);zim8=(ZIM8);\ zre9=(ZRE9);zim9=(ZIM9);\ status=rhombus((CRE1),(CRE2),(CIM1),(CIM2),(X1),(X2),(Y1),(Y2),(ITER)) static int rhombus(DBLS cre1, DBLS cre2, DBLS cim1, DBLS cim2, int x1, int x2, int y1, int y2, long iter) { /* The following variables do not need their values saved */ /* used in scanning */ static long far savecolor, color, helpcolor; static int far x,y,z,savex; #if 0 static DBLS far re,im,restep,imstep,interstep,helpre; static DBLS far zre,zim; /* interpolation coefficients */ static DBLS far br10,br11,br12,br20,br21,br22,br30,br31,br32; static DBLS far bi10,bi11,bi12,bi20,bi21,bi22,bi30,bi31,bi32; /* ratio of interpolated test point to iterated one */ static DBLS far l1,l2; /* squares of key values */ static DBLS far rq1,iq1; static DBLS far rq2,iq2; static DBLS far rq3,iq3; static DBLS far rq4,iq4; static DBLS far rq5,iq5; static DBLS far rq6,iq6; static DBLS far rq7,iq7; static DBLS far rq8,iq8; static DBLS far rq9,iq9; /* test points */ static DBLS far cr1,cr2; static DBLS far ci1,ci2; static DBLS far tzr1,tzi1,tzr2,tzi2,tzr3,tzi3,tzr4,tzi4; static DBLS far trq1,tiq1,trq2,tiq2,trq3,tiq3,trq4,tiq4; #else #define re mem_static[ 0] #define im mem_static[ 1] #define restep mem_static[ 2] #define imstep mem_static[ 3] #define interstep mem_static[ 4] #define helpre mem_static[ 5] #define zre mem_static[ 6] #define zim mem_static[ 7] #define br10 mem_static[ 8] #define br11 mem_static[ 9] #define br12 mem_static[10] #define br20 mem_static[11] #define br21 mem_static[12] #define br22 mem_static[13] #define br30 mem_static[14] #define br31 mem_static[15] #define br32 mem_static[16] #define bi10 mem_static[17] #define bi11 mem_static[18] #define bi12 mem_static[19] #define bi20 mem_static[20] #define bi21 mem_static[21] #define bi22 mem_static[22] #define bi30 mem_static[23] #define bi31 mem_static[24] #define bi32 mem_static[25] #define l1 mem_static[26] #define l2 mem_static[27] #define rq1 mem_static[28] #define iq1 mem_static[29] #define rq2 mem_static[30] #define iq2 mem_static[31] #define rq3 mem_static[32] #define iq3 mem_static[33] #define rq4 mem_static[34] #define iq4 mem_static[35] #define rq5 mem_static[36] #define iq5 mem_static[37] #define rq6 mem_static[38] #define iq6 mem_static[39] #define rq7 mem_static[40] #define iq7 mem_static[41] #define rq8 mem_static[42] #define iq8 mem_static[43] #define rq9 mem_static[44] #define iq9 mem_static[45] #define cr1 mem_static[46] #define cr2 mem_static[47] #define ci1 mem_static[48] #define ci2 mem_static[49] #define tzr1 mem_static[50] #define tzi1 mem_static[51] #define tzr2 mem_static[52] #define tzi2 mem_static[53] #define tzr3 mem_static[54] #define tzi3 mem_static[55] #define tzr4 mem_static[56] #define tzi4 mem_static[57] #define trq1 mem_static[58] #define tiq1 mem_static[59] #define trq2 mem_static[60] #define tiq2 mem_static[61] #define trq3 mem_static[62] #define tiq3 mem_static[63] #define trq4 mem_static[64] #define tiq4 mem_static[65] #endif /* number of iterations before SOI iteration cycle */ static long far before; static int far avail; /* the variables below need to have local copis for recursive calls */ DBLS far *mem; DBLS far *mem_static; /* center of rectangle */ DBLS midr=(cre1+cre2)/2,midi=(cim1+cim2)/2; #if 0 /* saved values of key values */ DBLS sr1,si1,sr2,si2,sr3,si3,sr4,si4; DBLS sr5,si5,sr6,si6,sr7,si7,sr8,si8,sr9,si9; /* key values for subsequent rectangles */ DBLS re10,re11,re12,re13,re14,re15,re16,re17,re18,re19,re20,re21; DBLS im10,im11,im12,im13,im14,im15,im16,im17,im18,im19,im20,im21; DBLS re91,re92,re93,re94,im91,im92,im93,im94; #else #define sr1 mem[ 0] #define si1 mem[ 1] #define sr2 mem[ 2] #define si2 mem[ 3] #define sr3 mem[ 4] #define si3 mem[ 5] #define sr4 mem[ 6] #define si4 mem[ 7] #define sr5 mem[ 8] #define si5 mem[ 9] #define sr6 mem[10] #define si6 mem[11] #define sr7 mem[12] #define si7 mem[13] #define sr8 mem[14] #define si8 mem[15] #define sr9 mem[16] #define si9 mem[17] #define re10 mem[18] #define re11 mem[19] #define re12 mem[20] #define re13 mem[21] #define re14 mem[22] #define re15 mem[23] #define re16 mem[24] #define re17 mem[25] #define re18 mem[26] #define re19 mem[27] #define re20 mem[28] #define re21 mem[29] #define im10 mem[30] #define im11 mem[31] #define im12 mem[32] #define im13 mem[33] #define im14 mem[34] #define im15 mem[35] #define im16 mem[36] #define im17 mem[37] #define im18 mem[38] #define im19 mem[39] #define im20 mem[40] #define im21 mem[41] #define re91 mem[42] #define re92 mem[43] #define re93 mem[44] #define re94 mem[45] #define im91 mem[46] #define im92 mem[47] #define im93 mem[48] #define im94 mem[49] #endif int status = 0; rhombus_depth++; #if 1 /* what we go through under DOS to deal with memory! We re-use the sizeofstring array (8k). The first 660 bytes is for static variables, then we make our own "stack" with copies for each recursive call of rhombus() for the rest. */ mem_static = (DBLS far *)sizeofstring; mem = mem_static+ 66 + 50*rhombus_depth; #endif if((avail = stackavail()) < minstackavail) minstackavail = avail; if(rhombus_depth > max_rhombus_depth) max_rhombus_depth = rhombus_depth; rhombus_stack[rhombus_depth] = avail; if(keypressed()) { status = 1; goto rhombus_done; } if(iter>maxit) { putbox(x1,y1,x2,y2,0); status = 0; goto rhombus_done; } if((y2-y1<=SCAN) || (avail < minstack)) { /* finish up the image by scanning the rectangle */ scan: INTERPOLATE(cre1,midr,cre2,zre1,zre5,zre2,br10,br11,br12); INTERPOLATE(cre1,midr,cre2,zre6,zre9,zre7,br20,br21,br22); INTERPOLATE(cre1,midr,cre2,zre3,zre8,zre4,br30,br31,br32); INTERPOLATE(cim1,midi,cim2,zim1,zim6,zim3,bi10,bi11,bi12); INTERPOLATE(cim1,midi,cim2,zim5,zim9,zim8,bi20,bi21,bi22); INTERPOLATE(cim1,midi,cim2,zim2,zim7,zim4,bi30,bi31,bi32); restep=(cre2-cre1)/(x2-x1); imstep=(cim2-cim1)/(y2-y1); interstep=INTERLEAVE*restep; for(y=y1, im=cim1; yx-INTERLEAVE; z--,helpre-=restep) { zre=GET_SCAN_REAL(helpre,im); zim=GET_SCAN_IMAG(helpre,im); helpcolor=iteration(helpre,im,zre,zim,iter); if(helpcolor < 0) { status = 1; goto rhombus_done; } else if(helpcolor==savecolor) break; (*plot)(z,y,(int)(helpcolor&255)); } if(savexsavex; z--,helpre-=restep) { zre=GET_SCAN_REAL(helpre,im); zim=GET_SCAN_IMAG(helpre,im); helpcolor=iteration(helpre,im,zre,zim,iter); if(helpcolor < 0) { status = 1; goto rhombus_done; } else if(helpcolor==savecolor) break; (*plot)(z,y,(int)(helpcolor&255)); } if(savex16.0|| (rq2+iq2)>16.0|| (rq3+iq3)>16.0|| (rq4+iq4)>16.0|| (rq5+iq5)>16.0|| (rq6+iq6)>16.0|| (rq7+iq7)>16.0|| (rq8+iq8)>16.0|| (rq9+iq9)>16.0|| (trq1+tiq1)>16.0|| (trq2+tiq2)>16.0|| (trq3+tiq3)>16.0|| (trq4+tiq4)>16.0) break; /* if maximum number of iterations is reached, the whole rectangle can be assumed part of M. This is of course best case behavior of SOI, we seldomly get there */ if(iter>maxit) { putbox(x1,y1,x2,y2,0); status = 0; goto rhombus_done; } /* now for all test points, check whether they exceed the allowed tolerance. if so, subdivide */ l1=GET_REAL(cr1,ci1); l1=(tzr1==0.0)? (l1==0.0)?1.0:1000.0: l1/tzr1; if(FABS(1.0-l1)>twidth) break; l2=GET_IMAG(cr1,ci1); l2=(tzi1==0.0)? (l2==0.0)?1.0:1000.0: l2/tzi1; if(FABS(1.0-l2)>twidth) break; l1=GET_REAL(cr2,ci1); l1=(tzr2==0.0)? (l1==0.0)?1.0:1000.0: l1/tzr2; if(FABS(1.0-l1)>twidth) break; l2=GET_IMAG(cr2,ci1); l2=(tzi2==0.0)? (l2==0.0)?1.0:1000.0: l2/tzi2; if(FABS(1.0-l2)>twidth) break; l1=GET_REAL(cr1,ci2); l1=(tzr3==0.0)? (l1==0.0)?1.0:1000.0: l1/tzr3; if(FABS(1.0-l1)>twidth) break; l2=GET_IMAG(cr1,ci2); l2=(tzi3==0.0)? (l2==0.0)?1.0:1000.0: l2/tzi3; if(FABS(1.0-l2)>twidth) break; l1=GET_REAL(cr2,ci2); l1=(tzr4==0.0)? (l1==0.0)?1.0:1000.0: l1/tzr4; if(FABS(1.0-l1)>twidth) break; l2=GET_IMAG(cr2,ci2); l2=(tzi4==0.0)? (l2==0.0)?1.0:1000.0: l2/tzi4; if(FABS(1.0-l2)>twidth) break; } iter--; /* this is a little heuristic I tried to improve performance. */ if(iter-before<10) { zre1=sr1; zim1=si1; zre2=sr2; zim2=si2; zre3=sr3; zim3=si3; zre4=sr4; zim4=si4; zre5=sr5; zim5=si5; zre6=sr6; zim6=si6; zre7=sr7; zim7=si7; zre8=sr8; zim8=si8; zre9=sr9; zim9=si9; goto scan; } /* compute key values for subsequent rectangles */ re10=interpolate(cre1,midr,cre2,sr1,sr5,sr2,cr1); im10=interpolate(cre1,midr,cre2,si1,si5,si2,cr1); re11=interpolate(cre1,midr,cre2,sr1,sr5,sr2,cr2); im11=interpolate(cre1,midr,cre2,si1,si5,si2,cr2); re20=interpolate(cre1,midr,cre2,sr3,sr8,sr4,cr1); im20=interpolate(cre1,midr,cre2,si3,si8,si4,cr1); re21=interpolate(cre1,midr,cre2,sr3,sr8,sr4,cr2); im21=interpolate(cre1,midr,cre2,si3,si8,si4,cr2); re15=interpolate(cre1,midr,cre2,sr6,sr9,sr7,cr1); im15=interpolate(cre1,midr,cre2,si6,si9,si7,cr1); re16=interpolate(cre1,midr,cre2,sr6,sr9,sr7,cr2); im16=interpolate(cre1,midr,cre2,si6,si9,si7,cr2); re12=interpolate(cim1,midi,cim2,sr1,sr6,sr3,ci1); im12=interpolate(cim1,midi,cim2,si1,si6,si3,ci1); re14=interpolate(cim1,midi,cim2,sr2,sr7,sr4,ci1); im14=interpolate(cim1,midi,cim2,si2,si7,si4,ci1); re17=interpolate(cim1,midi,cim2,sr1,sr6,sr3,ci2); im17=interpolate(cim1,midi,cim2,si1,si6,si3,ci2); re19=interpolate(cim1,midi,cim2,sr2,sr7,sr4,ci2); im19=interpolate(cim1,midi,cim2,si2,si7,si4,ci2); re13=interpolate(cim1,midi,cim2,sr5,sr9,sr8,ci1); im13=interpolate(cim1,midi,cim2,si5,si9,si8,ci1); re18=interpolate(cim1,midi,cim2,sr5,sr9,sr8,ci2); im18=interpolate(cim1,midi,cim2,si5,si9,si8,ci2); re91=GET_SAVED_REAL(cr1,ci1); re92=GET_SAVED_REAL(cr2,ci1); re93=GET_SAVED_REAL(cr1,ci2); re94=GET_SAVED_REAL(cr2,ci2); im91=GET_SAVED_IMAG(cr1,ci1); im92=GET_SAVED_IMAG(cr2,ci1); im93=GET_SAVED_IMAG(cr1,ci2); im94=GET_SAVED_IMAG(cr2,ci2); RHOMBUS(cre1,midr,cim1,midi,x1,((x1+x2)>>1),y1,((y1+y2)>>1), sr1,si1, sr5,si5, sr6,si6, sr9,si9, re10,im10, re12,im12, re13,im13, re15,im15, re91,im91, iter); RHOMBUS(midr,cre2,cim1,midi,(x1+x2)>>1,x2,y1,(y1+y2)>>1, sr5,si5, sr2,si2, sr9,si9, sr7,si7, re11,im11, re13,im13, re14,im14, re16,im16, re92,im92, iter); RHOMBUS(cre1,midr,midi,cim2,x1,(x1+x2)>>1,(y1+y2)>>1,y2, sr6,si6, sr9,si9, sr3,si3, sr8,si8, re15,im15, re17,im17, re18,im18, re20,im20, re93,im93, iter); RHOMBUS(midr,cre2,midi,cim2,(x1+x2)>>1,x2,(y1+y2)>>1,y2, sr9,si9, sr7,si7, sr8,si8, sr4,si4, re16,im16, re18,im18, re19,im19, re21,im21, re94,im94, iter); rhombus_done: rhombus_depth--; return(status); } #if (_MSC_VER >= 700) #pragma code_seg () #endif void soi_ldbl(void) { int status; DBLS tolerance=0.1; DBLS stepx, stepy; DBLS xxminl, xxmaxl, yyminl, yymaxl; minstackavail = 30000; rhombus_depth = -1; max_rhombus_depth = 0; if(bf_math) { xxminl = bftofloat(bfxmin); yyminl = bftofloat(bfymin); xxmaxl = bftofloat(bfxmax); yymaxl = bftofloat(bfymax); } else { xxminl = xxmin; yyminl = yymin; xxmaxl = xxmax; yymaxl = yymax; } twidth=tolerance/(xdots-1); stepx = (xxmaxl - xxminl) / xdots; stepy = (yyminl - yymaxl) / ydots; equal = (stepx < stepy ? stepx : stepy); RHOMBUS(xxminl,xxmaxl,yymaxl,yyminl, 0,xdots,0,ydots, xxminl,yymaxl, xxmaxl,yymaxl, xxminl,yyminl, xxmaxl,yyminl, (xxmaxl+xxminl)/2,yymaxl, xxminl,(yymaxl+yyminl)/2, xxmaxl,(yymaxl+yyminl)/2, (xxmaxl+xxminl)/2,yyminl, (xxminl+xxmaxl)/2,(yymaxl+yyminl)/2, 1); }