Conto.cin

// Conro.cin is the C++ routine to make the contourplot in the EPS format // It can be called as conto(o,g,w,v,X,Y,M,N, Lev ,-p,p); // FILE *o is the output file; it should be opened for writing and the EPS header should be already there. // (The header can be written with routine ado.cin ). // double *g is single-dimensional array of length (M+1)*(N+1) used to transfer values of the function to the routine. // g[m+(M+1)*n] is interpreted as value of the function at the point of grid with numbers m,n; // -1<m<M+1; -1<n<N+1 // double *w is working array of length (M+1)*(N+1). // char *v is working array of length (M+1)*(N+1), // v it is used to store the mark of each sell as "visited" to avoid drawing the same line twice. // double *X is array of length M+1; the abscissas of the grid points should be stored there at the calling of conto. // double *Y is array of length N+1; the ordinates of the grid points should be stored there at the calling of conto. // int M is number of cells along abscissas; number of the grid points along x axis is M+1 // int N is number of cells along ordinates; number of the grid points along y axis is N+1 // double Lev, level to be drawn. (At a single call, the only one level is drawn) // double p and -p, should be something of type double; p and -p determine the interval used for plotting: // values smaller than Lev-p or greater than Lev+p are interpreted as "singularities" of the function. // (only once I used non–symmetric limits, but I still keep this option, some expression may be placed instead of -p) // Routine 'conto is used in generator Tetre2215.cc to plot the contours of tetration. // Please let me know if any problem with this routine. // Copyleft 2008-2011 by Dmitrii Kouznetsov.

//#define o(x,y) fprintf(o,"%5.3f %5.3f o\n",1.*(x),1.*(y));
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) include"ado.cin"
 * 6) define DB double
 * 7) define DO(x,y) for(x=0;x<y;x++)
 * 8) define M(x,y) fprintf(o,"%6.4f %6.4f M\n",1.*(x),1.*(y));
 * 9) define L(x,y) fprintf(o,"%6.4f %6.4f L\n",1.*(x),1.*(y));
 * 1) define Mxy M(x,y)
 * 2) define Lxy L(x,y)
 * 3) define f(m,n) F[(m)*N1+(n)]
 * 4) define z(m,n) Z[(m)*N1+(n)]
 * 5) define zmn z(m,n)
 * 6) define zMn z(m+1,n)
 * 7) define zmN z(m,n+1)
 * 8) define zMN z(m+1,n+1)
 * 9) define fmn f(m,n)
 * 10) define fMn f(m+1,n)
 * 11) define fmN f(m,n+1)
 * 12) define fMN f(m+1,n+1)
 * 13) define Xm X[m]
 * 14) define XM X[m+1]
 * 15) define Yn Y[n]
 * 16) define YN Y[n+1]
 * 17) define bdpq {b=f(m,n+1);d=f(m+1,n+1);p=f(m,n);q=f(m+1,n);}
 * 18) define UPP 1
 * 19) define LEF 2
 * 20) define DOW 3
 * 21) define RIG 4

DB drift(FILE *o,DB *F,char *Z,DB *X,DB *Y,int M,int N,int m,int n,int K) {int M1=M+1,N1=N+1; DB b,d, p,q, x,y, B,D,P,Q; int mO=m,nO=n; //printf("drift: K=%2d, m=%2d n=%2d \n",K,m,n);

if(K==UPP) goto Up; if(K==LEF) goto Le; if(K==DOW) goto Do; if(K==RIG) goto Ri; Up:if(zmn=='b'||zmn=='d'||zmn=='p'||zmn=='q'||zmn=='o'){return 0.;} if(zmn=='|'||zmn=='+'||zmn=='/'||zmn=='L'){if(m==mO&&n==nO)fprintf(o,"C\n");return 0.;} bdpq; //printf("Up: m=%2d n=%2d bdpq=%5.2f %5.2f %5.2f %5.2f\n",m,n,b,d,p,q); //getchar; if(b*d<0){x=Xm+(XM-Xm)*b/(b-d);y=YN;Lxy;if(zmn=='-')zmn='+';else zmn='|';n++; if(n>=N) return 0.; goto Up;} if(q*d<0){y=Yn+(YN-Yn)*q/(q-d);x=XM;Lxy;zmn='/';m++;if(m>=M)return 0; goto Ri;} if(b*p<0){y=Yn+(YN-Yn)*p/(p-b);x=Xm;Lxy;zmn='L';m--;if(m<0)return 0; goto Le;} //printf("handle zero, m=%2d n=%2d\n", m,n); if(d*d==0){ zmn='o';m++;n++;L(X[m],Y[n]); //printf("Go to UR"); goto UR;} if(b*b==0){zmn='o';n++; L(X[m],Y[n]);m--; goto UL;} //end Up Le:if(zmn=='b'||zmn=='d'||zmn=='p'||zmn=='q'||zmn=='o'){return 0.;} if(zmn=='-'||zmn=='+'||zmn=='/'||zmn=='L'){if(m==mO&&n==nO)fprintf(o,"C\n");return 0.;} bdpq; //printf("Le: m=%2d n=%2d bdpq=%5.2f %5.2f %5.2f %5.2f\n",m,n,b,d,p,q); if(b*p<0){y=Yn+(YN-Yn)*p/(p-b);x=Xm;Lxy;if(zmn=='|') zmn='+'; else zmn='-';m--;if(m<0)return 0; goto Le;} if(p*q<0){x=Xm+(XM-Xm)*p/(p-q);y=Yn;Lxy;zmn='/';n--;if(n<0)return 0; goto Do;} if(b*d<0){x=Xm+(XM-Xm)*b/(b-d);y=YN;Lxy;zmn='L';n++;if(n>=N)return 0; goto Up;} //printf("Le Handles zero\n"); if(p*p==0){zmn='o';L(Xm,Yn);m--;n--;if(m<0||n<0) return 0;// printf("go to LD\n"); goto LD;} if(b*b==0){zmn='o';n++;L(Xm,Yn);m--;if(m<0||n>=N)return 0;// printf("go to LU\n"); goto LU;} //end Le

Do://come to cell m,n from the up and expect to go down. if(zmn=='b'||zmn=='d'||zmn=='p'||zmn=='q'||zmn=='o') return 0.; if(zmn=='|'||zmn=='+'||zmn=='/'||zmn=='L'){if(m==mO&&n==nO)fprintf(o,"C\n");return 0.;} bdpq; //printf("Do: m=%2d n=%2d bdpq=%5.2f %5.2f %5.2f %5.2f\n",m,n,b,d,p,q); if(p*q<0){x=Xm+(XM-Xm)*p/(p-q);y=Yn;Lxy;if(zmn=='-')zmn='+'; else zmn='|';n--;if(n<0)return 0; goto Do;} if(b*p<0){y=Yn+(YN-Yn)*p/(p-b);x=Xm;Lxy;zmn='/';m--;if(m<0) return 0; goto Le;} if(q*d<0){y=Yn+(YN-Yn)*q/(q-d);x=XM;Lxy;zmn='L';m++;if(m>=M) return 0; goto Ri;} //printf("handle zero\n"); if(p*p==0){zmn='o';L(Xm,Yn);m--;n--; goto DL;} if(q*q==0){zmn='o';m++;L(Xm,Yn);n--; goto DR;} //end Do

Ri: //expect to go right.. if(zmn=='b'||zmn=='d'||zmn=='p'||zmn=='q'||zmn=='o')return 0.; if(zmn=='-'||zmn=='+'||zmn=='/'||zmn=='L'){if(m==mO&&n==nO)fprintf(o,"C\n");return 0.;} bdpq;//printf("Ri: m=%2d n=%2d bdpq=%5.2f %5.2f %5.2f %5.2f\n",m,n,b,d,p,q); if(d*q<0){y=Yn+(YN-Yn)*q/(q-d);x=XM;Lxy;if(zmn=='-') zmn='+'; else zmn='|';m++;if(m>=M)return 0; goto Ri;} if(b*d<0){x=Xm+(XM-Xm)*b/(b-d);y=YN;Lxy;zmn='/';n++;if(n>=N) return 0; goto Up;} if(p*q<0){x=Xm+(XM-Xm)*p/(p-q);y=Yn;Lxy;zmn='L';n--;if(n<0)return 0; goto Do;} //printf("handle zero\n"); if(d*d==0){zmn='o';m++;n++;L(Xm,Yn); goto UR;} if(q*q==0){zmn='o';m++;L(Xm,Yn);n--; goto DR;} //if(n<0 ||m>=M) return 0; goto Ri;} return 0; //end Ri

DL: LD: //printf("LD m=%2d n=%2d (may be negative)\n",m,n); //came to the cell (m,n) from upper right corner. //This cell may exist at the mesh; check this option first. if(m<0&&n<0) return 0; //corner of the mesh; if(m<0){m++;bdpq;if(p*q<=0 && zmn==' ') goto Do; return 0;} if(n<0){n++;bdpq;if(b*p<=0 && zmn==' ') goto Le; return 0;} bdpq; // pri("inside. bdpq=%5.2f %5.2f %5.2f %5.2f\n", b,d,p,q); if(p*q<=0 && zmn==' ') goto Do; if(b*p<=0 && zmn==' ') goto Le; Q=f(m+2,n); //pri("Q=%5.2f\n",Q); if(Q*q<=0){m++; if(zmn==' ') {//printf("go to Do, m=%2d n=%2d\n",m,n); goto Do;} return 0;} B=f(m,n+2); if(B*b<=0){n++; if(zmn==' ') goto Le; return 0;} return 0; LU:UL: //printf("UL: m=%2d n=%2d ( may be out of mesh)\n",m,n); //come from right down. if(m<0&&n>=N) return 0; //corner of the mesh; if(m<0){m++;bdpq;if(b*d<=0 && zmn==' ') goto Up; return 0;} if(n>=N){n--;bdpq;if(b*p<=0 && zmn==' ') goto Le; return 0;} bdpq; //pri("inside. bdpq=%5.2f %5.2f %5.2f %5.2f\n", b,d,p,q); if(b*p<=0 && zmn==' ') goto Le; if(b*d<=0 && zmn==' ') goto Up; D=f(m+2,n+1); //pri("D=%5.2f\n",D); if(D*d<=0){m++;if(zmn==' ') goto Up;} //Q=f(m-1,n+1); //pr("Q=%5.2f\n",Q); if(Q*q<=0){m--;if(zmn==' ') goto Le;} P=f(m,n-1); //pri("P=%5.2f\n",P); if(P*p<=0){n--;if(zmn==' ') goto Le;} //if(p*p==0){L(X[m],Y[n]) zmn='-'; Z[m*N1+n-1]='-'; m--;n--; goto LD;} return 0; RU: UR: //printf("UR: m=%2d n=%2d\n",m,n); //come from left down. May be out of mesh. if(m>=M&&n>=N) return 0; //corner of the mesh; if(m>=M){m--;bdpq;if(b*d<=0 && zmn==' ') goto Up; return 0;} //more lines //  if(m>=M){m--;bdpq;if(b*d< 0 && zmn==' ') goto Up; return 0;}  // less lines if(n>=N){n--;bdpq;if(d*q<=0 && zmn==' ') goto Ri; return 0;} //more lines //  if(n>=N){n--;bdpq;if(d*q<=0 && zmn==' ') goto Ri; return 0;} //less bdpq; //pri("inside. bdpq=%5.2f %5.2f %5.2f %5.2f\n", b,d,p,q); if(d*q<=0 && zmn==' ') goto Ri; if(b*d<=0 && zmn==' ') goto Up; B=f(m-1,n+1); //pri("Q=%5.2f\n",Q); if(B*b<=0){m--; if(zmn==' ') goto Up; return 0;} Q=f(m+1,n-1); //pri("D=%5.2f\n",D); if(Q*q<=0){n--; if(zmn==' ') goto Ri; return 0;} return 0; DR: RD: //printf("RD: m=%3d n=%2d\n",m,n); if(m>=M&&n<0) return 0; //corner of the mesh; if(m>=M){m--;bdpq;if(p*q<=0 && zmn==' ') goto Do; return 0;} if(n<0 ){n++;bdpq;if(b*p<=0 && zmn==' ') goto Ri; return 0;} bdpq; //pri("inside. bdpq=%5.2f %5.2f %5.2f %5.2f\n", b,d,p,q); if(p*q<=0 && zmn==' ') goto Do; if(d*q<=0 && zmn==' ') goto Ri; Q=f(m+2,n); //pri("Q=%5.2f\n",Q); if(Q*q<=0){m++; if(zmn==' ') {//printf("go to Do, m=%2d n=%2d\n",m,n); goto Do;} return 0;} D=f(m+1,n+2); //pri("D=%5.2f\n",D); if(D*d<=0){n++; if(zmn==' ') goto Ri; return 0;} return 0;}//end drift DB conto(FILE *o,DB *G,DB *F,char *Z,DB *X, DB *Y,int M,int N,DB L,DB L1,DB L2) {int m,n; int M1=M+1,N1=N+1; DB w,	b,d, p,q, x,y; // printf("conto (copyleft 2008 by Dmitrii Kouznetsov) draws level L=%6.3f\n",L); printf("conto draws L=%6.3f\n",L); //for(n=N;n>=0;n--){DO(m,M1)printf("%5.2f",G[m*N1+n]); printf("\n");} //getchar; //DO(m,M1){ M(X[m],Y[0]);L(X[m],Y[N]);} //DO(n,N1){ M(X[0],Y[n]);L(X[M],Y[n]);} //fprintf(o,".001 W 0 0 0 RGB S\n"); DO(m,M1)DO(n,N1)z(m,n)=' '; DO(m,M1)DO(n,N1) { w=G[m*N1+n]-L; if(L1 0) z(m-1,n )='q'; if(n>0) {z(m,n-1)='b'; if(m> 0 )z(m-1,n-1)='d';} } } //for(n=N;n>=0;n--){DO(m,M1)pri("%5.2f",F[m*N1+n]); printf("\n");} //for(n=N;n>=0;n--){DO(m,M1)printf("%2c", Z[m*N1+n]); printf("\n");} //getchar; //printf("Z1 Z2= %c %d  %c %d \n",Z[1],Z[1],Z[2],Z[2]); //DB t,u,v;//Begin with singularities // if singularity at the down-left of the cell DO(m,M-1) DO(n,N-1) { if(zmn=='p') {bdpq; //pri("Sp: %2d %2d %5.2f %5.2f %5.2f %5.3f\n",m,n,b,d,p,q); if(b*d<0&&z(m,n+1)==' '){x=Xm+(XM-Xm)*b/(b-d);y=YN;Mxy; drift(o,F,Z,X,Y,M,N,m,n+1,UPP);} if(q*d<0&&z(m+1,n)==' '){y=Yn+(YN-Yn)*q/(q-d);x=XM;Mxy; drift(o,F,Z,X,Y,M,N,m+1,n,RIG);} if(d*d==0&&z(m+1,n+1)==' '){                   M(XM,YN); drift(o,F,Z,X,Y,M,N,m+1,n+1,RIG);} } } // Check for singularity at down-right for(m=1;m<M;m++) DO(n,N-1) {if(zmn=='q') //how about to go up-left? {bdpq; //pri("Sq: %2d %2d %5.2f %5.2f %5.2f %5.3f\n",m,n,b,d,p,q); if(b*d<0&&z(m,n+1)==' '){x=Xm+(XM-Xm)*b/(b-d);y=YN;Mxy;drift(o,F,Z,X,Y,M,N,m,n+1,UPP);} if(b*p<0&&z(m-1,n)==' '){y=Yn+(YN-Yn)*p/(p-b);x=Xm;Mxy;drift(o,F,Z,X,Y,M,N,m-1,n,LEF);} if(b*b==0&&z(m-1,n+1)==' '){                   M(Xm,YN);drift(o,F,Z,X,Y,M,N,m-1,n+1,LEF);} } } //Check for singularity at the top left corger. How about to go down-right? DO(m,M-1) for(n=1;n<N;n++) { if(zmn=='b') {bdpq; //pri("Sb: %2d %2d %5.2f %5.2f %5.2f %5.3f\n",m,n,b,d,p,q); if(q*p<0&&z(m,n-1)==' '){x=Xm+(XM-Xm)*p/(p-q);y=Yn;Mxy;drift(o,F,Z,X,Y,M,N,m,n-1,DOW);} if(q*d<0&&z(m+1,n)==' '){y=Yn+(YN-Yn)*q/(q-d);x=XM;Mxy;drift(o,F,Z,X,Y,M,N,m+1,n,RIG);} if(q*q==0&&z(m-1,n-1)==' '){                 M(XM,Yn);drift(o,F,Z,X,Y,M,N,m+1,n-1,RIG);} } } for(m=1;m<M;m++) for(n=1;n<N;n++) { if(zmn=='d') // singularity at the up-right corner of this sell. go down-left? {bdpq; //pri("Sd: %2d %2d %5.2f %5.2f %5.2f %5.3f\n",m,n,b,d,p,q); if(p*q<0&&z(m,n-1)==' '){x=Xm+(XM-Xm)*p/(p-q);y=Yn;Mxy;drift(o,F,Z,X,Y,M,N,m,n-1,DOW);} if(p*b<0&&z(n-1,n)==' '){y=Yn+(YN-Yn)*p/(p-b);x=Xm;Mxy;drift(o,F,Z,X,Y,M,N,m-1,n,LEF);} if(p*p==0&&z(m-1,n-1)==' '){                 M(Xm,Yn);drift(o,F,Z,X,Y,M,N,m-1,n-1,LEF);} } } //Trace the margin of the domain

n=0; // printf("n=%3d\n",n); DO(m,M) { if(zmn==' ')	{ bdpq; if(p*q<=0){ if(p>q || q>p) { x=Xm+(XM-Xm)*p/(p-q); y=Yn; Mxy; drift(o,F,Z,X,Y,M,N,m,n,UPP);}} } }

n=N-1; //printf("n=%3d\n",n); DO(m,M) { if(zmn==' '){bdpq; if(b*d<=0){ if(b>d || d>b) {	x=Xm+(XM-Xm)*b/(b-d); y=YN; Mxy; drift(o,F,Z,X,Y,M,N,m,n,DOW);}} }   } m=0; //printf("m=%3d\n",m); DO(n,N) { if(zmn==' '){bdpq; if(b*p<=0) { if(p>b || pd || q0;n--) for(m=M-1;m>0;m--) {    if(zmn==' ')	{ bdpq; if(d*q<0){    y=Yn+(YN-Yn)*q/(q-d); x=XM;Mxy; drift(o,F,Z,X,Y,M,N,m+1,n,RIG); if(zmn==' '){ Mxy; drift(o,F,Z,X,Y,M,N,m,n,LEF); } 			 } 		}  }

//  if(zmn==' ')	{ if(b*d<0){ 	x=Xm+(XM-Xm)*b/(b-d);	 y=YN; Mxy; //				 drift(o,F,Z,X,Y,M,N,m,n,UPP);}}} return 0;} //end
 * 1) undef Mxy
 * 2) undef Lxy
 * 3) undef f
 * 4) undef z
 * 5) undef zmn
 * 6) undef zMn
 * 7) undef zmN
 * 8) undef zMN
 * 9) undef fmn
 * 10) undef fMn
 * 11) undef fmN
 * 12) undef fMN
 * 13) undef Xm
 * 14) undef XM
 * 15) undef Yn
 * 16) undef YN
 * 17) undef bdpq
 * 18) undef UPP
 * 19) undef LEF
 * 20) undef DOW
 * 21) undef RIG

/* End of routine

*/