Conto.cin
Revision as of 06:59, 1 December 2018 by Maintenance script (talk | contribs)
// 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.
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#include"ado.cin"
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#define M(x,y) fprintf(o,"%6.4f %6.4f M\n",1.*(x),1.*(y));
#define L(x,y) fprintf(o,"%6.4f %6.4f L\n",1.*(x),1.*(y));
//#define o(x,y) fprintf(o,"%5.3f %5.3f o\n",1.*(x),1.*(y));
#define Mxy M(x,y)
#define Lxy L(x,y)
#define f(m,n) F[(m)*N1+(n)]
#define z(m,n) Z[(m)*N1+(n)]
#define zmn z(m,n)
#define zMn z(m+1,n)
#define zmN z(m,n+1)
#define zMN z(m+1,n+1)
#define fmn f(m,n)
#define fMn f(m+1,n)
#define fmN f(m,n+1)
#define fMN f(m+1,n+1)
#define Xm X[m]
#define XM X[m+1]
#define Yn Y[n]
#define YN Y[n+1]
#define bdpq {b=f(m,n+1);d=f(m+1,n+1);p=f(m,n);q=f(m+1,n);}
#define UPP 1
#define LEF 2
#define DOW 3
#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<w && w<L2) { F[m*N1+n]=w;}
else{ //o(X[m],Y[n]);
F[m*N1+n]=0; z(m,n)='p';if(m> 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 || p<b)
{ y=Yn+(YN-Yn)*p/(p-b);
x=Xm; Mxy;
drift(o,F,Z,X,Y,M,N,m,n,RIG);}}
}
}
// This was repaired
m=M-1; //printf("m=%3d\n",m);
DO(n,N)
{ if(zmn==' '){bdpq;
if(d*q<=0) { if( q>d || q<d )
{ y=Yn+(YN-Yn)*q/(q-d);
x=XM; Mxy;
drift(o,F,Z,X,Y,M,N,m,n,LEF);}}
}
}
//Check if any loops inside the domain
// for(n=1;n<N-1;n++)
// for(m=1;m<M-1;m++)
for(n=N-1;n>0;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
#undef Mxy
#undef Lxy
#undef f
#undef z
#undef zmn
#undef zMn
#undef zmN
#undef zMN
#undef fmn
#undef fMn
#undef fmN
#undef fMN
#undef Xm
#undef XM
#undef Yn
#undef YN
#undef bdpq
#undef UPP
#undef LEF
#undef DOW
#undef RIG
/* End of routine */