// generate double bivariate Chebychev polynomial
public static bool bchgen(projUV a, projUV b, int nu, int nv, projUV[][] f, ProjFunc func)
{
projUV arg, bma, bpa;
projUV[] t, c;
bma.u = 0.5 * (b.u - a.u); bma.v = 0.5 * (b.v - a.v);
bpa.u = 0.5 * (b.u + a.u); bpa.v = 0.5 * (b.v + a.v);
for (int i = 0; i < nu; i++)
{
arg.u = Math.Cos(Proj.PI * (i + 0.5) / nu) * bma.u + bpa.u;
for (int j = 0; j < nv; j++)
{
arg.v = Math.Cos(Proj.PI * (j + 0.5) / nv) * bma.v + bpa.v;
f[i][j] = func(arg);
if (f[i][j].u == Libc.HUGE_VAL)
{
return(true);
}
}
}
try
{
c = new projUV[nu];
}
catch
{
return(true);
}
double fac = 2.0 / nu;
for (int j = 0; j < nv; j++)
{
for (int i = 0; i < nu; i++)
{
arg.u = arg.v = 0.0;
for (int k = 0; k < nu; k++)
{
double d = Math.Cos(Proj.PI * i * (k + 0.5) / nu);
arg.u += f[k][j].u * d;
arg.v += f[k][j].v * d;
}
arg.u *= fac;
arg.v *= fac;
c[i] = arg;
}
for (int i = 0; i < nu; i++)
{
f[i][j] = c[i];
}
}
try
{
c = new projUV[nv];
}
catch
{
return(true);
}
fac = 2.0 / nv;
for (int i = 0; i < nu; i++)
{
t = f[i];
for (int j = 0; j < nv; j++)
{
arg.u = arg.v = 0.0;
for (int k = 0; k < nv; k++)
{
double d = Math.Cos(Proj.PI * j * (k + 0.5) / nv);
arg.u += t[k].u * d;
arg.v += t[k].v * d;
}
arg.u *= fac;
arg.v *= fac;
c[j] = arg;
}
f[i] = c;
c = t;
}
return(false);
}
public static Tseries mk_cheby(projUV a, projUV b, double res, ref projUV resid, ProjFunc func, int nu, int nv, bool power)
{
try
{
projUV[][] w = new projUV[nu][];
for (int k = 0; k < nu; k++)
{
w[k] = new projUV[nv];
}
if (bchgen(a, b, nu, nv, w, func))
{
return(null);
}
// analyse coefficients and adjust until residual OK
double cutres = res;
int i = 4;
for (; i > 0; i--)
{
eval(w, nu, nv, cutres, ref resid);
if (resid.u < res && resid.v < res)
{
break;
}
cutres *= 0.5;
}
// warn of too many tries
if (i <= 0)
{
resid.u = -resid.u;
}
double ab;
double[] p;
int[] ncu = new int[nu];
int[] ncv = new int[nv];
// apply cut resolution and set pointers
int nru = 0, nrv = 0;
for (int j = 0; j < nu; ++j)
{
ncu[j] = ncv[j] = 0; // clear column maxes
projUV[] s = w[j];
for (i = 0; i < nv; i++)
{
// < resolution ?
ab = Math.Abs(s[i].u);
if (ab < cutres)
{
s[i].u = 0.0; // clear coefficient
}
else
{
ncu[j] = i + 1; // update column max
}
ab = Math.Abs(s[i].v);
if (ab < cutres)
{
s[i].v = 0.0; // same for v coef's
}
else
{
ncv[j] = i + 1;
}
}
if (ncu[j] != 0)
{
nru = j + 1; // update row max
}
if (ncv[j] != 0)
{
nrv = j + 1;
}
}
if (power)
{ // convert to bivariate power series
if (!bch2bps(a, b, w, nu, nv))
{
return(null);
}
// possible change in some row counts, so readjust
nru = nrv = 0;
for (int j = 0; j < nu; ++j)
{
ncu[j] = ncv[j] = 0; // clear column maxes
projUV[] s = w[j];
for (i = 0; i < nv; i++)
{
if (s[i].u != 0)
{
ncu[j] = i + 1; // update column max
}
if (s[i].v != 0)
{
ncv[j] = i + 1;
}
}
if (ncu[j] != 0)
{
nru = j + 1; // update row max
}
if (ncv[j] != 0)
{
nrv = j + 1;
}
}
Tseries T = makeT(nru, nrv);
if (T != null)
{
T.a = a;
T.b = b;
T.mu = nru - 1;
T.mv = nrv - 1;
T.power = 1;
for (i = 0; i < nru; ++i) // store coefficient rows for u
{
T.cu[i].m = ncu[i];
if (T.cu[i].m != 0)
{
p = T.cu[i].c = new double[ncu[i]];
projUV[] s = w[i];
for (int j = 0; j < ncu[i]; j++)
{
p[j] = s[j].u;
}
}
}
for (i = 0; i < nrv; ++i) // same for v
{
T.cv[i].m = ncv[i];
if (T.cv[i].m != 0)
{
p = T.cv[i].c = new double[ncv[i]];
projUV[] s = w[i];
for (int j = 0; j < ncv[i]; j++)
{
p[j] = s[j].v;
}
}
}
}
return(T);
}
else
{
Tseries T = makeT(nru, nrv);
if (T != null)
{
// else make returned Chebyshev coefficient structure
T.mu = nru - 1; // save row degree
T.mv = nrv - 1;
T.a.u = a.u + b.u; // set argument scaling
T.a.v = a.v + b.v;
T.b.u = 1.0 / (b.u - a.u);
T.b.v = 1.0 / (b.v - a.v);
T.power = 0;
for (i = 0; i < nru; ++i) // store coefficient rows for u
{
T.cu[i].m = ncu[i];
if (T.cu[i].m != 0)
{
p = T.cu[i].c = new double[ncu[i]];
projUV[] s = w[i];
for (int j = 0; j < ncu[i]; j++)
{
p[j] = s[j].u;
}
}
}
for (i = 0; i < nrv; ++i) // same for v
{
T.cv[i].m = ncv[i];
if (T.cv[i].m != 0)
{
p = T.cv[i].c = new double[ncv[i]];
projUV[] s = w[i];
for (int j = 0; j < ncv[i]; j++)
{
p[j] = s[j].v;
}
}
}
}
return(T);
}
}
catch
{
return(null);
}
}
public static Tseries mk_cheby(projUV a, projUV b, double res, ref projUV resid, ProjFunc func, int nu, int nv, bool power)
{
try
{
projUV[][] w=new projUV[nu][];
for(int k=0; k<nu; k++) w[k]=new projUV[nv];
if(bchgen(a, b, nu, nv, w, func)) return null;
// analyse coefficients and adjust until residual OK
double cutres=res;
int i=4;
for(; i>0; i--)
{
eval(w, nu, nv, cutres, ref resid);
if(resid.u<res&&resid.v<res) break;
cutres*=0.5;
}
// warn of too many tries
if(i<=0) resid.u=-resid.u;
double ab;
double[] p;
int[] ncu=new int[nu];
int[] ncv=new int[nv];
// apply cut resolution and set pointers
int nru=0, nrv=0;
for(int j=0; j<nu; ++j)
{
ncu[j]=ncv[j]=0; // clear column maxes
projUV[] s=w[j];
for(i=0; i<nv; i++)
{
// < resolution ?
ab=Math.Abs(s[i].u);
if(ab<cutres) s[i].u=0.0; // clear coefficient
else ncu[j]=i+1; // update column max
ab=Math.Abs(s[i].v);
if(ab<cutres) s[i].v=0.0; // same for v coef's
else ncv[j]=i+1;
}
if(ncu[j]!=0) nru=j+1; // update row max
if(ncv[j]!=0) nrv=j+1;
}
if(power)
{ // convert to bivariate power series
if(!bch2bps(a, b, w, nu, nv)) return null;
// possible change in some row counts, so readjust
nru=nrv=0;
for(int j=0; j<nu; ++j)
{
ncu[j]=ncv[j]=0; // clear column maxes
projUV[] s=w[j];
for(i=0; i<nv; i++)
{
if(s[i].u!=0) ncu[j]=i+1; // update column max
if(s[i].v!=0) ncv[j]=i+1;
}
if(ncu[j]!=0) nru=j+1; // update row max
if(ncv[j]!=0) nrv=j+1;
}
Tseries T=makeT(nru, nrv);
if(T!=null)
{
T.a=a;
T.b=b;
T.mu=nru-1;
T.mv=nrv-1;
T.power=1;
for(i=0; i<nru; ++i) // store coefficient rows for u
{
T.cu[i].m=ncu[i];
if(T.cu[i].m!=0)
{
p=T.cu[i].c=new double[ncu[i]];
projUV[] s=w[i];
for(int j=0; j<ncu[i]; j++) p[j]=s[j].u;
}
}
for(i=0; i<nrv; ++i) // same for v
{
T.cv[i].m=ncv[i];
if(T.cv[i].m!=0)
{
p=T.cv[i].c=new double[ncv[i]];
projUV[] s=w[i];
for(int j=0; j<ncv[i]; j++) p[j]=s[j].v;
}
}
}
return T;
}
else
{
Tseries T=makeT(nru, nrv);
if(T!=null)
{
// else make returned Chebyshev coefficient structure
T.mu=nru-1; // save row degree
T.mv=nrv-1;
T.a.u=a.u+b.u; // set argument scaling
T.a.v=a.v+b.v;
T.b.u=1.0/(b.u-a.u);
T.b.v=1.0/(b.v-a.v);
T.power=0;
for(i=0; i<nru; ++i) // store coefficient rows for u
{
T.cu[i].m=ncu[i];
if(T.cu[i].m!=0)
{
p=T.cu[i].c=new double[ncu[i]];
projUV[] s=w[i];
for(int j=0; j<ncu[i]; j++) p[j]=s[j].u;
}
}
for(i=0; i<nrv; ++i) // same for v
{
T.cv[i].m=ncv[i];
if(T.cv[i].m!=0)
{
p=T.cv[i].c=new double[ncv[i]];
projUV[] s=w[i];
for(int j=0; j<ncv[i]; j++) p[j]=s[j].v;
}
}
}
return T;
}
}
catch
{
return null;
}
}
public static void gen_cheb(bool inverse, ProjFunc proj, string s, PJ P, int iargc, string[] iargv)
{
InputFunc input=Proj.dmstor;
if(inverse) input=Libc.strtod;
int errin=0;
projUV low, upp;
low.u=low.v=upp.u=upp.v=0;
if(s.Length>0) low.u=input(s, out s); else errin++;
if(s.Length>1&&s[0]==',') upp.u=input(s.Substring(1), out s); else errin++;
if(s.Length>1&&s[0]==',') low.v=input(s.Substring(1), out s); else errin++;
if(s.Length>1&&s[0]==',') upp.v=input(s.Substring(1), out s); else errin++;
if(errin!=0) emess(16, "null or absent -T parameters");
int NU=15, NV=15, res=-1;
if(s.Length>1&&s[0]==',')
{
s=s.Substring(1);
if(s[0]!=',') res=Libc.strtol(s, out s, 10);
}
if(s.Length>1&&s[0]==',')
{
s=s.Substring(1);
if(s[0]!=',') NU=Libc.strtol(s, out s, 10);
}
if(s.Length>1&&s[0]==',')
{
s=s.Substring(1);
if(s[0]!=',') NV=Libc.strtol(s, out s, 10);
}
bool pwr=s.Length>0&&s.StartsWith(",P");
Console.WriteLine("#proj_{0}\n#\trun-line:", pwr?"Power":"Chebyshev");
// proj execution audit trail
if(iargc>0)
{
int n=0;
for(int i=0; i<iargc; i++)
{
string arg=iargv[i];
if(arg[0]!='+')
{
if(n==0)
{
Console.Write("#");
n++;
}
Console.Write(" "+arg);
n+=arg.Length+1;
if(n>50)
{
Console.WriteLine(); n=0;
}
}
}
if(n!=0) Console.WriteLine();
}
Console.WriteLine("# projection parameters");
Console.WriteLine("#"+P.DescriptionName);
Console.WriteLine("#"+P.DescriptionParameters);
Console.WriteLine("#"+P.DescriptionType);
Console.WriteLine("#"+P.ToProj4String());
if(low.u==upp.u||low.v>=upp.v) emess(16, "approx. argument range error");
if(low.u>upp.u) low.u-=Proj.TWOPI;
if(NU<2||NV<2) emess(16, "approx. work dimensions ({0} {1}) too small", NU, NV);
projUV resid=new projUV();
Tseries F=mk_cheby(low, upp, Math.Pow(10.0, res)*0.5, ref resid, proj, NU, NV, pwr);
if(F==null) emess(16, "generation of approx failed\nreason: {0}\n", Proj.pj_strerrno(Libc.errno));
Console.WriteLine("{0},{1:G12},{2:G12},{3:G12},{4:G12},{5:G12}", inverse?'I':'F', P.lam0*Proj.RAD_TO_DEG,
low.u*(inverse?1.0:Proj.RAD_TO_DEG), upp.u*(inverse?1.0:Proj.RAD_TO_DEG),
low.v*(inverse?1.0:Proj.RAD_TO_DEG), upp.v*(inverse?1.0:Proj.RAD_TO_DEG));
string fmt;
if(pwr) fmt="G15";
else if(res<=0) fmt=string.Format("F{0}", -res+1);
else fmt="F0";
p_series(F, Console.Out, fmt);
Console.WriteLine("# |u,v| sums {0} {1}\n#end_proj_{2}", resid.u, resid.v, pwr?"Power":"Chebyshev");
}
// generate double bivariate Chebychev polynomial
public static bool bchgen(projUV a, projUV b, int nu, int nv, projUV[][] f, ProjFunc func)
{
projUV arg, bma, bpa;
projUV[] t, c;
bma.u=0.5*(b.u-a.u); bma.v=0.5*(b.v-a.v);
bpa.u=0.5*(b.u+a.u); bpa.v=0.5*(b.v+a.v);
for(int i=0; i<nu; i++)
{
arg.u=Math.Cos(Proj.PI*(i+0.5)/nu)*bma.u+bpa.u;
for(int j=0; j<nv; j++)
{
arg.v=Math.Cos(Proj.PI*(j+0.5)/nv)*bma.v+bpa.v;
f[i][j]=func(arg);
if(f[i][j].u==Libc.HUGE_VAL) return true;
}
}
try
{
c=new projUV[nu];
}
catch
{
return true;
}
double fac=2.0/nu;
for(int j=0; j<nv; j++)
{
for(int i=0; i<nu; i++)
{
arg.u=arg.v=0.0;
for(int k=0; k<nu; k++)
{
double d=Math.Cos(Proj.PI*i*(k+0.5)/nu);
arg.u+=f[k][j].u*d;
arg.v+=f[k][j].v*d;
}
arg.u*=fac;
arg.v*=fac;
c[i]=arg;
}
for(int i=0; i<nu; i++) f[i][j]=c[i];
}
try
{
c=new projUV[nv];
}
catch
{
return true;
}
fac=2.0/nv;
for(int i=0; i<nu; i++)
{
t=f[i];
for(int j=0; j<nv; j++)
{
arg.u=arg.v=0.0;
for(int k=0; k<nv; k++)
{
double d=Math.Cos(Proj.PI*j*(k+0.5)/nv);
arg.u+=t[k].u*d;
arg.v+=t[k].v*d;
}
arg.u*=fac;
arg.v*=fac;
c[j]=arg;
}
f[i]=c;
c=t;
}
return false;
}
public static void gen_cheb(bool inverse, ProjFunc proj, string s, PJ P, int iargc, string[] iargv)
{
InputFunc input = Proj.dmstor;
if (inverse)
{
input = Libc.strtod;
}
int errin = 0;
projUV low, upp;
low.u = low.v = upp.u = upp.v = 0;
if (s.Length > 0)
{
low.u = input(s, out s);
}
else
{
errin++;
}
if (s.Length > 1 && s[0] == ',')
{
upp.u = input(s.Substring(1), out s);
}
else
{
errin++;
}
if (s.Length > 1 && s[0] == ',')
{
low.v = input(s.Substring(1), out s);
}
else
{
errin++;
}
if (s.Length > 1 && s[0] == ',')
{
upp.v = input(s.Substring(1), out s);
}
else
{
errin++;
}
if (errin != 0)
{
emess(16, "null or absent -T parameters");
}
int NU = 15, NV = 15, res = -1;
if (s.Length > 1 && s[0] == ',')
{
s = s.Substring(1);
if (s[0] != ',')
{
res = Libc.strtol(s, out s, 10);
}
}
if (s.Length > 1 && s[0] == ',')
{
s = s.Substring(1);
if (s[0] != ',')
{
NU = Libc.strtol(s, out s, 10);
}
}
if (s.Length > 1 && s[0] == ',')
{
s = s.Substring(1);
if (s[0] != ',')
{
NV = Libc.strtol(s, out s, 10);
}
}
bool pwr = s.Length > 0 && s.StartsWith(",P");
Console.WriteLine("#proj_{0}\n#\trun-line:", pwr?"Power":"Chebyshev");
// proj execution audit trail
if (iargc > 0)
{
int n = 0;
for (int i = 0; i < iargc; i++)
{
string arg = iargv[i];
if (arg[0] != '+')
{
if (n == 0)
{
Console.Write("#");
n++;
}
Console.Write(" " + arg);
n += arg.Length + 1;
if (n > 50)
{
Console.WriteLine(); n = 0;
}
}
}
if (n != 0)
{
Console.WriteLine();
}
}
Console.WriteLine("# projection parameters");
Console.WriteLine("#" + P.DescriptionName);
Console.WriteLine("#" + P.DescriptionParameters);
Console.WriteLine("#" + P.DescriptionType);
Console.WriteLine("#" + P.ToProj4String());
if (low.u == upp.u || low.v >= upp.v)
{
emess(16, "approx. argument range error");
}
if (low.u > upp.u)
{
low.u -= Proj.TWOPI;
}
if (NU < 2 || NV < 2)
{
emess(16, "approx. work dimensions ({0} {1}) too small", NU, NV);
}
projUV resid = new projUV();
Tseries F = mk_cheby(low, upp, Math.Pow(10.0, res) * 0.5, ref resid, proj, NU, NV, pwr);
if (F == null)
{
emess(16, "generation of approx failed\nreason: {0}\n", Proj.pj_strerrno(Libc.errno));
}
Console.WriteLine("{0},{1:G12},{2:G12},{3:G12},{4:G12},{5:G12}", inverse?'I':'F', P.lam0 * Proj.RAD_TO_DEG,
low.u * (inverse?1.0:Proj.RAD_TO_DEG), upp.u * (inverse?1.0:Proj.RAD_TO_DEG),
low.v * (inverse?1.0:Proj.RAD_TO_DEG), upp.v * (inverse?1.0:Proj.RAD_TO_DEG));
string fmt;
if (pwr)
{
fmt = "G15";
}
else if (res <= 0)
{
fmt = string.Format("F{0}", -res + 1);
}
else
{
fmt = "F0";
}
p_series(F, Console.Out, fmt);
Console.WriteLine("# |u,v| sums {0} {1}\n#end_proj_{2}", resid.u, resid.v, pwr?"Power":"Chebyshev");
}
