// entry point
public static bool bch2bps(projUV a, projUV b, projUV[][] c, int nu, int nv)
{
if(nu<1||nv<1) return false;
try
{
projUV[][] d=new projUV[nu][];
for(int i=0; i<nu; i++)
{
d[i]=new projUV[nv];
// do rows to power series
rows(c[i], d[i], nv);
rowshft(a.v, b.v, d[i], nv);
}
// do columns to power series
cols(d, c, nu, nv);
colshft(a.u, b.u, c, nu, nv);
return true;
}
catch
{
return false;
}
}
// convert columns to power series
static void cols(projUV[][] c, projUV[][] d, int nu, int nv)
{
projUV[][] dd=new projUV[nu][];
for(int i=0; i<nu; i++) dd[i]=new projUV[nv];
projUV[] sv=new projUV[nv];
bclear(d, nu, nv);
bclear(dd, nu, nv);
bmove(d[0], c[nu-1], nv);
for(int j=nu-2; j>=1; j--)
{
for(int k=nu-j; k>=1; k--)
{
bmove(sv, d[k], nv);
submop(d[k], 2.0, d[k-1], dd[k], nv);
bmove(dd[k], sv, nv);
}
bmove(sv, d[0], nv);
subop(d[0], c[j], dd[0], nv);
bmove(dd[0], sv, nv);
}
for(int j=nu-1; j>=1; j--) subop(d[j], d[j-1], dd[j], nv);
submop(d[0], 0.5, c[0], dd[0], nv);
}
// entry point
public static bool bch2bps(projUV a, projUV b, projUV[][] c, int nu, int nv)
{
if (nu < 1 || nv < 1)
{
return(false);
}
try
{
projUV[][] d = new projUV[nu][];
for (int i = 0; i < nu; i++)
{
d[i] = new projUV[nv];
// do rows to power series
rows(c[i], d[i], nv);
rowshft(a.v, b.v, d[i], nv);
}
// do columns to power series
cols(d, c, nu, nv);
colshft(a.u, b.u, c, nu, nv);
return(true);
}
catch
{
return(false);
}
}
// convert columns to power series
static void cols(projUV[][] c, projUV[][] d, int nu, int nv)
{
projUV[][] dd = new projUV[nu][];
for (int i = 0; i < nu; i++)
{
dd[i] = new projUV[nv];
}
projUV[] sv = new projUV[nv];
bclear(d, nu, nv);
bclear(dd, nu, nv);
bmove(d[0], c[nu - 1], nv);
for (int j = nu - 2; j >= 1; j--)
{
for (int k = nu - j; k >= 1; k--)
{
bmove(sv, d[k], nv);
submop(d[k], 2.0, d[k - 1], dd[k], nv);
bmove(dd[k], sv, nv);
}
bmove(sv, d[0], nv);
subop(d[0], c[j], dd[0], nv);
bmove(dd[0], sv, nv);
}
for (int j = nu - 1; j >= 1; j--)
{
subop(d[j], d[j - 1], dd[j], nv);
}
submop(d[0], 0.5, c[0], dd[0], nv);
}
// bivariate power polynomial entry point
public static projUV bpseval(projUV @in, Tseries T)
{
projUV @out;
@[email protected]=0.0;
for(int i=T.mu; i>=0; --i)
{
double row=0.0;
int m=T.cu[i].m;
if(m!=0)
{
int c=m;
while((m--)!=0) row=T.cu[i].c[--c][email protected]*row;
}
@[email protected]*@out.u;
}
for(int i=T.mv; i>=0; --i)
{
double row=0.0;
int m=T.cv[i].m;
if(m!=0)
{
int c=m;
while((m--)!=0) row=T.cv[i].c[--c][email protected]*row;
}
@[email protected]*@out.v;
}
return @out;
}
// general entry point selecting evaluation mode
public static projUV biveval(projUV @in, Tseries T)
{
if (T.power != 0)
{
return(bpseval(@in, T));
}
return(bcheval(@in, T));
}
//单点-正投影
public PointF GetXYFromLatLon(PointF pointOrg, MapHandle.config.ProjPara proj)
{
pointOrg.X = (float)(pointOrg.X * DEG2RAD);
pointOrg.Y = (float)(pointOrg.Y * DEG2RAD);
//投影参数初始化
IntPtr pj = ProjWrapper.pj_init_plus(getSrcProj(proj));
projUV temp = new projUV(pointOrg.X, pointOrg.Y);
projUV coord = ProjWrapper.pj_fwd(temp, pj);
PointF pointPrj = new PointF();
pointPrj.X = (float)(coord.U);
pointPrj.Y = (float)(coord.V);
return pointPrj;
}
//单点-反投影
public PointF GetLatLonFromXY(PointF pointXY, MapHandle.config.ProjPara proj)
{
//投影参数初始化
PointF result = new PointF();
IntPtr pj = ProjWrapper.pj_init_plus(getSrcProj(proj));
projUV temp = new projUV(pointXY.X, pointXY.Y);
projUV coord = ProjWrapper.pj_inv(temp, pj);
result.X = (float)(coord.U);
result.Y = (float)(coord.V);
result.X = (float)(result.X * RAD2DEG);
result.Y = (float)(result.Y * RAD2DEG);
return result;
}
//单点-反投影
public PointF GetLatLonFromXY(PointF pointXY, MapHandle.config.ProjPara proj)
{
//投影参数初始化
PointF result = new PointF();
IntPtr pj = ProjWrapper.pj_init_plus(getSrcProj(proj));
projUV temp = new projUV(pointXY.X, pointXY.Y);
projUV coord = ProjWrapper.pj_inv(temp, pj);
result.X = (float)(coord.U);
result.Y = (float)(coord.V);
result.X = (float)(result.X * RAD2DEG);
result.Y = (float)(result.Y * RAD2DEG);
return(result);
}
//单点-正投影
public PointF GetXYFromLatLon(PointF pointOrg, MapHandle.config.ProjPara proj)
{
pointOrg.X = (float)(pointOrg.X * DEG2RAD);
pointOrg.Y = (float)(pointOrg.Y * DEG2RAD);
//投影参数初始化
IntPtr pj = ProjWrapper.pj_init_plus(getSrcProj(proj));
projUV temp = new projUV(pointOrg.X, pointOrg.Y);
projUV coord = ProjWrapper.pj_fwd(temp, pj);
PointF pointPrj = new PointF();
pointPrj.X = (float)(coord.U);
pointPrj.Y = (float)(coord.V);
return(pointPrj);
}
// column adjust for range -1 to 1 to a to b
static void colshft(double a, double b, projUV[][] d, int n, int m)
{
double cnst=2.0/(b-a);
double fac=cnst;
for(int j=1; j<n; j++)
{
dmult(d[j], fac, m);
fac*=cnst;
}
cnst=0.5*(a+b);
for(int j=0; j<=n-2; j++)
for(int k=n-2; k>=j; k--)
dadd(d[k], d[k+1], cnst, m);
}
static double ceval(PW_COEF[] C, int n, projUV w, projUV w2)
{
double d = 0, dd = 0;
int j;
PW_COEF C1;
for (; n != 0; n--)
{
C1 = C[n];
j = C1.m;
double tmp = d;
if (j != 0)
{
double vd = 0.0, vdd = 0.0;
j--;
for (; j != 0; j--)
{
double tmp2 = vd;
vd = w2.v * tmp2 - vdd + C1.c[j];
vdd = tmp2;
}
d = w2.u * tmp - dd + w.v * vd - vdd + 0.5 * C1.c[j];
}
else
{
d = w2.u * tmp - dd;
}
dd = tmp;
}
C1 = C[0];
j = C1.m;
if (j != 0)
{
double vd = 0.0, vdd = 0.0;
j--;
for (; j != 0; j--)
{
double tmp2 = vd;
vd = w2.v * tmp2 - vdd + C1.c[j];
vdd = tmp2;
}
return(w.u * d - dd + 0.5 * (w.v * vd - vdd + 0.5 * C1.c[j]));
}
return(w.u * d - dd);
}
static double ceval(PW_COEF[] C, int n, projUV w, projUV w2)
{
double d=0, dd=0;
int j;
PW_COEF C1;
for(; n!=0; n--)
{
C1=C[n];
j=C1.m;
double tmp=d;
if(j!=0)
{
double vd=0.0, vdd=0.0;
j--;
for(; j!=0; j--)
{
double tmp2=vd;
vd=w2.v*tmp2-vdd+C1.c[j];
vdd=tmp2;
}
d=w2.u*tmp-dd+w.v*vd-vdd+0.5*C1.c[j];
}
else d=w2.u*tmp-dd;
dd=tmp;
}
C1=C[0];
j=C1.m;
if(j!=0)
{
double vd=0.0, vdd=0.0;
j--;
for(; j!=0; j--)
{
double tmp2=vd;
vd=w2.v*tmp2-vdd+C1.c[j];
vdd=tmp2;
}
return w.u*d-dd+0.5*(w.v*vd-vdd+0.5*C1.c[j]);
}
return w.u*d-dd;
}
// sum coefficients less than res
static void eval(projUV[][] w, int nu, int nv, double res, ref projUV resid)
{
resid.u = resid.v = 0.0;
for (int i = 0; i < nu; i++)
{
for (int j = 0; j < nv; j++)
{
projUV s = w[i][j];
double ab = Math.Abs(s.u);
if (ab < res)
{
resid.u += ab;
}
ab = Math.Abs(s.v);
if (ab < res)
{
resid.v += ab;
}
}
}
}
// bivariate power polynomial entry point
public static projUV bpseval(projUV @in, Tseries T)
{
projUV @out;
@out.u = @out.v = 0.0;
for (int i = T.mu; i >= 0; --i)
{
double row = 0.0;
int m = T.cu[i].m;
if (m != 0)
{
int c = m;
while ((m--) != 0)
{
row = T.cu[i].c[--c] + @in.v * row;
}
}
@out.u = row + @in.u * @out.u;
}
for (int i = T.mv; i >= 0; --i)
{
double row = 0.0;
int m = T.cv[i].m;
if (m != 0)
{
int c = m;
while ((m--) != 0)
{
row = T.cv[i].c[--c] + @in.v * row;
}
}
@out.v = row + @in.u * @out.v;
}
return(@out);
}
// bivariate Chebyshev polynomial entry point
public static projUV bcheval(projUV @in, Tseries T)
{
projUV w2, w, @out;
// scale to +-1
w.u = (@in.u + @in.u - T.a.u) * T.b.u;
w.v = (@in.v + @in.v - T.a.v) * T.b.v;
if (Math.Abs(w.u) > NEAR_ONE || Math.Abs(w.v) > NEAR_ONE)
{
@out.u = @out.v = Libc.HUGE_VAL;
Proj.pj_errno = -36;
}
else
{ // double evaluation
w2.u = w.u + w.u;
w2.v = w.v + w.v;
@out.u = ceval(T.cu, T.mu, w, w2);
@out.v = ceval(T.cv, T.mv, w, w2);
}
return(@out);
}
// bivariate Chebyshev polynomial entry point
public static projUV bcheval(projUV @in, Tseries T)
{
projUV w2, w, @out;
// scale to +-1
w.u=(@[email protected])*T.b.u;
w.v=(@[email protected])*T.b.v;
if(Math.Abs(w.u)>NEAR_ONE||Math.Abs(w.v)>NEAR_ONE)
{
@[email protected]=Libc.HUGE_VAL;
Proj.pj_errno=-36;
}
else
{ // double evaluation
w2.u=w.u+w.u;
w2.v=w.v+w.v;
@out.u=ceval(T.cu, T.mu, w, w2);
@out.v=ceval(T.cv, T.mv, w, w2);
}
return @out;
}
// convert row to pover series
static void rows(projUV[] c, projUV[] d, int n)
{
projUV[] dd = new projUV[n];
projUV sv;
sv.u = sv.v = 0.0;
for (int j = 0; j < n; j++)
{
d[j] = dd[j] = sv;
}
d[0] = c[n - 1];
for (int j = n - 2; j >= 1; j--)
{
for (int k = n - j; k >= 1; k--)
{
sv = d[k];
d[k].u = 2.0 * d[k - 1].u - dd[k].u;
d[k].v = 2.0 * d[k - 1].v - dd[k].v;
dd[k] = sv;
}
sv = d[0];
d[0].u = -dd[0].u + c[j].u;
d[0].v = -dd[0].v + c[j].v;
dd[0] = sv;
}
for (int j = n - 1; j >= 1; j--)
{
d[j].u = d[j - 1].u - dd[j].u;
d[j].v = d[j - 1].v - dd[j].v;
}
d[0].u = -dd[0].u + 0.5 * c[0].u;
d[0].v = -dd[0].v + 0.5 * c[0].v;
}
// 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;
}
// move vector
static void bmove(projUV[] a, projUV[] b, int n)
{
for(int i=0; i<n; i++) a[i]=b[i];
}
// basic support procedures
// clear matrix rows to zero
static void bclear(projUV[][] p, int n, int m)
{
for(int i=0; i<n; i++)
for(int j=0; j<m; j++)
p[i][j].u=p[i][j].v=0;
}
// a = b - c
static void subop(projUV[] a, projUV[] b, projUV[] c, int n)
{
for(int i=0; i<n; i++)
{
a[i].u=b[i].u-c[i].u;
a[i].v=b[i].v-c[i].v;
}
}
// row adjust a = a - m * b
static void dadd(projUV[] a, projUV[] b, double m, int n)
{
for(int i=0; i<n; i++)
{
a[i].u-=m*b[i].u;
a[i].v-=m*b[i].v;
}
}
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;
}
}
// sum coefficients less than res
static void eval(projUV[][] w, int nu, int nv, double res, ref projUV resid)
{
resid.u=resid.v=0.0;
for(int i=0; i<nu; i++)
{
for(int j=0; j<nv; j++)
{
projUV s=w[i][j];
double ab=Math.Abs(s.u);
if(ab<res) resid.u+=ab;
ab=Math.Abs(s.v);
if(ab<res) resid.v+=ab;
}
}
}
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");
}
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);
}
}
// multiply vector a by scalar m
static void dmult(projUV[] a, double m, int n)
{
for(int i=0; i<n; i++)
{
a[i].u*=m;
a[i].v*=m;
}
}
// 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);
}
// convert row to pover series
static void rows(projUV[] c, projUV[] d, int n)
{
projUV[] dd=new projUV[n];
projUV sv;
sv.u=sv.v=0.0;
for(int j=0; j<n; j++) d[j]=dd[j]=sv;
d[0]=c[n-1];
for(int j=n-2; j>=1; j--)
{
for(int k=n-j; k>=1; k--)
{
sv=d[k];
d[k].u=2.0*d[k-1].u-dd[k].u;
d[k].v=2.0*d[k-1].v-dd[k].v;
dd[k]=sv;
}
sv=d[0];
d[0].u=-dd[0].u+c[j].u;
d[0].v=-dd[0].v+c[j].v;
dd[0]=sv;
}
for(int j=n-1; j>=1; j--)
{
d[j].u=d[j-1].u-dd[j].u;
d[j].v=d[j-1].v-dd[j].v;
}
d[0].u=-dd[0].u+0.5*c[0].u;
d[0].v=-dd[0].v+0.5*c[0].v;
}
// general entry point selecting evaluation mode
public static projUV biveval(projUV @in, Tseries T)
{
if(T.power!=0) return bpseval(@in, T);
return bcheval(@in, T);
}
// row adjust for range -1 to 1 to a to b
static void rowshft(double a, double b, projUV[] d, int n)
{
double cnst=2.0/(b-a);
double fac=cnst;
for(int j=1; j<n; j++)
{
d[j].u*=fac;
d[j].v*=fac;
fac*=cnst;
}
cnst=0.5*(a+b);
for(int j=0; j<=n-2; ++j)
{
for(int k=n-2; k>=j; k--)
{
d[k].u-=cnst*d[k+1].u;
d[k].v-=cnst*d[k+1].v;
}
}
}
// a = m * b - c
static void submop(projUV[] a, double m, projUV[] b, projUV[] c, int n)
{
for(int i=0; i<n; i++)
{
a[i].u=m*b[i].u-c[i].u;
a[i].v=m*b[i].v-c[i].v;
}
}
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");
}
