void
PatchSample::sample_frustum(double hfov, double vfov, int nh, int nv,
Vector3d p, Vector3d u,
MatrixXd &mx, MatrixXd &my, MatrixXd &mz)
{
//TBD: check input args
// pointing, up, left
p = p/p.norm();
u = u/u.norm();
Vector3d l = u.cross(p);
// sample like a camera would
double ll = (tan(hfov/2.0)*((double)(nh-1)))/nh;
double uu = (tan(vfov/2.0)*((double)(nv-1)))/nv;
RowVectorXd y;
y.setLinSpaced(nh,-ll,ll);
MatrixXd yy;
yy = y.replicate(nv,1);
VectorXd z;
z.setLinSpaced(nv,-uu,uu);
MatrixXd zz;
zz = z.replicate(1,nh);
MatrixXd xx = MatrixXd::Ones(nv,nh);
MatrixXd nn = (xx.array().square() + yy.array().square() + zz.array().square()).cwiseSqrt();
xx = xx.array() / nn.array();
yy = yy.array() / nn.array();
zz = zz.array() / nn.array();
// rotation matrix
Matrix3d rr;
rr << p, l, u;
// rotate points
MatrixXd xyz;
MatrixXd cam (3,xx.rows()*xx.cols());
cam.row(0) = vectorizeColWise(xx);
cam.row(1) = vectorizeColWise(yy);
cam.row(2) = vectorizeColWise(zz);
xyz = rr*cam;
// extract coordinates
xx = xyz.row(0);
yy = xyz.row(1);
zz = xyz.row(2);
mx = Map<MatrixXd>(xx.data(),nv,nh);
my = Map<MatrixXd>(yy.data(),nv,nh);
mz = Map<MatrixXd>(zz.data(),nv,nh);
}
int main()
{
VectorXd v;
v.setLinSpaced(5,0,1);
// std::cout<<JacobiP(v,0,0,4);
// std::cout<<Vandermonde1D(4,v);
// std::cout<<JacobiGQ(0,0,4);
int K=4;
int N=3;
int Nv=K+1;
startUp1d ob(N,K);
}
MatrixXd NumInt::GuassQaudrature(const int& N, double& a, double& b) {
int N0=N-1;
const int N1 = N0+1;
const int N2 = N0+2;
VectorXd xu;
xu.setLinSpaced(N1,-1.0,1.0);
// Legendre-Gauss-Vandermonde Matrix
//Matrix<double,N1,N2> L = Matrix<double,N1,N2>::Zero();
MatrixXd L(N1,N2);
L = MatrixXd::Zero(N1,N2);
// Derivative of Legendre-Gauss-Vandermonde Matrix
//Matrix<double,N1,1> Lp = Matrix<double,N1,1>::Zero();
VectorXd Lp(N1);
Lp = VectorXd::Zero(N1);
VectorXd dum;
dum.setLinSpaced(N1,0.0,N0);
ArrayXd y;
y = cos((2*dum.array()+1)*M_PI/(2*N0+2))+(0.27/N1)*sin(M_PI*xu.array()*N0/N2);
double deps = std::numeric_limits<double>::epsilon();
//Initial Guess
//Array<double,N1,1> y0 = Array<double,N1,1>::Constant(2);
ArrayXd y0 = ArrayXd::Constant(N1,2);
while ((y-y0).abs().matrix().maxCoeff() > deps) {
// L.col(0) = Matrix<double,N1,1>::Constant(1);
L.col(0) = VectorXd::Constant(N1,1);
//Lp = Matrix<double,N1,1>::Zero();
Lp = VectorXd::Zero(N1);
L.col(1) = y;
for (int k=1; k!=N1; k++)
{
L.col(k+1) = ((2*k+1)*L.col(k).cwiseProduct(y.matrix())-k*L.col(k-1))/(k+1);
}
Lp = (N2)*(L.col(N0)-L.col(N1).cwiseProduct(y.matrix())).cwiseQuotient((1-y.square()).matrix());
y0 = y;
y = y0-(L.col(N1).cwiseQuotient(Lp)).array();
}
// Gauss Points
//Matrix<double,N1,1> z = ((a*(1-y)+b*(1+y))/2).matrix();
VectorXd z(N1);
z = ((a*(1-y)+b*(1+y))/2).matrix();
// Gauss Weights
//Matrix<double,N1,1> w;
VectorXd w(N1);
w = (b-a)/(((1-y.square()).matrix()).cwiseProduct(Lp.cwiseProduct(Lp))).array()*pow((double)N2/N1,2);
// Store
//Matrix<double,N1,2> zw;
Matrix<double,Dynamic,Dynamic> zw(N1,2);
zw.col(0)=z;
zw.col(1)=w;
return zw;
}