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ExtraFunctions.cpp
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ExtraFunctions.cpp
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//
// ExtraFunctions.cpp
// testigl
//
// Created by Amir Vaxman on 18/12/14.
// Copyright (c) 2014 Amir Vaxman. All rights reserved.
//
#include "ExtraFunctions.h"
#include <hedra/EigenSolverWrapper.h>
using namespace Eigen;
using namespace std;
typedef std::complex<double> Complex;
void GetComplexMobiusCoeffs(Complex& a, Complex& b, Complex& c, Complex& d, const Vector3cd& z, const Vector3cd& w)
{
Vector3cd zw=z.cwiseProduct(w);
Vector3cd ones=Vector3cd::Ones();
Matrix3cd amat,bmat,cmat,dmat;
amat.col(0)=zw; amat.col(1)=w; amat.col(2)=ones;
bmat.col(0)=zw; bmat.col(1)=z; bmat.col(2)=w;
cmat.col(0)=z; cmat.col(1)=w; cmat.col(2)=ones;
dmat.col(0)=zw; dmat.col(1)=z; dmat.col(2)=ones;
a=amat.determinant();
b=bmat.determinant();
c=cmat.determinant();
d=dmat.determinant();
Complex TotalDet=a*d-b*c;
Complex Sign=(real(a)>0 ? 1.0 : -1.0);
a/=sqrt(TotalDet)*Sign;
b/=sqrt(TotalDet)*Sign;
c/=sqrt(TotalDet)*Sign;
d/=sqrt(TotalDet)*Sign;
}
Vector2cd GetSingleMobius(const VectorXcd& OrigVc, const VectorXcd& X)
{
//estimating target global mobius transformation
MatrixXcd MobMat(X.rows(),2);
MobMat.col(0)=OrigVc;
MobMat.col(1).setConstant(1.0);
VectorXcd GFunc(X.size());
for (int i=0;i<X.rows();i++)
GFunc(i)=Complex(1.0)/X(i);
Matrix2cd A=(MobMat.adjoint()*MobMat);
Vector2cd b=(MobMat.adjoint()*GFunc);
Vector2cd Result=A.colPivHouseholderQr().solve(b);
cout<<"Total Target Mobius Error: "<<(MobMat*Result-GFunc).lpNorm<Infinity>()<<endl;
return(Result);
}
VectorXcd SolveComplexSytem(const SparseMatrix<Complex>& A, const VectorXcd& b)
{
//creating real matrices
SparseMatrix<double> rA(A.rows()*2, A.cols()*2);
vector<Triplet<double> > RealTris(A.nonZeros()*4);
int Counter=0;
for (int k=0; k<A.outerSize(); k++){
for (SparseMatrix<Complex>::InnerIterator it(A,k); it; ++it){
RealTris[Counter++]=Triplet<double>(it.row(), it.col(), it.value().real());
RealTris[Counter++]=Triplet<double>(it.row(), it.col()+A.cols(), -it.value().imag());
RealTris[Counter++]=Triplet<double>(it.row()+A.rows(), it.col(), it.value().imag());
RealTris[Counter++]=Triplet<double>(it.row()+A.rows(), it.col()+A.cols(), it.value().real());
}
}
rA.setFromTriplets(RealTris.begin(), RealTris.end());
VectorXd rb(b.rows()*2);
rb<<b.real(), b.imag();
MatrixXd RawSolution=hedra::optimization::EigenSingleSolveWrapper<Eigen::SimplicialLDLT<Eigen::SparseMatrix<double> > >(rA, rb, false);
int ComplexSize=A.cols();
VectorXcd Solution(ComplexSize);
for (int i=0;i<ComplexSize;i++)
Solution[i]=Complex(RawSolution(i), RawSolution(ComplexSize+i));
return Solution;
}
RowVector4d Rot2Quat(Matrix3d& R)
{
double Rxx = R(0,0); double Rxy = R(0,1); double Rxz = R(0,2);
double Ryx = R(1,0); double Ryy = R(1,1); double Ryz = R(1,2);
double Rzx = R(2,0); double Rzy = R(2,1); double Rzz = R(2,2);
double w = sqrt( R.trace() + 1 ) / 2;
double x = sqrt( 1 + Rxx - Ryy - Rzz ) / 2;
double y = sqrt( 1 + Ryy - Rxx - Rzz ) / 2;
double z = sqrt( 1 + Rzz - Ryy - Rxx ) / 2;
VectorXd TestVec(4); TestVec<<w,x,y,z;
int MinIndex;
TestVec.maxCoeff(&MinIndex);
if( MinIndex == 0 ){
x = ( Rzy - Ryz ) / (4*w);
y = ( Rxz - Rzx ) / (4*w);
z = ( Ryx - Rxy ) / (4*w);
}
if( MinIndex == 1 ){
w = ( Rzy - Ryz ) / (4*x);
y = ( Rxy + Ryx ) / (4*x);
z = ( Rzx + Rxz ) / (4*x);
}
if( MinIndex == 2 ){
w = ( Rxz - Rzx ) / (4*y);
x = ( Rxy + Ryx ) / (4*y);
z = ( Ryz + Rzy ) / (4*y);
}
if( MinIndex == 3 ){
w = ( Ryx - Rxy ) / (4*z);
x = ( Rzx + Rxz ) / (4*z);
y = ( Ryz + Rzy ) / (4*z);
}
RowVector4d Result; Result<<w,x,y,z;
return Result;
}
MatrixXd GetCenters(const MatrixXd& V, const MatrixXi& D, const MatrixXi& F)
{
MatrixXd Centers(D.rows(),3); Centers.setZero();
for (int i=0;i<D.rows();i++)
for (int j=0;j<D(i);j++)
Centers.row(i)+=V.row(F(i,j))/(double)D(i,0);
return Centers;
}