Coord ParamDistortion::ComputeBarycentric(const vector<ParamCoord>& tri_vtx_array, ParamCoord vtx_param_coord)
{
zjucad::matrix::matrix<double> coord_matrix(3, 3);
for(size_t c=0; c<3; ++c)
{
coord_matrix(0, c) = tri_vtx_array[c].s_coord;
coord_matrix(1, c) = tri_vtx_array[c].t_coord;
coord_matrix(2, c) = 1.0;
}
inv(coord_matrix);
zjucad::matrix::matrix<double> right_matrix(3, 1);
right_matrix(0, 0) = vtx_param_coord.s_coord;
right_matrix(1, 0) = vtx_param_coord.t_coord;
right_matrix(2, 0) = 1.0;
zjucad::matrix::matrix<double> result_matrix = coord_matrix*right_matrix;
return Coord(result_matrix(0, 0), result_matrix(1, 0), result_matrix(2, 0));
}
Mat3d ReducedStVKCubatureForceModel::computeF_gradient(const int &ele,const int &vert_idx,const int &vert_idx_dim) const
{
//vert_idx denotes the j-th vertex, vert_idx_dim is the k-th coordinate of the j-th vertex
//we get the result as dF_i/dx_j^k, which is the derivative force of vertex i to the vertex j on the coordinate k
//identity vector definition
if((vert_idx>4)||(vert_idx_dim>3))
{
std::cout<<"the vert_idx or the vert_idx_dim is out of range, they should be smaller than 3";
}
Mat3d result_matrix(0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0);
std::vector<Vec3d> e_vector;
e_vector.resize(3,Vec3d(0.0,0.0,0.0));
e_vector[0][0]=1.0;
e_vector[1][1]=1.0;
e_vector[2][2]=1.0;
Mat3d e_matrix(0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0);
Mat3d DmInv=computeDmInv(ele);
//Mat3d DmInv(1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0);
//for j=1,2,3 we have dF/dx_j^k=e_k*e_j^T*Dm^-1
for(unsigned int row_idx=0;row_idx<3;++row_idx)
{
for(unsigned int col_idx=0;col_idx<3;++col_idx)
{
e_matrix[row_idx][col_idx]=e_vector[vert_idx_dim][row_idx]*e_vector[vert_idx][col_idx];
}
}
//compute dF/dx_4
if(vert_idx==3)
{
Mat3d vert_cord_matrix(0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0);
if(vert_idx_dim==0)
{
vert_cord_matrix[0][0]=vert_cord_matrix[0][1]=vert_cord_matrix[0][2]=-1.0;
}
else if(vert_idx_dim==1)
{
vert_cord_matrix[1][0]=vert_cord_matrix[1][1]=vert_cord_matrix[1][2]=-1.0;
}
else if(vert_idx_dim==2)
{
vert_cord_matrix[2][0]=vert_cord_matrix[2][1]=vert_cord_matrix[2][2]=-1.0;
}
else
{
}
result_matrix=vert_cord_matrix*DmInv;
}
else
{
//compute dF/dx_j^k,j=1,2,3;k=1,2,3
result_matrix=e_matrix*DmInv;
}
return result_matrix;
}
MatrixMxN<Scalar> MatrixMxN<Scalar>::transpose() const
{
unsigned int rows = (*this).rows();
unsigned int cols = (*this).cols();
Scalar *result = new Scalar[rows*cols];
for(unsigned int i = 0; i < rows; ++i)
for(unsigned int j = 0; j < cols; ++j)
result[j*rows+i] = (*this)(i,j);
MatrixMxN<Scalar> result_matrix(cols,rows,result);
delete result;
return result_matrix;
}
MatrixMxN<Scalar> MatrixMxN<Scalar>::operator* (Scalar scale) const
{
unsigned int rows = (*this).rows();
unsigned int cols = (*this).cols();
Scalar *result = new Scalar[rows*cols];
for(unsigned int i = 0; i < rows; ++i)
for(unsigned int j = 0; j < cols; ++j)
result[i*cols+j] = (*this)(i,j) * scale;
MatrixMxN<Scalar> result_matrix(rows,cols,result);
delete result;
return result_matrix;
}
MatrixMxN<Scalar> MatrixMxN<Scalar>::operator/ (Scalar scale) const
{
if(abs(scale)<std::numeric_limits<Scalar>::epsilon())
{
std::cerr<<"Matrix Divide by zero error!\n";
std::exit(EXIT_FAILURE);
}
unsigned int rows = (*this).rows();
unsigned int cols = (*this).cols();
Scalar *result = new Scalar[rows*cols];
for(unsigned int i = 0; i < rows; ++i)
for(unsigned int j = 0; j < cols; ++j)
result[i*cols+j] = (*this)(i,j) / scale;
MatrixMxN<Scalar> result_matrix(rows,cols,result);
delete result;
return result_matrix;
}
MatrixMxN<Scalar> MatrixMxN<Scalar>::operator- (const MatrixMxN<Scalar> &mat2) const
{
unsigned int rows = (*this).rows();
unsigned int cols = (*this).cols();
unsigned int rows2 = mat2.rows();
unsigned int cols2 = mat2.cols();
bool size_match = (rows==rows2)&&(cols==cols2);
if(!size_match)
{
std::cerr<<"Cannot subtract two matrix of different sizes!\n";
std::exit(EXIT_FAILURE);
}
Scalar *result = new Scalar[rows*cols];
for(unsigned int i = 0; i < rows; ++i)
for(unsigned int j = 0; j < cols; ++j)
result[i*cols+j] = (*this)(i,j) - mat2(i,j);
MatrixMxN<Scalar> result_matrix(rows, cols, result);
delete result;
return result_matrix;
}
