79 lines
3.2 KiB
C++
79 lines
3.2 KiB
C++
// This file is part of libigl, a simple c++ geometry processing library.
|
|
//
|
|
// Copyright (C) 2018 Alec Jacobson <alecjacobson@gmail.com>
|
|
//
|
|
// This Source Code Form is subject to the terms of the Mozilla Public License
|
|
// v. 2.0. If a copy of the MPL was not distributed with this file, You can
|
|
// obtain one at http://mozilla.org/MPL/2.0/.
|
|
#include "grad_intrinsic.h"
|
|
#include "grad.h"
|
|
|
|
template <typename Derivedl, typename DerivedF, typename Gtype>
|
|
IGL_INLINE void igl::grad_intrinsic(
|
|
const Eigen::MatrixBase<Derivedl>&l,
|
|
const Eigen::MatrixBase<DerivedF>&F,
|
|
Eigen::SparseMatrix<Gtype> &G)
|
|
{
|
|
assert(F.cols() ==3 && "Only triangles supported");
|
|
// number of vertices
|
|
const int n = F.maxCoeff()+1;
|
|
// number of faces
|
|
const int m = F.rows();
|
|
// JD: There is a pretty subtle bug when using a fixed column size for this matrix.
|
|
// When calling igl::grad(V, ...), the two code paths `grad_tet` and `grad_tri`
|
|
// will be compiled. It turns out that `igl::grad_tet` calls `igl::volume`, which
|
|
// reads the coordinates of the `V` matrix into `RowVector3d`. If the matrix `V`
|
|
// has a known compile-time size of 2, this produces a compilation error when
|
|
// libigl is compiled in header-only mode. In static mode this doesn't happen
|
|
// because the matrix `V` is probably implicitly copied into a `Eigen::MatrixXd`.
|
|
// This is a situation that could be solved using `if constexpr` in C++17.
|
|
// In C++11, the alternative is to use SFINAE and `std::enable_if` (ugh).
|
|
typedef Eigen::Matrix<Gtype,Eigen::Dynamic,Eigen::Dynamic> MatrixX2S;
|
|
MatrixX2S V2 = MatrixX2S::Zero(3*m,2);
|
|
// 1=[x,y]
|
|
// /\
|
|
// l3 / \ l2
|
|
// / \
|
|
// / \
|
|
// 2-----------3
|
|
// l1
|
|
//
|
|
// x = (l2²-l1²-l3²)/(-2*l1)
|
|
// y = sqrt(l3² - x²)
|
|
//
|
|
//
|
|
// Place 3rd vertex at [l(:,1) 0]
|
|
V2.block(2*m,0,m,1) = l.col(0);
|
|
// Place second vertex at [0 0]
|
|
// Place third vertex at [x y]
|
|
V2.block(0,0,m,1) =
|
|
(l.col(1).cwiseAbs2()-l.col(0).cwiseAbs2()-l.col(2).cwiseAbs2()).array()/
|
|
(-2.*l.col(0)).array();
|
|
V2.block(0,1,m,1) =
|
|
(l.col(2).cwiseAbs2() - V2.block(0,0,m,1).cwiseAbs2()).array().sqrt();
|
|
DerivedF F2(F.rows(),F.cols());
|
|
std::vector<Eigen::Triplet<Gtype> > Pijv;
|
|
Pijv.reserve(F.size());
|
|
for(int f = 0;f<m;f++)
|
|
{
|
|
for(int c = 0;c<F.cols();c++)
|
|
{
|
|
F2(f,c) = f+c*m;
|
|
Pijv.emplace_back(F2(f,c),F(f,c),1);
|
|
}
|
|
}
|
|
Eigen::SparseMatrix<Gtype> P(m*3,n);
|
|
P.setFromTriplets(Pijv.begin(),Pijv.end());
|
|
Eigen::SparseMatrix<Gtype> G2;
|
|
grad(V2,F2,G2);
|
|
G = G2*P;
|
|
}
|
|
|
|
#ifdef IGL_STATIC_LIBRARY
|
|
// Explicit template instantiation
|
|
// generated by autoexplicit.sh
|
|
template void igl::grad_intrinsic<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::SparseMatrix<double, 0, int>&);
|
|
// generated by autoexplicit.sh
|
|
template void igl::grad_intrinsic<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::SparseMatrix<double, 0, int>&);
|
|
#endif
|