99 lines
5.3 KiB
C++
99 lines
5.3 KiB
C++
// This file is part of libigl, a simple c++ geometry processing library.
|
|
//
|
|
// Copyright (C) 2014 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 "dihedral_angles.h"
|
|
#include "edge_lengths.h"
|
|
#include "face_areas.h"
|
|
|
|
#include <cassert>
|
|
|
|
template <
|
|
typename DerivedV,
|
|
typename DerivedT,
|
|
typename Derivedtheta,
|
|
typename Derivedcos_theta>
|
|
IGL_INLINE void igl::dihedral_angles(
|
|
const Eigen::PlainObjectBase<DerivedV>& V,
|
|
const Eigen::PlainObjectBase<DerivedT>& T,
|
|
Eigen::PlainObjectBase<Derivedtheta>& theta,
|
|
Eigen::PlainObjectBase<Derivedcos_theta>& cos_theta)
|
|
{
|
|
using namespace Eigen;
|
|
assert(T.cols() == 4);
|
|
Matrix<typename Derivedtheta::Scalar,Dynamic,6> l;
|
|
edge_lengths(V,T,l);
|
|
Matrix<typename Derivedtheta::Scalar,Dynamic,4> s;
|
|
face_areas(l,s);
|
|
return dihedral_angles_intrinsic(l,s,theta,cos_theta);
|
|
}
|
|
|
|
template <
|
|
typename DerivedL,
|
|
typename DerivedA,
|
|
typename Derivedtheta,
|
|
typename Derivedcos_theta>
|
|
IGL_INLINE void igl::dihedral_angles_intrinsic(
|
|
const Eigen::PlainObjectBase<DerivedL>& L,
|
|
const Eigen::PlainObjectBase<DerivedA>& A,
|
|
Eigen::PlainObjectBase<Derivedtheta>& theta,
|
|
Eigen::PlainObjectBase<Derivedcos_theta>& cos_theta)
|
|
{
|
|
using namespace Eigen;
|
|
const int m = L.rows();
|
|
assert(m == A.rows());
|
|
// Law of cosines
|
|
// http://math.stackexchange.com/a/49340/35376
|
|
Matrix<typename Derivedtheta::Scalar,Dynamic,6> H_sqr(m,6);
|
|
H_sqr.col(0) = (1./16.) * (4. * L.col(3).array().square() * L.col(0).array().square() -
|
|
((L.col(1).array().square() + L.col(4).array().square()) -
|
|
(L.col(2).array().square() + L.col(5).array().square())).square());
|
|
H_sqr.col(1) = (1./16.) * (4. * L.col(4).array().square() * L.col(1).array().square() -
|
|
((L.col(2).array().square() + L.col(5).array().square()) -
|
|
(L.col(3).array().square() + L.col(0).array().square())).square());
|
|
H_sqr.col(2) = (1./16.) * (4. * L.col(5).array().square() * L.col(2).array().square() -
|
|
((L.col(3).array().square() + L.col(0).array().square()) -
|
|
(L.col(4).array().square() + L.col(1).array().square())).square());
|
|
H_sqr.col(3) = (1./16.) * (4. * L.col(0).array().square() * L.col(3).array().square() -
|
|
((L.col(4).array().square() + L.col(1).array().square()) -
|
|
(L.col(5).array().square() + L.col(2).array().square())).square());
|
|
H_sqr.col(4) = (1./16.) * (4. * L.col(1).array().square() * L.col(4).array().square() -
|
|
((L.col(5).array().square() + L.col(2).array().square()) -
|
|
(L.col(0).array().square() + L.col(3).array().square())).square());
|
|
H_sqr.col(5) = (1./16.) * (4. * L.col(2).array().square() * L.col(5).array().square() -
|
|
((L.col(0).array().square() + L.col(3).array().square()) -
|
|
(L.col(1).array().square() + L.col(4).array().square())).square());
|
|
cos_theta.resize(m,6);
|
|
cos_theta.col(0) = (H_sqr.col(0).array() -
|
|
A.col(1).array().square() - A.col(2).array().square()).array() /
|
|
(-2.*A.col(1).array() * A.col(2).array());
|
|
cos_theta.col(1) = (H_sqr.col(1).array() -
|
|
A.col(2).array().square() - A.col(0).array().square()).array() /
|
|
(-2.*A.col(2).array() * A.col(0).array());
|
|
cos_theta.col(2) = (H_sqr.col(2).array() -
|
|
A.col(0).array().square() - A.col(1).array().square()).array() /
|
|
(-2.*A.col(0).array() * A.col(1).array());
|
|
cos_theta.col(3) = (H_sqr.col(3).array() -
|
|
A.col(3).array().square() - A.col(0).array().square()).array() /
|
|
(-2.*A.col(3).array() * A.col(0).array());
|
|
cos_theta.col(4) = (H_sqr.col(4).array() -
|
|
A.col(3).array().square() - A.col(1).array().square()).array() /
|
|
(-2.*A.col(3).array() * A.col(1).array());
|
|
cos_theta.col(5) = (H_sqr.col(5).array() -
|
|
A.col(3).array().square() - A.col(2).array().square()).array() /
|
|
(-2.*A.col(3).array() * A.col(2).array());
|
|
|
|
theta = cos_theta.array().acos();
|
|
|
|
cos_theta.resize(m,6);
|
|
|
|
}
|
|
#ifdef IGL_STATIC_LIBRARY
|
|
// Explicit template instantiation
|
|
template void igl::dihedral_angles_intrinsic< Eigen::Matrix<double, -1, 6, 0, -1, 6>, Eigen::Matrix<double, -1, 4, 0, -1, 4>, Eigen::Matrix<double, -1, 6, 0, -1, 6>, Eigen::Matrix<double, -1, 6, 0, -1, 6> >(const Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 6, 0, -1, 6> >&, const Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 4, 0, -1, 4> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 6, 0, -1, 6> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 6, 0, -1, 6> >&);
|
|
template void igl::dihedral_angles<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
|
|
#endif
|