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94 lines
4.7 KiB
C++
94 lines
4.7 KiB
C++
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla Public License
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// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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// obtain one at http://mozilla.org/MPL/2.0/.
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#include "dihedral_angles.h"
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#include <cassert>
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template <
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typename DerivedV,
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typename DerivedT,
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typename Derivedtheta,
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typename Derivedcos_theta>
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IGL_INLINE void igl::dihedral_angles(
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Eigen::PlainObjectBase<DerivedV>& V,
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Eigen::PlainObjectBase<DerivedT>& T,
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Eigen::PlainObjectBase<Derivedtheta>& theta,
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Eigen::PlainObjectBase<Derivedcos_theta>& cos_theta)
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{
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using namespace Eigen;
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assert(T.cols() == 4);
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Matrix<typename Derivedtheta::Scalar,Dynamic,6> l;
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edge_lengths(V,T,l);
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Matrix<typename Derivedtheta::Scalar,Dynamic,4> s;
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face_areas(l,s);
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return dihedral_angles_intrinsic(l,s,theta,cos_theta);
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}
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template <
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typename DerivedL,
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typename DerivedA,
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typename Derivedtheta,
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typename Derivedcos_theta>
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IGL_INLINE void igl::dihedral_angles_intrinsic(
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Eigen::PlainObjectBase<DerivedL>& L,
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Eigen::PlainObjectBase<DerivedA>& A,
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Eigen::PlainObjectBase<Derivedtheta>& theta,
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Eigen::PlainObjectBase<Derivedcos_theta>& cos_theta)
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{
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using namespace Eigen;
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const int m = L.rows();
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assert(m == A.rows());
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// Law of cosines
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// http://math.stackexchange.com/a/49340/35376
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Matrix<typename Derivedtheta::Scalar,Dynamic,6> H_sqr(m,6);
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H_sqr.col(0) = (1./16.) * (4. * L.col(3).array().square() * L.col(0).array().square() -
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((L.col(1).array().square() + L.col(4).array().square()) -
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(L.col(2).array().square() + L.col(5).array().square())).square());
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H_sqr.col(1) = (1./16.) * (4. * L.col(4).array().square() * L.col(1).array().square() -
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((L.col(2).array().square() + L.col(5).array().square()) -
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(L.col(3).array().square() + L.col(0).array().square())).square());
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H_sqr.col(2) = (1./16.) * (4. * L.col(5).array().square() * L.col(2).array().square() -
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((L.col(3).array().square() + L.col(0).array().square()) -
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(L.col(4).array().square() + L.col(1).array().square())).square());
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H_sqr.col(3) = (1./16.) * (4. * L.col(0).array().square() * L.col(3).array().square() -
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((L.col(4).array().square() + L.col(1).array().square()) -
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(L.col(5).array().square() + L.col(2).array().square())).square());
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H_sqr.col(4) = (1./16.) * (4. * L.col(1).array().square() * L.col(4).array().square() -
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((L.col(5).array().square() + L.col(2).array().square()) -
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(L.col(0).array().square() + L.col(3).array().square())).square());
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H_sqr.col(5) = (1./16.) * (4. * L.col(2).array().square() * L.col(5).array().square() -
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((L.col(0).array().square() + L.col(3).array().square()) -
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(L.col(1).array().square() + L.col(4).array().square())).square());
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cos_theta.resize(m,6);
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cos_theta.col(0) = (H_sqr.col(0).array() -
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A.col(1).array().square() - A.col(2).array().square()).array() /
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(-2.*A.col(1).array() * A.col(2).array());
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cos_theta.col(1) = (H_sqr.col(1).array() -
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A.col(2).array().square() - A.col(0).array().square()).array() /
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(-2.*A.col(2).array() * A.col(0).array());
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cos_theta.col(2) = (H_sqr.col(2).array() -
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A.col(0).array().square() - A.col(1).array().square()).array() /
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(-2.*A.col(0).array() * A.col(1).array());
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cos_theta.col(3) = (H_sqr.col(3).array() -
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A.col(3).array().square() - A.col(0).array().square()).array() /
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(-2.*A.col(3).array() * A.col(0).array());
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cos_theta.col(4) = (H_sqr.col(4).array() -
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A.col(3).array().square() - A.col(1).array().square()).array() /
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(-2.*A.col(3).array() * A.col(1).array());
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cos_theta.col(5) = (H_sqr.col(5).array() -
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A.col(3).array().square() - A.col(2).array().square()).array() /
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(-2.*A.col(3).array() * A.col(2).array());
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theta = cos_theta.array().acos();
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cos_theta.resize(m,6);
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}
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template instantiation
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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> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 6, 0, -1, 6> >&, 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> >&);
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#endif
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