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109 lines
4.5 KiB
109 lines
4.5 KiB
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2013 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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#ifndef IGL_DOUBLEAREA_H
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#define IGL_DOUBLEAREA_H
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#include "igl_inline.h"
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#include <Eigen/Dense>
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namespace igl
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{
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/// Computes twice the area for each input triangle or quad.
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///
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/// @tparam DerivedV derived type of eigen matrix for V (e.g. derived from
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/// MatrixXd)
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/// @tparam DerivedF derived type of eigen matrix for F (e.g. derived from
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/// MatrixXi)
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/// @tparam DeriveddblA derived type of eigen matrix for dblA (e.g. derived from
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/// MatrixXd)
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/// @param[in] V #V by dim list of mesh vertex positions
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/// @param[in] F #F by simplex_size list of mesh faces (must be triangles or quads)
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/// @param[out] dblA #F list of triangle[quad] double areas (SIGNED only for 2D input)
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///
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/// \bug For dim==3 complexity is O(#V + #F). Not just O(#F). This is a big deal
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/// if you have 1 million unreferenced vertices and 1 face.
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template <typename DerivedV, typename DerivedF, typename DeriveddblA>
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IGL_INLINE void doublearea(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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Eigen::PlainObjectBase<DeriveddblA> & dblA);
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/// Compute the twice the signed area of a each triangle.
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///
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/// @param[in] A #F by dim list of triangle corner positions
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/// @param[in] B #F by dim list of triangle corner positions
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/// @param[in] C #F by dim list of triangle corner positions
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/// @param[out] D #F list of triangle double areas
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template <
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typename DerivedA,
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typename DerivedB,
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typename DerivedC,
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typename DerivedD>
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IGL_INLINE void doublearea(
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const Eigen::MatrixBase<DerivedA> & A,
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const Eigen::MatrixBase<DerivedB> & B,
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const Eigen::MatrixBase<DerivedC> & C,
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Eigen::PlainObjectBase<DerivedD> & D);
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/// Compute the twice the signed area of a single triangle.
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///
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/// @param[in] A triangle corner position
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/// @param[in] B triangle corner position
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/// @param[in] C triangle corner position
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/// @return 2*signed area of triangle
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///
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/// \fileinfo
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template <
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typename DerivedA,
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typename DerivedB,
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typename DerivedC>
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IGL_INLINE typename DerivedA::Scalar doublearea_single(
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const Eigen::MatrixBase<DerivedA> & A,
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const Eigen::MatrixBase<DerivedB> & B,
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const Eigen::MatrixBase<DerivedC> & C);
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/// Compute twice the area of each intrinsic triangle in a mesh.
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///
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/// @param[in] l #F by dim list of edge lengths using
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/// for triangles, columns correspond to edges 23,31,12
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/// @param[in] nan_replacement what value should be used for triangles whose given
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/// edge lengths do not obey the triangle inequality. These may be very
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/// wrong (e.g., [100 1 1]) or may be nearly degenerate triangles whose
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/// floating point side length computation leads to breach of the triangle
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/// inequality. One may wish to set this parameter to 0 if side lengths l
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/// are _known_ to come from a valid embedding (e.g., some mesh (V,F)). In
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/// that case, the only circumstance the triangle inequality is broken is
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/// when the triangle is nearly degenerate and floating point error
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/// dominates: hence replacing with zero is reasonable.
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/// @param[out] dblA #F list of triangle double areas
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template <typename Derivedl, typename DeriveddblA>
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IGL_INLINE void doublearea(
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const Eigen::MatrixBase<Derivedl> & l,
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const typename Derivedl::Scalar nan_replacement,
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Eigen::PlainObjectBase<DeriveddblA> & dblA);
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/// \overload
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///
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/// \brief default behavior is to assert on NaNs and leave them in place
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template <typename Derivedl, typename DeriveddblA>
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IGL_INLINE void doublearea(
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const Eigen::MatrixBase<Derivedl> & l,
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Eigen::PlainObjectBase<DeriveddblA> & dblA);
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/// Computes twice the area for each input quadrilateral.
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///
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/// @param[in] V #V by dim list of mesh vertex positions
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/// @param[in] F #F by simplex_size list of mesh faces (must be quadrilaterals)
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/// @param[out] dblA #F list of quadrilateral double areas
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///
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/// \fileinfo
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template <typename DerivedV, typename DerivedF, typename DeriveddblA>
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IGL_INLINE void doublearea_quad(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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Eigen::PlainObjectBase<DeriveddblA> & dblA);
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}
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#ifndef IGL_STATIC_LIBRARY
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# include "doublearea.cpp"
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#endif
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#endif
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