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44 lines
1.8 KiB
44 lines
1.8 KiB
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2023 Alec Jacobson
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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_LSCM_HESSIAN_H
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#define IGL_LSCM_HESSIAN_H
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#include <Eigen/Dense>
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#include <Eigen/Sparse>
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namespace igl
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{
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/// Compute a Least-squares conformal map parametrization (equivalently
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/// derived in "Intrinsic Parameterizations of Surface Meshes" [Desbrun et al.
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/// 2002] and "Least Squares Conformal Maps for Automatic Texture Atlas
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/// Generation" [Lévy et al. 2002]), though this implementation follows the
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/// derivation in: "Spectral Conformal Parameterization" [Mullen et al. 2008]
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/// (note, this does **not** implement the Eigen-decomposition based method in
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/// [Mullen et al. 2008], which is not equivalent). Input should be a manifold
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/// mesh (also no unreferenced vertices) and "boundary" (fixed vertices) `b`
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/// should contain at least two vertices per connected component.
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///
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/// @param[in] V #V by 3 list of mesh vertex positions
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/// @param[in] F #F by 3 list of mesh faces (must be triangles)
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/// @param[in] b #b boundary indices into V
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/// @param[in] bc #b by 2 list of boundary values
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/// @param[out] UV #V by 2 list of 2D mesh vertex positions in UV space
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/// @param[out] Q #Vx2 by #Vx2 symmetric positive semi-definite matrix for computing LSCM energy
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/// @return true only on solver success.
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///
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template <typename DerivedV, typename DerivedF, typename QScalar>
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void lscm_hessian(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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Eigen::SparseMatrix<QScalar> & Q);
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}
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#ifndef IGL_STATIC_LIBRARY
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#include "lscm_hessian.cpp"
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#endif
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#endif
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