123 lines
3.8 KiB
C++
123 lines
3.8 KiB
C++
// 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_HARMONIC_H
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#define IGL_HARMONIC_H
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#include "igl_inline.h"
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#include <Eigen/Core>
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#include <Eigen/Sparse>
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namespace igl
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{
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// Compute k-harmonic weight functions "coordinates".
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//
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//
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// Inputs:
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// V #V by dim vertex positions
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// F #F by simplex-size list of element indices
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// b #b boundary indices into V
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// bc #b by #W list of boundary values
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// k power of harmonic operation (1: harmonic, 2: biharmonic, etc)
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// Outputs:
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// W #V by #W list of weights
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//
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template <
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typename DerivedV,
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typename DerivedF,
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typename Derivedb,
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typename Derivedbc,
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typename DerivedW>
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IGL_INLINE bool harmonic(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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const Eigen::MatrixBase<Derivedb> & b,
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const Eigen::MatrixBase<Derivedbc> & bc,
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const int k,
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Eigen::PlainObjectBase<DerivedW> & W);
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// Compute harmonic map using uniform laplacian operator
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//
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// Inputs:
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// F #F by simplex-size list of element indices
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// b #b boundary indices into V
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// bc #b by #W list of boundary values
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// k power of harmonic operation (1: harmonic, 2: biharmonic, etc)
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// Outputs:
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// W #V by #W list of weights
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//
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template <
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typename DerivedF,
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typename Derivedb,
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typename Derivedbc,
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typename DerivedW>
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IGL_INLINE bool harmonic(
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const Eigen::MatrixBase<DerivedF> & F,
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const Eigen::MatrixBase<Derivedb> & b,
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const Eigen::MatrixBase<Derivedbc> & bc,
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const int k,
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Eigen::PlainObjectBase<DerivedW> & W);
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// Compute a harmonic map using a given Laplacian and mass matrix
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//
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// Inputs:
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// L #V by #V discrete (integrated) Laplacian
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// M #V by #V mass matrix
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// b #b boundary indices into V
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// bc #b by #W list of boundary values
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// k power of harmonic operation (1: harmonic, 2: biharmonic, etc)
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// Outputs:
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// W #V by #V list of weights
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template <
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typename DerivedL,
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typename DerivedM,
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typename Derivedb,
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typename Derivedbc,
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typename DerivedW>
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IGL_INLINE bool harmonic(
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const Eigen::SparseMatrix<DerivedL> & L,
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const Eigen::SparseMatrix<DerivedM> & M,
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const Eigen::MatrixBase<Derivedb> & b,
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const Eigen::MatrixBase<Derivedbc> & bc,
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const int k,
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Eigen::PlainObjectBase<DerivedW> & W);
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// Build the discrete k-harmonic operator (computing integrated quantities).
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// That is, if the k-harmonic PDE is Q x = 0, then this minimizes x' Q x
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//
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// Inputs:
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// L #V by #V discrete (integrated) Laplacian
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// M #V by #V mass matrix
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// k power of harmonic operation (1: harmonic, 2: biharmonic, etc)
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// Outputs:
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// Q #V by #V discrete (integrated) k-Laplacian
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template <
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typename DerivedL,
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typename DerivedM,
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typename DerivedQ>
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IGL_INLINE void harmonic(
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const Eigen::SparseMatrix<DerivedL> & L,
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const Eigen::SparseMatrix<DerivedM> & M,
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const int k,
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Eigen::SparseMatrix<DerivedQ> & Q);
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// Inputs:
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// V #V by dim vertex positions
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// F #F by simplex-size list of element indices
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// k power of harmonic operation (1: harmonic, 2: biharmonic, etc)
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// Outputs:
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// Q #V by #V discrete (integrated) k-Laplacian
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template <
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typename DerivedV,
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typename DerivedF,
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typename DerivedQ>
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IGL_INLINE void harmonic(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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const int k,
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Eigen::SparseMatrix<DerivedQ> & Q);
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};
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#ifndef IGL_STATIC_LIBRARY
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#include "harmonic.cpp"
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#endif
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#endif
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