79 lines
2.8 KiB
C++
79 lines
2.8 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_ARAP_LINEAR_BLOCK_H
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#define IGL_ARAP_LINEAR_BLOCK_H
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#include "igl_inline.h"
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#include <Eigen/Sparse>
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#include <igl/ARAPEnergyType.h>
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namespace igl
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{
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// ARAP_LINEAR_BLOCK constructs a block of the matrix which constructs the
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// linear terms of a given arap energy. When treating rotations as knowns
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// (arranged in a column) then this constructs Kd of K such that the linear
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// portion of the energy is as a column:
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// K * R = [Kx Z ... Ky Z ...
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// Z Kx ... Z Ky ...
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// ... ]
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// These blocks are also used to build the "covariance scatter matrices".
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// Here we want to build a scatter matrix that multiplies against positions
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// (treated as known) producing covariance matrices to fit each rotation.
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// Notice that in the case of the RHS of the poisson solve the rotations are
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// known and the positions unknown, and vice versa for rotation fitting.
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// These linear block just relate the rotations to the positions, linearly in
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// each.
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//
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// Templates:
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// MatV vertex position matrix, e.g. Eigen::MatrixXd
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// MatF face index matrix, e.g. Eigen::MatrixXd
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// Scalar e.g. double
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// Inputs:
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// V #V by dim list of initial domain positions
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// F #F by #simplex size list of triangle indices into V
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// d coordinate of linear constructor to build
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// energy ARAPEnergyType enum value defining which energy is being used.
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// See ARAPEnergyType.h for valid options and explanations.
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// Outputs:
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// Kd #V by #V/#F block of the linear constructor matrix corresponding to
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// coordinate d
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//
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template <typename MatV, typename MatF, typename Scalar>
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IGL_INLINE void arap_linear_block(
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const MatV & V,
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const MatF & F,
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const int d,
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const igl::ARAPEnergyType energy,
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Eigen::SparseMatrix<Scalar> & Kd);
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// Helper functions for each energy type
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template <typename MatV, typename MatF, typename Scalar>
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IGL_INLINE void arap_linear_block_spokes(
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const MatV & V,
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const MatF & F,
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const int d,
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Eigen::SparseMatrix<Scalar> & Kd);
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template <typename MatV, typename MatF, typename Scalar>
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IGL_INLINE void arap_linear_block_spokes_and_rims(
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const MatV & V,
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const MatF & F,
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const int d,
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Eigen::SparseMatrix<Scalar> & Kd);
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template <typename MatV, typename MatF, typename Scalar>
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IGL_INLINE void arap_linear_block_elements(
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const MatV & V,
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const MatF & F,
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const int d,
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Eigen::SparseMatrix<Scalar> & Kd);
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}
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#ifndef IGL_STATIC_LIBRARY
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# include "arap_linear_block.cpp"
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#endif
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#endif
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