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94 lines
3.7 KiB
C++
94 lines
3.7 KiB
C++
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 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_LBS_MATRIX_H
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#define IGL_LBS_MATRIX_H
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#include "igl_inline.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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// LBS_MATRIX Linear blend skinning can be expressed by V' = M * T where V' is
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// a #V by dim matrix of deformed vertex positions (one vertex per row), M is a
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// #V by (dim+1)*#T (composed of weights and rest positions) and T is a
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// #T*(dim+1) by dim matrix of #T stacked transposed transformation matrices.
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// See equations (1) and (2) in "Fast Automatic Skinning Transformations"
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// [Jacobson et al 2012]
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//
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// Inputs:
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// V #V by dim list of rest positions
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// W #V+ by #T list of weights
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// Outputs:
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// M #V by #T*(dim+1)
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//
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// In MATLAB:
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// kron(ones(1,size(W,2)),[V ones(size(V,1),1)]).*kron(W,ones(1,size(V,2)+1))
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IGL_INLINE void lbs_matrix(
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const Eigen::MatrixXd & V,
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const Eigen::MatrixXd & W,
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Eigen::MatrixXd & M);
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// LBS_MATRIX construct a matrix that when multiplied against a column of
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// affine transformation entries computes new coordinates of the vertices
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//
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// I'm not sure it makes since that the result is stored as a sparse matrix.
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// The number of non-zeros per row *is* dependent on the number of mesh
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// vertices and handles.
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//
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// Inputs:
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// V #V by dim list of vertex rest positions
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// W #V by #handles list of correspondence weights
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// Output:
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// M #V * dim by #handles * dim * (dim+1) matrix such that
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// new_V(:) = LBS(V,W,A) = reshape(M * A,size(V)), where A is a column
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// vectors formed by the entries in each handle's dim by dim+1
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// transformation matrix. Specifcally, A =
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// reshape(permute(Astack,[3 1 2]),n*dim*(dim+1),1)
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// or A = [Lxx;Lyx;Lxy;Lyy;tx;ty], and likewise for other dim
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// if Astack(:,:,i) is the dim by (dim+1) transformation at handle i
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IGL_INLINE void lbs_matrix_column(
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const Eigen::MatrixXd & V,
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const Eigen::MatrixXd & W,
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Eigen::SparseMatrix<double>& M);
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IGL_INLINE void lbs_matrix_column(
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const Eigen::MatrixXd & V,
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const Eigen::MatrixXd & W,
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Eigen::MatrixXd & M);
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// Same as LBS_MATRIX above but instead of giving W as a full matrix of weights
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// (each vertex has #handles weights), a constant number of weights are given
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// for each vertex.
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//
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// Inputs:
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// V #V by dim list of vertex rest positions
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// W #V by k list of k correspondence weights per vertex
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// WI #V by k list of k correspondence weight indices per vertex. Such that
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// W(j,WI(i)) gives the ith most significant correspondence weight on vertex j
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// Output:
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// M #V * dim by #handles * dim * (dim+1) matrix such that
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// new_V(:) = LBS(V,W,A) = reshape(M * A,size(V)), where A is a column
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// vectors formed by the entries in each handle's dim by dim+1
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// transformation matrix. Specifcally, A =
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// reshape(permute(Astack,[3 1 2]),n*dim*(dim+1),1)
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// or A = [Lxx;Lyx;Lxy;Lyy;tx;ty], and likewise for other dim
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// if Astack(:,:,i) is the dim by (dim+1) transformation at handle i
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//
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IGL_INLINE void lbs_matrix_column(
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const Eigen::MatrixXd & V,
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const Eigen::MatrixXd & W,
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const Eigen::MatrixXi & WI,
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Eigen::SparseMatrix<double>& M);
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IGL_INLINE void lbs_matrix_column(
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const Eigen::MatrixXd & V,
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const Eigen::MatrixXd & W,
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const Eigen::MatrixXi & WI,
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Eigen::MatrixXd & M);
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}
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#ifndef IGL_STATIC_LIBRARY
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#include "lbs_matrix.cpp"
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#endif
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#endif
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