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src/libigl/igl/biharmonic_coordinates.h

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+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_BIHARMONIC_COORDINATES_H
+#define IGL_BIHARMONIC_COORDINATES_H
+#include "igl_inline.h"
+#include <Eigen/Dense>
+#include <vector>
+namespace igl
+{
+  // Compute "discrete biharmonic generalized barycentric coordinates" as
+  // described in "Linear Subspace Design for Real-Time Shape Deformation"
+  // [Wang et al. 2015]. Not to be confused with "Bounded Biharmonic Weights
+  // for Real-Time Deformation" [Jacobson et al. 2011] or "Biharmonic
+  // Coordinates" (2D complex barycentric coordinates) [Weber et al. 2012].
+  // These weights minimize a discrete version of the squared Laplacian energy
+  // subject to positional interpolation constraints at selected vertices
+  // (point handles) and transformation interpolation constraints at regions
+  // (region handles).
+  //
+  // Templates:
+  //   HType  should be a simple index type e.g. `int`,`size_t`
+  // Inputs:
+  //   V  #V by dim list of mesh vertex positions
+  //   T  #T by dim+1 list of / triangle indices into V      if dim=2
+  //                          \ tetrahedron indices into V   if dim=3
+  //   S  #point-handles+#region-handles list of lists of selected vertices for
+  //     each handle. Point handles should have singleton lists and region
+  //     handles should have lists of size at least dim+1 (and these points
+  //     should be in general position).
+  // Outputs:
+  //   W  #V by #points-handles+(#region-handles * dim+1) matrix of weights so
+  //     that columns correspond to each handles generalized barycentric
+  //     coordinates (for point-handles) or animation space weights (for region
+  //     handles).
+  // returns true only on success
+  //
+  // Example:
+  //
+  //     MatrixXd W;
+  //     igl::biharmonic_coordinates(V,F,S,W);
+  //     const size_t dim = T.cols()-1;
+  //     MatrixXd H(W.cols(),dim);
+  //     {
+  //       int c = 0;
+  //       for(int h = 0;h<S.size();h++)
+  //       {
+  //         if(S[h].size()==1)
+  //         {
+  //           H.row(c++) = V.block(S[h][0],0,1,dim);
+  //         }else
+  //         {
+  //           H.block(c,0,dim+1,dim).setIdentity();
+  //           c+=dim+1;
+  //         }
+  //       }
+  //     }
+  //     assert( (V-(W*H)).array().maxCoeff() < 1e-7 );
+  template <
+    typename DerivedV,
+    typename DerivedT,
+    typename SType,
+    typename DerivedW>
+  IGL_INLINE bool biharmonic_coordinates(
+    const Eigen::PlainObjectBase<DerivedV> & V,
+    const Eigen::PlainObjectBase<DerivedT> & T,
+    const std::vector<std::vector<SType> > & S,
+    Eigen::PlainObjectBase<DerivedW> & W);
+  // k  2-->biharmonic, 3-->triharmonic
+  template <
+    typename DerivedV,
+    typename DerivedT,
+    typename SType,
+    typename DerivedW>
+  IGL_INLINE bool biharmonic_coordinates(
+    const Eigen::PlainObjectBase<DerivedV> & V,
+    const Eigen::PlainObjectBase<DerivedT> & T,
+    const std::vector<std::vector<SType> > & S,
+    const int k,
+    Eigen::PlainObjectBase<DerivedW> & W);
+
+};
+#  ifndef IGL_STATIC_LIBRARY
+#    include "biharmonic_coordinates.cpp"
+#  endif
+#endif