Peiqi Wang HW4

include/arap_precompute.h

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+#ifndef ARAP_PRECOMPUTE_H
+#define ARAP_PRECOMPUTE_H
+#include <Eigen/Core>
+#include <Eigen/Sparse>
+
+namespace igl
+{
+  template <typename T> struct min_quad_with_fixed_data;
+}
+
+// Precompute data needed to efficiently conduct local-global iterations for an
+// arap deformation. This includes the `data` struct employed by
+// `igl::min_quad_with_fixed` to solve the global step" and constructing the
+// bi-linear form `K` that mixes rotation degrees of freedom with unknown
+// positions for preparing the covariance matrices of the local step and the
+// linear term of the global step.
+//
+// Inputs:
+//   V  #V by dim vertex positions
+//   F  #F by simplex-size list of element indices
+//   b  #b indices into V of handle vertices
+// Outputs:
+//   data  pre-factorized system matrix etc. (see `igl::min_quad_with_fixed`)
+//   K  #R*dim by #V
+void arap_precompute(
+  const Eigen::MatrixXd & V,
+  const Eigen::MatrixXi & F,
+  const Eigen::VectorXi & b,
+  igl::min_quad_with_fixed_data<double> & data,
+  Eigen::SparseMatrix<double> & K);
+
+#endif
+

include/arap_single_iteration.h

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+#ifndef ARAP_SINGLE_ITERATION_H
+#define ARAP_SINGLE_ITERATION_H
+#include <Eigen/Core>
+#include <Eigen/Sparse>
+
+namespace igl
+{
+  template <typename T> struct min_quad_with_fixed_data;
+}
+
+// Given precomputed data (`data` and `K`), handle _positions_ `bc` and current
+// positions of all vertices `U`, conduct a _single_ iteration of the
+// local-global solver for minimizing the as-rigid-as-possible energy. Output
+// the _positions_ of all vertices of the mesh (by overwriting `U`).
+//
+// Inputs:
+//   data  pre-factorized system matrix etc. (see `arap_precompute`
+//   K  pre-constructed bi-linear term of energy combining rotations and
+//     positions
+//   U  #V by dim list of current positions (see output)
+// Outputs:
+//   U  #V by dim list of new positions (see input)
+void arap_single_iteration(
+  const igl::min_quad_with_fixed_data<double> & data,
+  const Eigen::SparseMatrix<double> & K,
+  const Eigen::MatrixXd & bc,
+  Eigen::MatrixXd & U);
+
+#endif

include/biharmonic_precompute.h

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+#ifndef BIHARMONIC_PRECOMPUTE_H
+#define BIHARMONIC_PRECOMPUTE_H
+#include <Eigen/Core>
+
+namespace igl
+{
+  template <typename T> struct min_quad_with_fixed_data;
+}
+
+// Precompute data needed to efficiently solve for a biharmonic deformation
+// given a mesh with vertices `V` and faces `F` and a list of selected vertices
+// as indices `b` into `V`. The output should be a prefacorized system using
+// the `data` struct employed by `igl::min_quad_with_fixed`.
+//
+// Inputs:
+//   V  #V by dim vertex positions
+//   F  #F by simplex-size list of element indices
+//   b  #b indices into V of handle vertices
+// Outputs:
+//   data  pre-factorized system matrix etc. (see `igl::min_quad_with_fixed`)
+void biharmonic_precompute(
+  const Eigen::MatrixXd & V,
+  const Eigen::MatrixXi & F,
+  const Eigen::VectorXi & b,
+  igl::min_quad_with_fixed_data<double> & data);
+
+#endif

include/biharmonic_solve.h

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+#ifndef BIHARMONIC_SOLVE_H
+#define BIHARMONIC_SOLVE_H
+#include <Eigen/Core>
+
+namespace igl
+{
+  template <typename T> struct min_quad_with_fixed_data;
+}
+
+// Given precomputation data and a list of handle _displacements_ determine
+// _displacements_ for all vertices in the mesh.
+//
+// Inputs:
+//   data  pre-factorized system matrix etc. (see `biharmonic_precompute`
+//   bc  #b by 3 list of displacements for each handle vertex
+// Outputs:
+//   D  #V by 3 list of displacements
+void biharmonic_solve(
+  const igl::min_quad_with_fixed_data<double> & data,
+  const Eigen::MatrixXd & bc,
+  Eigen::MatrixXd & D);
+
+
+#endif
+