libigl/include/igl/bijective_composite_harmonic_mapping.h

// This file is part of libigl, a simple c++ geometry processing library.
// 
// Copyright (C) 2017 Alec Jacobson <[email protected]>
// 
// 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_BIJECTIVE_COMPOSITE_HARMONIC_MAPPING_H
#define IGL_BIJECTIVE_COMPOSITE_HARMONIC_MAPPING_H
#include "igl_inline.h"
#include <Eigen/Core>

namespace igl 
{
  /// Compute a injective planar mapping of a triangulated polygon (V,F) subjected to
  /// boundary conditions (b,bc). The mapping should be bijective in the sense
  /// that no triangles' areas become negative (this assumes they started
  /// positive). This mapping is computed by "composing" harmonic mappings
  /// between incremental morphs of the boundary conditions. This is a bit like
  /// a discrete version of "Bijective Composite Mean Value Mappings" [Schneider
  /// et al. 2013] but with a discrete harmonic map (cf. harmonic coordinates)
  /// instead of mean value coordinates. This is inspired by "Embedding a
  /// triangular graph within a given boundary" [Xu et al. 2011].
  ///
  /// @param[in] V  #V by 2 list of triangle mesh vertex positions
  /// @param[in] F  #F by 3 list of triangle indices into V
  /// @param[in] b  #b list of boundary indices into V
  /// @param[in] bc  #b by 2 list of boundary conditions corresponding to b
  /// @param[out] U  #V by 2 list of output mesh vertex locations
  /// @return true if and only if U contains a successful bijectie mapping
  ///
  /// 
  template <
    typename DerivedV,
    typename DerivedF,
    typename Derivedb,
    typename Derivedbc,
    typename DerivedU>
  IGL_INLINE bool bijective_composite_harmonic_mapping(
    const Eigen::MatrixBase<DerivedV> & V,
    const Eigen::MatrixBase<DerivedF> & F,
    const Eigen::MatrixBase<Derivedb> & b,
    const Eigen::MatrixBase<Derivedbc> & bc,
    Eigen::PlainObjectBase<DerivedU> & U);
  ///  \overload
  ///  @param[in] min_steps  minimum number of steps to take from V(b,:) to bc
  ///  @param[in] max_steps  minimum number of steps to take from V(b,:) to bc (if
  ///     max_steps == min_steps then no further number of steps will be tried)
  ///  @param[in] num_inner_iters  number of iterations of harmonic solves to run after
  ///     for each morph step (to try to push flips back in)
  ///  @param[in] test_for_flips  whether to check if flips occurred (and trigger more
  ///     steps). if test_for_flips = false then this function always returns
  ///     true
  template <
    typename DerivedV,
    typename DerivedF,
    typename Derivedb,
    typename Derivedbc,
    typename DerivedU>
  IGL_INLINE bool bijective_composite_harmonic_mapping(
    const Eigen::MatrixBase<DerivedV> & V,
    const Eigen::MatrixBase<DerivedF> & F,
    const Eigen::MatrixBase<Derivedb> & b,
    const Eigen::MatrixBase<Derivedbc> & bc,
    const int min_steps,
    const int max_steps,
    const int num_inner_iters,
    const bool test_for_flips,
    Eigen::PlainObjectBase<DerivedU> & U);
}

#ifndef IGL_STATIC_LIBRARY
#  include "bijective_composite_harmonic_mapping.cpp"
#endif
#endif