80 lines
3.1 KiB
C
80 lines
3.1 KiB
C
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// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2017 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_BIJECTIVE_COMPOSITE_HARMONIC_MAPPING_H
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#define IGL_BIJECTIVE_COMPOSITE_HARMONIC_MAPPING_H
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#include "igl_inline.h"
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#include <Eigen/Core>
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namespace igl
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{
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// Compute a planar mapping of a triangulated polygon (V,F) subjected to
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// boundary conditions (b,bc). The mapping should be bijective in the sense
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// that no triangles' areas become negative (this assumes they started
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// positive). This mapping is computed by "composing" harmonic mappings
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// between incremental morphs of the boundary conditions. This is a bit like
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// a discrete version of "Bijective Composite Mean Value Mappings" [Schneider
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// et al. 2013] but with a discrete harmonic map (cf. harmonic coordinates)
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// instead of mean value coordinates. This is inspired by "Embedding a
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// triangular graph within a given boundary" [Xu et al. 2011].
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//
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// Inputs:
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// V #V by 2 list of triangle mesh vertex positions
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// F #F by 3 list of triangle indices into V
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// b #b list of boundary indices into V
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// bc #b by 2 list of boundary conditions corresponding to b
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// Outputs:
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// U #V by 2 list of output mesh vertex locations
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// Returns true if and only if U contains a successful bijectie mapping
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//
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//
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template <
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typename DerivedV,
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typename DerivedF,
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typename Derivedb,
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typename Derivedbc,
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typename DerivedU>
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IGL_INLINE bool bijective_composite_harmonic_mapping(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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const Eigen::MatrixBase<Derivedb> & b,
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const Eigen::MatrixBase<Derivedbc> & bc,
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Eigen::PlainObjectBase<DerivedU> & U);
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//
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// Inputs:
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// min_steps minimum number of steps to take from V(b,:) to bc
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// max_steps minimum number of steps to take from V(b,:) to bc (if
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// max_steps == min_steps then no further number of steps will be tried)
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// num_inner_iters number of iterations of harmonic solves to run after
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// for each morph step (to try to push flips back in)
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// test_for_flips whether to check if flips occurred (and trigger more
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// steps). if test_for_flips = false then this function always returns
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// true
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//
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template <
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typename DerivedV,
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typename DerivedF,
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typename Derivedb,
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typename Derivedbc,
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typename DerivedU>
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IGL_INLINE bool bijective_composite_harmonic_mapping(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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const Eigen::MatrixBase<Derivedb> & b,
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const Eigen::MatrixBase<Derivedbc> & bc,
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const int min_steps,
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const int max_steps,
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const int num_inner_iters,
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const bool test_for_flips,
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Eigen::PlainObjectBase<DerivedU> & U);
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}
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#ifndef IGL_STATIC_LIBRARY
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# include "bijective_composite_harmonic_mapping.cpp"
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#endif
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#endif
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