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80 lines
2.9 KiB
80 lines
2.9 KiB
1 year ago
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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) 2015 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_HAUSDORFF_H
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#define IGL_HAUSDORFF_H
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#include "igl_inline.h"
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#include <Eigen/Dense>
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#include <functional>
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namespace igl
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{
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/// Compute the Hausdorff distance between mesh (VA,FA) and mesh
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/// (VB,FB). This is the
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///
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/// d(A,B) = max ( max min d(a,b) , max min d(b,a) )
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/// a∈A b∈B b∈B a∈A
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///
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/// \bug This is only computing max(min(va,B),min(vb,A)). This is
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/// better than max(min(va,Vb),min(vb,Va)). This (at least) is missing
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/// "edge-edge" cases like the distance between the two different
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/// triangulations of a non-planar quad in 3D. Even simpler, consider the
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/// Hausdorff distance between the non-convex, block letter V polygon (with 7
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/// vertices) in 2D and its convex hull. The Hausdorff distance is defined by
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/// the midpoint in the middle of the segment across the concavity and some
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/// non-vertex point _on the edge_ of the V.
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/// Known issue: due to the issue above, this also means that unreferenced
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/// vertices can give unexpected results. Therefore, we assume the inputs have
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/// no unreferenced vertices.
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///
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/// @param[in] VA #VA by 3 list of vertex positions
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/// @param[in] FA #FA by 3 list of face indices into VA
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/// @param[in] VB #VB by 3 list of vertex positions
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/// @param[in] FB #FB by 3 list of face indices into VB
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/// @param[out] d hausdorff distance
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template <
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typename DerivedVA,
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typename DerivedFA,
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typename DerivedVB,
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typename DerivedFB,
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typename Scalar>
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IGL_INLINE void hausdorff(
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const Eigen::MatrixBase<DerivedVA> & VA,
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const Eigen::MatrixBase<DerivedFA> & FA,
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const Eigen::MatrixBase<DerivedVB> & VB,
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const Eigen::MatrixBase<DerivedFB> & FB,
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Scalar & d);
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/// Compute lower and upper bounds (l,u) on the Hausdorff distance between a triangle
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/// (V) and a pointset (e.g., mesh, triangle soup) given by a distance function
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/// handle (dist_to_B).
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///
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/// @param[in] V #V by 3 list of corner positions so that V.row(i) is the position of the
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/// ith corner
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/// @param[in] dist_to_B function taking the x,y,z coordinate of a query position and
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/// outputting the closest-point distance to some point-set B
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/// @param[out] l lower bound on Hausdorff distance
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/// @param[out] u upper bound on Hausdorff distance
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///
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template <
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typename DerivedV,
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typename Scalar>
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IGL_INLINE void hausdorff(
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const Eigen::MatrixBase<DerivedV>& V,
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const std::function<
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Scalar(const Scalar &,const Scalar &, const Scalar &)> & dist_to_B,
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Scalar & l,
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Scalar & u);
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}
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#ifndef IGL_STATIC_LIBRARY
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# include "hausdorff.cpp"
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#endif
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#endif
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