87 lines
3.0 KiB
C
87 lines
3.0 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) 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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// HAUSDORFF 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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// Known issue: 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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// Inputs:
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// VA #VA by 3 list of vertex positions
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// FA #FA by 3 list of face indices into VA
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// VB #VB by 3 list of vertex positions
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// FB #FB by 3 list of face indices into VB
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// Outputs:
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// d hausdorff distance
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// //pair 2 by 3 list of "determiner points" so that pair(1,:) is from A
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// // and pair(2,:) is from B
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//
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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::PlainObjectBase<DerivedVA> & VA,
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const Eigen::PlainObjectBase<DerivedFA> & FA,
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const Eigen::PlainObjectBase<DerivedVB> & VB,
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const Eigen::PlainObjectBase<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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// Inputs:
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// V 3 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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// 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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// Outputs:
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// l lower bound on Hausdorff distance
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// 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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