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44 lines
1.5 KiB
44 lines
1.5 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) 2016 Michael Rabinovich <michaelrabinovich27@gmail.com>
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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_EULER_CHARACTERISTIC_H
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#define IGL_EULER_CHARACTERISTIC_H
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#include "igl_inline.h"
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#include <Eigen/Dense>
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#include <Eigen/Sparse>
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#include <vector>
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namespace igl
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{
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/// Computes the Euler characteristic of a given mesh (V,F)
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///
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/// χ = |V| - |E| + |F|
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///
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/// For example,
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/// - a single triangle has 3 - 3 + 1 = 1
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/// - a tetrahedron has 4 - 6 + 4 = 2
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///
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/// @param[in] F #F by dim list of mesh faces (must be triangles)
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/// @return An int containing the Euler characteristic
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///
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/// \note There is [some confusion](https://github.com/libigl/libigl/issues/2249#issue-1863608449) over the standard definition of Euler
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/// characteristic. libigl's definition agrees with
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/// [wikipedia](https://en.wikipedia.org/wiki/Euler_characteristic) and [David
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/// Eppstein's
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/// proofs](https://www.ics.uci.edu/~eppstein/junkyard/euler/all.html).
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template <typename DerivedF>
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IGL_INLINE int euler_characteristic(
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const Eigen::MatrixBase<DerivedF> & F);
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}
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#ifndef IGL_STATIC_LIBRARY
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# include "euler_characteristic.cpp"
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#endif
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#endif
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