You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
43 lines
1.5 KiB
43 lines
1.5 KiB
// This file is part of libigl, a simple c++ geometry processing library.
|
|
//
|
|
// Copyright (C) 2016 Michael Rabinovich <michaelrabinovich27@gmail.com>
|
|
// Copyright (C) 2017 Alec Jacobson <alecjacobson@gmail.com>
|
|
//
|
|
// 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_EULER_CHARACTERISTIC_H
|
|
#define IGL_EULER_CHARACTERISTIC_H
|
|
#include "igl_inline.h"
|
|
|
|
#include <Eigen/Dense>
|
|
#include <Eigen/Sparse>
|
|
#include <vector>
|
|
namespace igl
|
|
{
|
|
/// Computes the Euler characteristic of a given mesh (V,F)
|
|
///
|
|
/// χ = |V| - |E| + |F|
|
|
///
|
|
/// For example,
|
|
/// - a single triangle has 3 - 3 + 1 = 1
|
|
/// - a tetrahedron has 4 - 6 + 4 = 2
|
|
///
|
|
/// @param[in] F #F by dim list of mesh faces (must be triangles)
|
|
/// @return An int containing the Euler characteristic
|
|
///
|
|
/// \note There is [some confusion](https://github.com/libigl/libigl/issues/2249#issue-1863608449) over the standard definition of Euler
|
|
/// characteristic. libigl's definition agrees with
|
|
/// [wikipedia](https://en.wikipedia.org/wiki/Euler_characteristic) and [David
|
|
/// Eppstein's
|
|
/// proofs](https://www.ics.uci.edu/~eppstein/junkyard/euler/all.html).
|
|
template <typename DerivedF>
|
|
IGL_INLINE int euler_characteristic(
|
|
const Eigen::MatrixBase<DerivedF> & F);
|
|
}
|
|
|
|
#ifndef IGL_STATIC_LIBRARY
|
|
# include "euler_characteristic.cpp"
|
|
#endif
|
|
|
|
#endif
|
|
|