48 lines
1.6 KiB
C
48 lines
1.6 KiB
C
|
// This file is part of libigl, a simple c++ geometry processing library.
|
||
|
|
//
|
||
|
|
// Copyright (C) 2013 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_GRAD_H
|
||
|
|
#define IGL_GRAD_H
|
||
|
|
#include "igl_inline.h"
|
||
|
|
|
||
|
|
#include <Eigen/Core>
|
||
|
|
#include <Eigen/Sparse>
|
||
|
|
|
||
|
|
namespace igl {
|
||
|
|
// GRAD
|
||
|
|
// G = grad(V,F)
|
||
|
|
//
|
||
|
|
// Compute the numerical gradient operator
|
||
|
|
//
|
||
|
|
// Inputs:
|
||
|
|
// V #vertices by 3 list of mesh vertex positions
|
||
|
|
// F #faces by 3 list of mesh face indices [or a #faces by 4 list of tetrahedral indices]
|
||
|
|
// uniform boolean (default false) - Use a uniform mesh instead of the vertices V
|
||
|
|
// Outputs:
|
||
|
|
// G #faces*dim by #V Gradient operator
|
||
|
|
//
|
||
|
|
|
||
|
|
// Gradient of a scalar function defined on piecewise linear elements (mesh)
|
||
|
|
// is constant on each triangle [tetrahedron] i,j,k:
|
||
|
|
// grad(Xijk) = (Xj-Xi) * (Vi - Vk)^R90 / 2A + (Xk-Xi) * (Vj - Vi)^R90 / 2A
|
||
|
|
// where Xi is the scalar value at vertex i, Vi is the 3D position of vertex
|
||
|
|
// i, and A is the area of triangle (i,j,k). ^R90 represent a rotation of
|
||
|
|
// 90 degrees
|
||
|
|
//
|
||
|
|
template <typename DerivedV, typename DerivedF>
|
||
|
|
IGL_INLINE void grad(
|
||
|
|
const Eigen::MatrixBase<DerivedV>&V,
|
||
|
|
const Eigen::MatrixBase<DerivedF>&F,
|
||
|
|
Eigen::SparseMatrix<typename DerivedV::Scalar> &G,
|
||
|
|
bool uniform = false);
|
||
|
|
}
|
||
|
|
#ifndef IGL_STATIC_LIBRARY
|
||
|
|
# include "grad.cpp"
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#endif
|