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