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41 lines
1.5 KiB
41 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) 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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/// Gradient operator on a triangle mesh.
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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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/// @param[in] V #vertices by 3 list of mesh vertex positions
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/// @param[in] F #faces by 3 list of mesh face indices [or a #faces by 4 list of tetrahedral indices]
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/// @param[out] G #faces*dim by #V Gradient operator
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/// @param[in] uniform boolean (default false) - Use a uniform mesh instead of the vertices V
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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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