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| | SmoothingEnergy2D (const std::array< Vector2d, 3 > &pts, const double &M, const Vector3d &L_w) |
| | The smoothing energy of a vertex position on a polyline.
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TVector | initial_position () const |
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double | value (const TVector &x) override |
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void | gradient (const TVector &x, TVector &gradv) override |
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void | hessian (const TVector &x, THessian &hessian) override |
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void | hessian (const TVector &x, MatrixXd &hessian) override |
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void | solution_changed (const TVector &new_x) override |
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static void | local_mass_and_stiffness (const std::array< Vector2d, 3 > &pts, double &M, Vector3d &L_w) |
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static void | uniform_mass_and_stiffness (const std::array< Vector2d, 3 > &pts, double &M, Vector3d &L_w) |
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◆ SmoothingEnergy2D()
| wmtk::optimization::SmoothingEnergy2D::SmoothingEnergy2D |
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const std::array< Vector2d, 3 > & |
pts, |
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const double & |
M, |
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const Vector3d & |
L_w |
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The smoothing energy of a vertex position on a polyline.
Three positions must be provided, the optimized position (p0) and its two neighbors (p1, p2).
◆ m_L_w_row
| Vector3d wmtk::optimization::SmoothingEnergy2D::m_L_w_row |
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The first row of stiffness matrix L_w which belongs to the optimized vertex. By convention, this needs to be sorted such that the first entry belongs to the optimized vertex.
The full stiffness matrix L_w has shape NxN (more specifically in our case 3x3 as we have three points), but the rows of fixed vertices are empty. Therefore, we only need to store the one non-empty row of the optimized vertex. By convention of m_pts, this must be the first one, i.e., L_w.row(0).
◆ m_LTML_row
| Vector3d wmtk::optimization::SmoothingEnergy2D::m_LTML_row |
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We only need the first row of LTML, because all other vertices are fixed.
L = M_inv * L_w LTML = L^T * M * L = L_w^T * M_inv * L_w We only want to optimize one vertex, so we only need one row of LTML: LTML.row(0) = M_inv * L_w(0,0) * L_w.row(0) <– this is what is stored in m_LTML_row
◆ m_pts
| std::array<Vector2d, 3> wmtk::optimization::SmoothingEnergy2D::m_pts |
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The optimized point and its (two) neighbors. For the optimization, we use the convention that m_pts[0] is the optimized vertex and the neighbors m_pts[1] and m_pts[2] are fixed.
The documentation for this class was generated from the following files:
- /home/runner/work/wildmeshing-toolkit/wildmeshing-toolkit/src/wmtk/optimization/DirichletEnergy.hpp
- /home/runner/work/wildmeshing-toolkit/wildmeshing-toolkit/src/wmtk/optimization/DirichletEnergy.cpp
