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/* ----------------------------------------------------------------------- *
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* This file is part of GEL, http://www.imm.dtu.dk/GEL
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* Copyright (C) the authors and DTU Informatics
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* For license and list of authors, see ../../doc/intro.pdf
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* ----------------------------------------------------------------------- */
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/**
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* @file mesh_optimization.h
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* @brief Functions for energy minimization based mesh optimization.
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*/
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#ifndef __HMESH_MESH_OPTIMIZATION_H
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#define __HMESH_MESH_OPTIMIZATION_H
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#include <algorithm>
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#include "Manifold.h"
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#include "../CGLA/Vec3d.h"
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#include "../Geometry/Implicit.h"
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namespace HMesh
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{
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// forward declarations
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//class Manifold;
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//class HalfEdgeID;
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/// This class represents the energy of an edge. It is used in optimization schemes where edges are swapped (aka flipped). */
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class EnergyFun
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{
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public:
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virtual double delta_energy(const Manifold& m, HalfEdgeID h) const = 0;
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virtual double energy(const Manifold& m, HalfEdgeID h) const {return 0;}
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};
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class MinAngleEnergy: public EnergyFun
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{
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double min_angle(const CGLA::Vec3d& v0, const CGLA::Vec3d& v1, const CGLA::Vec3d& v2) const;
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double thresh;
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public:
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MinAngleEnergy(double _thresh): thresh(_thresh) {}
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double delta_energy(const HMesh::Manifold& m, HMesh::HalfEdgeID h) const;
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};
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class DihedralEnergy: public EnergyFun
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{
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const double gamma;
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const bool use_alpha;
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double cos_ang(const CGLA::Vec3d& n1, const CGLA::Vec3d& n2) const
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{
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return (std::max)(-1.0, (std::min)(1.0, CGLA::dot(n1, n2)));
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}
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double edge_alpha_energy(CGLA::Vec3d v1, CGLA::Vec3d v2, double ca) const
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{
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return pow(CGLA::length(v1-v2)*(acos(ca)), 1.0f/gamma);
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}
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double edge_c_energy(CGLA::Vec3d v1, CGLA::Vec3d v2, double ca) const
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{
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return pow(length(v1-v2)*(1-ca), 1.0f/gamma);
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}
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void compute_angles(const HMesh::Manifold & m, HMesh::HalfEdgeID h) const;
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mutable double ab_12;
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mutable double ab_a1;
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mutable double ab_b1;
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mutable double ab_2c;
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mutable double ab_2d;
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mutable double aa_12;
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mutable double aa_b1;
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mutable double aa_c1;
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mutable double aa_2a;
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mutable double aa_2d;
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public:
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DihedralEnergy(double _gamma = 4.0, bool _use_alpha=false):
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gamma(_gamma), use_alpha(_use_alpha) {}
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double energy(const HMesh::Manifold& m, HMesh::HalfEdgeID h) const;
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double delta_energy(const HMesh::Manifold& m, HMesh::HalfEdgeID h) const;
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double min_angle(const HMesh::Manifold& m, HMesh::HalfEdgeID h) const
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{
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compute_angles(m, h);
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return (std::min)((std::min)((std::min)((std::min)(aa_12, aa_b1), aa_c1), aa_2a), aa_2d);
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}
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};
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class CurvatureEnergy: public EnergyFun
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{
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double abs_mean_curv(const CGLA::Vec3d& v, const std::vector<CGLA::Vec3d>& ring) const;
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public:
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double delta_energy(const HMesh::Manifold& m, HMesh::HalfEdgeID h) const;
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};
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class ValencyEnergy: public EnergyFun
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{
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public:
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double delta_energy(const Manifold& m, HalfEdgeID h) const;
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};
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/// Optimize in a greedy fashion.
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void priority_queue_optimization(Manifold& m, const EnergyFun& efun);
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/// Optimize with simulated annealing. Avoids getting trapped in local minima
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void simulated_annealing_optimization(Manifold& m, const EnergyFun& efun, int max_iter=10000);
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/// Minimize the angle between adjacent triangles. Almost the same as mean curvature minimization
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void minimize_dihedral_angle(Manifold& m, int max_iter=10000, bool anneal=false, bool alpha=false, double gamma=4.0);
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/// Minimizes mean curvature. This is really the same as dihedral angle optimization except that we weight by edge length
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void minimize_curvature(Manifold& m, bool anneal=false);
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/// Minimizes gaussian curvature. Probably less useful than mean curvature.
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void minimize_gauss_curvature(Manifold& m, bool anneal=false);
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/// Maximizes the minimum angle of triangles. Makes the mesh more Delaunay.
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void maximize_min_angle(Manifold& m, float thresh, bool anneal=false);
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/// Tries to achieve valence 6 internally and 4 along edges.
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void optimize_valency(Manifold& m, bool anneal=false);
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/// Make radom flips. Useful for generating synthetic test cases.
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void randomize_mesh(Manifold& m, int max_iter);
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/// Perform many operations in order to equalize edge lengths.
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void edge_equalize(HMesh::Manifold& m, const Geometry::Implicit& imp, int max_iter);
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}
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#endif
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