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Error_quadric.h
1/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
2 * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
3 * Author(s): David Salinas
4 *
5 * Copyright (C) 2014 Inria
6 *
7 * Modification(s):
8 * - YYYY/MM Author: Description of the modification
9 */
10
11#ifndef GARLAND_HECKBERT_ERROR_QUADRIC_H_
12#define GARLAND_HECKBERT_ERROR_QUADRIC_H_
13
14#include <boost/optional/optional.hpp>
15
16#include <vector>
17#include <utility>
18
19template <typename Point> class Error_quadric {
20 private:
21 double coeff[10];
22
23 public:
24 Error_quadric() {
25 clear();
26 }
27
49 Error_quadric(const Point & p0, const Point & p1, const Point & p2) {
50 Point normal(unit_normal(p0, p1, p2));
51 double a = normal[0];
52 double b = normal[1];
53 double c = normal[2];
54 double d = -a * p0[0] - b * p0[1] - c * p0[2];
55 coeff[0] = a*a;
56 coeff[1] = a*b;
57 coeff[2] = a*c;
58 coeff[3] = a*d;
59 coeff[4] = b*b;
60 coeff[5] = b*c;
61 coeff[6] = b*d;
62 coeff[7] = c*c;
63 coeff[8] = c*d;
64 coeff[9] = d*d;
65
66 double area_p0p1p2 = std::sqrt(squared_area(p0, p1, p2));
67 for (auto& x : coeff)
68 x *= area_p0p1p2;
69 }
70
71 inline double squared_area(const Point& p0, const Point& p1, const Point& p2) {
72 // if (x1,x2,x3) = p1-p0 and (y1,y2,y3) = p2-p0
73 // then the squared area is = (u^2+v^2+w^2)/4
74 // with: u = x2 * y3 - x3 * y2;
75 // v = x3 * y1 - x1 * y3;
76 // w = x1 * y2 - x2 * y1;
77 Point p0p1(p1 - p0);
78 Point p0p2(p2 - p0);
79 double A = p0p1[1] * p0p2[2] - p0p1[2] * p0p2[1];
80 double B = p0p1[2] * p0p2[0] - p0p1[0] * p0p2[2];
81 double C = p0p1[0] * p0p2[1] - p0p1[1] * p0p2[0];
82 return 1. / 4. * (A * A + B * B + C * C);
83 }
84
85 void clear() {
86 for (auto& x : coeff)
87 x = 0;
88 }
89
90 Error_quadric& operator+=(const Error_quadric& other) {
91 if (this != &other) {
92 for (int i = 0; i < 10; ++i)
93 coeff[i] += other.coeff[i];
94 }
95 return *this;
96 }
97
101 inline double cost(const Point& point) const {
102 double cost =
103 coeff[0] * point.x() * point.x() + coeff[4] * point.y() * point.y() + coeff[7] * point.z() * point.z()
104 + 2 * (coeff[1] * point.x() * point.y() + coeff[5] * point.y() * point.z() + coeff[2] * point.z() * point.x())
105 + 2 * (coeff[3] * point.x() + coeff[6] * point.y() + coeff[8] * point.z())
106 + coeff[9];
107 if (cost < 0) {
108 return 0;
109 } else {
110 return cost;
111 }
112 }
113
114 inline double grad_determinant() const {
115 return
116 coeff[0] * coeff[4] * coeff[7]
117 - coeff[0] * coeff[5] * coeff[5]
118 - coeff[1] * coeff[1] * coeff[7]
119 + 2 * coeff[1] * coeff[5] * coeff[2]
120 - coeff[4] * coeff[2] * coeff[2];
121 }
122
127 inline Point solve_linear_gradient(double det) const {
128 return Point({
129 (-coeff[1] * coeff[5] * coeff[8] + coeff[1] * coeff[7] * coeff[6] + coeff[2] * coeff[8] * coeff[4] -
130 coeff[2] * coeff[5] * coeff[6] - coeff[3] * coeff[4] * coeff[7] + coeff[3] * coeff[5] * coeff[5])
131 / det,
132 (coeff[0] * coeff[5] * coeff[8] - coeff[0] * coeff[7] * coeff[6] - coeff[5] * coeff[2] * coeff[3] -
133 coeff[1] * coeff[2] * coeff[8] + coeff[6] * coeff[2] * coeff[2] + coeff[1] * coeff[3] * coeff[7])
134 / det,
135 (-coeff[8] * coeff[0] * coeff[4] + coeff[8] * coeff[1] * coeff[1] + coeff[2] * coeff[3] * coeff[4] +
136 coeff[5] * coeff[0] * coeff[6] - coeff[5] * coeff[1] * coeff[3] - coeff[1] * coeff[2] * coeff[6])
137 / det
138 });
139 }
140
146 boost::optional<Point> min_cost(double scale = 1) const {
147 // const double min_determinant = 1e-4 * scale*scale;
148 const double min_determinant = 1e-5;
149 boost::optional<Point> pt_res;
150 double det = grad_determinant();
151 if (std::abs(det) > min_determinant)
152 pt_res = solve_linear_gradient(det);
153 return pt_res;
154 }
155
156 friend std::ostream& operator<<(std::ostream& stream, const Error_quadric& quadric) {
157 stream << "\n[ " << quadric.coeff[0] << "," << quadric.coeff[1] << "," << quadric.coeff[2] << "," <<
158 quadric.coeff[3] << ";\n";
159 stream << " " << quadric.coeff[1] << "," << quadric.coeff[4] << "," << quadric.coeff[5] << "," <<
160 quadric.coeff[6] << ";\n";
161 stream << " " << quadric.coeff[2] << "," << quadric.coeff[5] << "," << quadric.coeff[7] << "," <<
162 quadric.coeff[8] << ";\n";
163 stream << " " << quadric.coeff[3] << "," << quadric.coeff[6] << "," << quadric.coeff[8] << "," <<
164 quadric.coeff[9] << "]";
165 return stream;
166 }
167};
168
169#endif // GARLAND_HECKBERT_ERROR_QUADRIC_H_
std::ostream & operator<<(std::ostream &os, const Permutahedral_representation< Vertex, OrderedSetPartition > &simplex)
Print a permutahedral representation to a stream.
Definition: Permutahedral_representation.h:173