OpenMEEG
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integrator.h
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1// Project Name: OpenMEEG (http://openmeeg.github.io)
2// © INRIA and ENPC under the French open source license CeCILL-B.
3// See full copyright notice in the file LICENSE.txt
4// If you make a copy of this file, you must either:
5// - provide also LICENSE.txt and modify this header to refer to it.
6// - replace this header by the LICENSE.txt content.
7
8#pragma once
9
10#include <cmath>
11#include <iostream>
12
13#include <vertex.h>
14#include <triangle.h>
15#include <mesh.h>
16
17namespace OpenMEEG {
18
19 class OPENMEEG_EXPORT Integrator {
20
21 typedef Vect3 Point;
22 typedef Point TrianglePoints[3];
23
24 static unsigned safe_order(const unsigned n) {
25 if (n>0 && n<4)
26 return n;
27 std::cout << "Unavailable Gauss order " << n << ": min is 1, max is 3" << std::endl;
28 return (n<1) ? 1 : 3;
29 }
30
31 public:
32
33 Integrator(const unsigned ord): Integrator(ord,0,0.0) { }
34 Integrator(const unsigned ord,const double tol): Integrator(ord,10,tol) { }
35 Integrator(const unsigned ord,const unsigned levels,const double tol=0.0001):
36 order(safe_order(ord)),tolerance(tol),max_depth(levels)
37 { }
38
39 double norm(const double a) const { return fabs(a); }
40 double norm(const Vect3& a) const { return a.norm(); }
41
42 // TODO: T can be deduced from Function.
43
44 template <typename Function>
45 decltype(auto) integrate(const Function& function,const Triangle& triangle) const {
46 const TrianglePoints tripts = { triangle.vertex(0), triangle.vertex(1), triangle.vertex(2) };
47 const auto& coarse = triangle_integration(function,tripts);
48 return (max_depth==0) ? coarse : adaptive_integration(function,tripts,coarse,max_depth);
49 }
50
51 private:
52
53 template <typename Function>
54 decltype(auto) triangle_integration(const Function& function,const TrianglePoints& triangle) const {
55 using T = decltype(function(Vect3()));
56 T result = 0.0;
57 for (unsigned i=0;i<nbPts[order];++i) {
58 Vect3 v(0.0,0.0,0.0);
59 for (unsigned j=0; j<3; ++j)
60 v.multadd(rules[order][i].barycentric_coordinates[j],triangle[j]);
61 result += rules[order][i].weight*function(v);
62 }
63
64 // compute double area of triangle defined by points
65
66 const double area2 = crossprod(triangle[1]-triangle[0],triangle[2]-triangle[0]).norm();
67 return result*area2;
68 }
69
70 template <typename T,typename Function>
71 T adaptive_integration(const Function& function,const TrianglePoints& triangle,const T& coarse,const unsigned level) const {
72 const Point midpoints[] = { 0.5*(triangle[1]+triangle[2]), 0.5*(triangle[2]+triangle[0]), 0.5*(triangle[0]+triangle[1]) };
73 const TrianglePoints new_triangles[] = {
74 { triangle[0], midpoints[1], midpoints[2] }, { midpoints[0], triangle[1], midpoints[2] },
75 { midpoints[0], midpoints[1], triangle[2] }, { midpoints[0], midpoints[1], midpoints[2] }
76 };
77
78 T refined = 0.0;
79 T integrals[4];
80 for (unsigned i=0; i<4; ++i) {
81 integrals[i] = triangle_integration(function,new_triangles[i]);
82 refined += integrals[i];
83 }
84
85 if (norm(coarse-refined)<=tolerance*norm(coarse) || level==0)
86 return refined;
87
88 T sum = 0.0;
89 for (unsigned i=0; i<4; ++i)
90 sum += adaptive_integration(function,new_triangles[i],integrals[i],level-1);
91 return sum;
92 }
93
94 static constexpr unsigned nbPts[4] = { 3, 6, 7, 16 };
95
96 const unsigned order;
97 const double tolerance;
98 const unsigned max_depth;
99
100 // Quadrature rules are from Marc Bonnet's book: Equations integrales..., Appendix B.3
101
102 struct QuadratureRule {
103 double barycentric_coordinates[3];
104 double weight;
105 };
106
107 static constexpr QuadratureRule rules[4][16] = {
108 { // Parameters for N=3
109 {{ 0.166666666666667, 0.166666666666667, 0.666666666666667 }, 0.166666666666667 },
110 {{ 0.166666666666667, 0.666666666666667, 0.166666666666667 }, 0.166666666666667 },
111 {{ 0.666666666666667, 0.166666666666667, 0.166666666666667 }, 0.166666666666667 },
112 {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 },
113 {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 },
114 {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 },
115 {{ 0.0, 0.0, 0.0 }, 0.0 }
116 },
117 { // Parameters for N=6
118 {{ 0.445948490915965, 0.445948490915965, 0.108103018168070 }, 0.111690794839005 },
119 {{ 0.445948490915965, 0.108103018168070, 0.445948490915965 }, 0.111690794839005 },
120 {{ 0.108103018168070, 0.445948490915965, 0.445948490915965 }, 0.111690794839005 },
121 {{ 0.091576213509771, 0.091576213509771, 0.816847572980458 }, 0.054975871827661 },
122 {{ 0.091576213509771, 0.816847572980458, 0.091576213509771 }, 0.054975871827661 },
123 {{ 0.816847572980458, 0.091576213509771, 0.091576213509771 }, 0.054975871827661 },
124 {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 },
125 {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 },
126 {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }
127 },
128 { // Parameters for N=7
129 {{ 0.333333333333333, 0.333333333333333, 0.333333333333333 }, 0.1125 },
130 {{ 0.470142064105115, 0.470142064105115, 0.059715871789770 }, 0.066197076394253 },
131 {{ 0.470142064105115, 0.059715871789770, 0.470142064105115 }, 0.066197076394253 },
132 {{ 0.059715871789770, 0.470142064105115, 0.470142064105115 }, 0.066197076394253 },
133 {{ 0.101286507323456, 0.101286507323456, 0.797426985353088 }, 0.062969590272414 },
134 {{ 0.101286507323456, 0.797426985353088, 0.101286507323456 }, 0.062969590272414 },
135 {{ 0.797426985353088, 0.101286507323456, 0.101286507323456 }, 0.062969590272414 },
136 {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 },
137 {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 }, {{ 0.0, 0.0, 0.0 }, 0.0 },
138 {{ 0.0, 0.0, 0.0 }, 0.0 }
139 },
140 { // Parameters for N=16
141 {{ 0.333333333333333, 0.333333333333333, 0.333333333333333 }, 0.072157803838893 },
142 {{ 0.081414823414554, 0.459292588292722, 0.459292588292722 }, 0.047545817133642 },
143 {{ 0.459292588292722, 0.081414823414554, 0.459292588292722 }, 0.047545817133642 },
144 {{ 0.459292588292722, 0.459292588292722, 0.081414823414554 }, 0.047545817133642 },
145 {{ 0.898905543365937, 0.050547228317031, 0.050547228317031 }, 0.016229248811599 },
146 {{ 0.050547228317031, 0.898905543365937, 0.050547228317031 }, 0.016229248811599 },
147 {{ 0.050547228317031, 0.050547228317031, 0.898905543365937 }, 0.016229248811599 },
148 {{ 0.658861384496479, 0.170569307751760, 0.170569307751761 }, 0.051608685267359 },
149 {{ 0.170569307751760, 0.658861384496479, 0.170569307751761 }, 0.051608685267359 },
150 {{ 0.170569307751760, 0.170569307751761, 0.658861384496479 }, 0.051608685267359 },
151 {{ 0.008394777409957, 0.728492392955404, 0.263112829634639 }, 0.013615157087217 },
152 {{ 0.728492392955404, 0.008394777409957, 0.263112829634639 }, 0.013615157087217 },
153 {{ 0.728492392955404, 0.263112829634639, 0.008394777409957 }, 0.013615157087217 },
154 {{ 0.008394777409957, 0.263112829634639, 0.728492392955404 }, 0.013615157087217 },
155 {{ 0.263112829634639, 0.008394777409957, 0.728492392955404 }, 0.013615157087217 },
156 {{ 0.263112829634639, 0.728492392955404, 0.008394777409957 }, 0.013615157087217 }
157 }
158 };
159 };
160}
Integrator(const unsigned ord, const unsigned levels, const double tol=0.0001)
Definition: integrator.h:35
Integrator(const unsigned ord, const double tol)
Definition: integrator.h:34
decltype(auto) integrate(const Function &function, const Triangle &triangle) const
Definition: integrator.h:45
double norm(const double a) const
Definition: integrator.h:39
Integrator(const unsigned ord)
Definition: integrator.h:33
double norm(const Vect3 &a) const
Definition: integrator.h:40
Triangle Triangle class.
Definition: triangle.h:45
Vertex & vertex(const unsigned &vindex)
Definition: triangle.h:83
Vect3.
Definition: vect3.h:28
double norm() const
Definition: vect3.h:63