| 1 | //
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| 2 | // triangle.cc
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| 3 | //
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| 4 | // Copyright (C) 1996 Limit Point Systems, Inc.
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| 5 | //
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| 6 | // Author: Curtis Janssen <cljanss@limitpt.com>
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| 7 | // Maintainer: LPS
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| 8 | //
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| 9 | // This file is part of the SC Toolkit.
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| 10 | //
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| 11 | // The SC Toolkit is free software; you can redistribute it and/or modify
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| 12 | // it under the terms of the GNU Library General Public License as published by
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| 13 | // the Free Software Foundation; either version 2, or (at your option)
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| 14 | // any later version.
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| 15 | //
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| 16 | // The SC Toolkit is distributed in the hope that it will be useful,
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| 17 | // but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 18 | // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 19 | // GNU Library General Public License for more details.
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| 20 | //
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| 21 | // You should have received a copy of the GNU Library General Public License
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| 22 | // along with the SC Toolkit; see the file COPYING.LIB. If not, write to
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| 23 | // the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
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| 24 | //
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| 25 | // The U.S. Government is granted a limited license as per AL 91-7.
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| 26 | //
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| 27 |
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| 28 | #ifdef __GNUC__
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| 29 | #pragma implementation
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| 30 | #endif
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| 31 |
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| 32 | #include <util/misc/formio.h>
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| 33 | #include <util/keyval/keyval.h>
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| 34 | #include <math/isosurf/triangle.h>
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| 35 | #include <math/scmat/vector3.h>
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| 36 |
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| 37 | using namespace std;
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| 38 | using namespace sc;
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| 39 |
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| 40 | /////////////////////////////////////////////////////////////////////////
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| 41 | // Triangle
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| 42 | ///////////////////////////////////////////////////////////////////////////
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| 43 | // Here is the layout of the vertices and edges in the triangles: |
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| 44 | // |
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| 45 | // vertex(1) (r=0, s=1) |
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| 46 | // + |
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| 47 | // / \ _edges[1].vertex(_orientation1) |
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| 48 | // / \ |
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| 49 | // / \ |
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| 50 | // / \ |
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| 51 | // / \ |
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| 52 | // / \ |
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| 53 | // _edges[0] / \ _edges[1] |
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| 54 | // (r = 0) / \ (1-r-s = 0) |
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| 55 | // / \ |
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| 56 | // / \ |
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| 57 | // / \ |
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| 58 | // / \ _edges[1].vertex(!_orientation1)|
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| 59 | // / \ |
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| 60 | // vertex(0)+---------------------------+ |
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| 61 | // (r=0, s=0) _edges[2] (s = 0) vertex(2) (r=1, s=0) |
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| 62 | // |
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| 63 | // Zienkiewicz and Taylor, "The Finite Element Method", 4th Ed, Vol 1, |
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| 64 | // use |
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| 65 | // L1 = 1 - r - s |
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| 66 | // L2 = r, |
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| 67 | // L3 = s. |
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| 68 | // I also use these below. |
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| 69 | ///////////////////////////////////////////////////////////////////////////
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| 70 |
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| 71 | Triangle::Triangle(const Ref<Edge>& v1, const Ref<Edge>& v2, const Ref<Edge>& v3,
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| 72 | unsigned int orientation0)
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| 73 | {
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| 74 | _orientation0 = orientation0;
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| 75 |
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| 76 | _edges[0] = v1;
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| 77 | _edges[1] = v2;
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| 78 | _edges[2] = v3;
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| 79 |
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| 80 | // edge 0 corresponds to r = 0
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| 81 | // edge 1 corresponds to (1-r-s) = 0
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| 82 | // edge 2 corresponds to s = 0
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| 83 | // edge 0 vertex _orientation0 is (r=0,s=0)
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| 84 | // edge 1 vertex _orientation1 is (r=0,s=1)
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| 85 | // edge 2 vertex _orientation2 is (r=1,s=0)
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| 86 | // edge 0 vertex (1-_orientation0) is edge 1 vertex _orientation1
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| 87 | // edge 1 vertex (1-_orientation1) is edge 2 vertex _orientation2
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| 88 | // edge 2 vertex (1-_orientation2) is edge 0 vertex _orientation0
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| 89 |
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| 90 | Ref<Edge> *e = _edges;
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| 91 |
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| 92 | // swap edges 1 and 2 if necessary
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| 93 | if (e[0]->vertex(1-_orientation0) != e[1]->vertex(0)) {
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| 94 | if (e[0]->vertex(1-_orientation0) != e[1]->vertex(1)) {
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| 95 | e[1] = v3;
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| 96 | e[2] = v2;
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| 97 | }
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| 98 | }
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| 99 |
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| 100 | // compute the orientation of _edge[1]
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| 101 | if (e[0]->vertex(1-_orientation0) == e[1]->vertex(0)) {
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| 102 | _orientation1 = 0;
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| 103 | }
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| 104 | else {
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| 105 | _orientation1 = 1;
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| 106 | }
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| 107 |
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| 108 | // compute the orientation of _edge[2]
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| 109 | if (e[1]->vertex(1-_orientation1) == e[2]->vertex(0)) {
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| 110 | _orientation2 = 0;
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| 111 | }
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| 112 | else {
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| 113 | _orientation2 = 1;
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| 114 | }
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| 115 |
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| 116 | // make sure that the triangle is really a triangle
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| 117 | if ( e[0]->vertex(1-_orientation0) != e[1]->vertex(_orientation1)
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| 118 | || e[1]->vertex(1-_orientation1) != e[2]->vertex(_orientation2)
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| 119 | || e[2]->vertex(1-_orientation2) != e[0]->vertex(_orientation0))
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| 120 | {
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| 121 | ExEnv::errn() << "Triangle: given edges that don't form a triangle" << endl;
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| 122 | abort();
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| 123 | }
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| 124 |
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| 125 | _order = 1;
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| 126 | _vertices = new Ref<Vertex>[3];
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| 127 |
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| 128 | _vertices[TriInterpCoef::ijk_to_index(_order, 0, 0)] = vertex(0);
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| 129 | _vertices[TriInterpCoef::ijk_to_index(0, 0, _order)] = vertex(1);
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| 130 | _vertices[TriInterpCoef::ijk_to_index(0, _order, 0)] = vertex(2);
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| 131 | }
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| 132 |
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| 133 | Triangle::~Triangle()
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| 134 | {
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| 135 | if (_vertices) delete[] _vertices;
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| 136 | }
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| 137 |
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| 138 | Ref<Vertex>
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| 139 | Triangle::vertex(int i)
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| 140 | {
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| 141 | return _edges[i]->vertex(orientation(i));
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| 142 | }
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| 143 |
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| 144 | unsigned int
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| 145 | Triangle::orientation(const Ref<Edge>& e) const
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| 146 | {
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| 147 | if (e == _edges[0]) return orientation(0);
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| 148 | if (e == _edges[1]) return orientation(1);
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| 149 | return orientation(2);
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| 150 | }
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| 151 |
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| 152 | int
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| 153 | Triangle::contains(const Ref<Edge>& e) const
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| 154 | {
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| 155 | if (_edges[0] == e) return 1;
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| 156 | if (_edges[1] == e) return 1;
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| 157 | if (_edges[2] == e) return 1;
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| 158 | return 0;
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| 159 | }
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| 160 |
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| 161 | double Triangle::flat_area()
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| 162 | {
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| 163 | double a = _edges[0]->straight_length();
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| 164 | double b = _edges[1]->straight_length();
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| 165 | double c = _edges[2]->straight_length();
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| 166 | double a2 = a*a;
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| 167 | double b2 = b*b;
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| 168 | double c2 = c*c;
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| 169 | return 0.25 * sqrt( 2.0 * (c2*b2 + c2*a2 + a2*b2)
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| 170 | - c2*c2 - b2*b2 - a2*a2);
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| 171 | }
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| 172 |
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| 173 | void Triangle::add_vertices(std::set<Ref<Vertex> >&set)
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| 174 | {
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| 175 | for (int i=0; i<3; i++) set.insert(_edges[i]->vertex(orientation(i)));
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| 176 | }
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| 177 |
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| 178 | void Triangle::add_edges(std::set<Ref<Edge> >&set)
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| 179 | {
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| 180 | for (int i=0; i<3; i++) set.insert(_edges[i]);
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| 181 | }
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| 182 |
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| 183 | void
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| 184 | Triangle::interpolate(double r,double s,const Ref<Vertex>&result,SCVector3&dA)
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| 185 | {
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| 186 | TriInterpCoefKey key(_order, r, s);
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| 187 | Ref<TriInterpCoef> coef = new TriInterpCoef(key);
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| 188 | interpolate(coef, r, s, result, dA);
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| 189 | }
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| 190 |
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| 191 | void
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| 192 | Triangle::interpolate(const Ref<TriInterpCoef>& coef,
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| 193 | double r, double s,
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| 194 | const Ref<Vertex>&result, SCVector3&dA)
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| 195 | {
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| 196 | unsigned int i, j, k;
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| 197 |
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| 198 | //double L1 = 1 - r - s;
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| 199 | //double L2 = r;
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| 200 | //double L3 = s;
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| 201 |
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| 202 | SCVector3 tmp(0.0);
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| 203 | SCVector3 x_s(0.0);
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| 204 | SCVector3 x_r(0.0);
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| 205 | for (i=0; i<=_order; i++) {
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| 206 | for (j=0; j <= _order-i; j++) {
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| 207 | k = _order - i - j;
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| 208 | int index = TriInterpCoef::ijk_to_index(i,j,k);
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| 209 | tmp += coef->coef(i,j,k)*_vertices[index]->point();
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| 210 | x_s += coef->sderiv(i,j,k)*_vertices[index]->point();
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| 211 | x_r += coef->rderiv(i,j,k)*_vertices[index]->point();
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| 212 | }
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| 213 | }
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| 214 | result->set_point(tmp);
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| 215 |
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| 216 | if (result->has_normal()) {
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| 217 | for (i=0; i<_order; i++) {
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| 218 | for (j=0; j <= _order-i; j++) {
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| 219 | k = _order - i - j;
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| 220 | int index = TriInterpCoef::ijk_to_index(i,j,k);
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| 221 | tmp += coef->coef(i,j,k)*_vertices[index]->point();
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| 222 | }
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| 223 | }
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| 224 | result->set_normal(tmp);
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| 225 | }
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| 226 |
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| 227 | // Find the surface element
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| 228 | dA = x_r.cross(x_s);
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| 229 | }
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| 230 |
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| 231 | void
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| 232 | Triangle::interpolate(double r, double s,
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| 233 | const Ref<Vertex>&result, SCVector3&dA,
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| 234 | const Ref<Volume> &vol, double isoval)
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| 235 | {
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| 236 | // set up an initial dummy norm
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| 237 | SCVector3 norm(0.0);
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| 238 | result->set_normal(norm);
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| 239 |
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| 240 | // initial guess
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| 241 | interpolate(r,s,result,dA);
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| 242 |
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| 243 | // now refine that guess
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| 244 | SCVector3 trialpoint = result->point();
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| 245 | SCVector3 trialnorm = result->normal();
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| 246 | SCVector3 newpoint;
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| 247 | vol->solve(trialpoint,trialnorm,isoval,newpoint);
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| 248 | // compute the true normal
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| 249 | vol->set_x(newpoint);
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| 250 | if (vol->gradient_implemented()) {
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| 251 | vol->get_gradient(trialnorm);
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| 252 | }
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| 253 | trialnorm.normalize();
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| 254 | result->set_point(newpoint);
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| 255 | result->set_normal(trialnorm);
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| 256 | }
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| 257 |
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| 258 | void
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| 259 | Triangle::flip()
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| 260 | {
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| 261 | _orientation0 = _orientation0?0:1;
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| 262 | _orientation1 = _orientation1?0:1;
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| 263 | _orientation2 = _orientation2?0:1;
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| 264 | }
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| 265 |
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| 266 | void
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| 267 | Triangle::set_order(int order, const Ref<Volume>&vol, double isovalue)
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| 268 | {
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| 269 | if (order > max_order) {
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| 270 | ExEnv::errn() << scprintf("Triangle::set_order: max_order = %d but order = %d\n",
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| 271 | max_order, order);
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| 272 | abort();
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| 273 | }
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| 274 |
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| 275 | unsigned int i, j, k;
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| 276 |
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| 277 | if (edge(0)->order() != order
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| 278 | ||edge(1)->order() != order
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| 279 | ||edge(2)->order() != order) {
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| 280 | ExEnv::errn() << "Triangle::set_order: edge order doesn't match" << endl;
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| 281 | abort();
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| 282 | }
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| 283 |
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| 284 | _order = order;
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| 285 | delete[] _vertices;
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| 286 |
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| 287 | _vertices = new Ref<Vertex>[TriInterpCoef::order_to_nvertex(_order)];
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| 288 |
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| 289 | // fill in the corner vertices
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| 290 | _vertices[TriInterpCoef::ijk_to_index(_order, 0, 0)] = vertex(0);
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| 291 | _vertices[TriInterpCoef::ijk_to_index(0, 0, _order)] = vertex(1);
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| 292 | _vertices[TriInterpCoef::ijk_to_index(0, _order, 0)] = vertex(2);
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| 293 |
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| 294 | // fill in the interior edge vertices
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| 295 | for (i = 1; i < _order; i++) {
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| 296 | j = _order - i;
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| 297 | _vertices[TriInterpCoef::ijk_to_index(0, i, j)]
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| 298 | = _edges[1]->interior_vertex(_orientation1?i:j);
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| 299 | _vertices[TriInterpCoef::ijk_to_index(j, 0, i)]
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| 300 | = _edges[0]->interior_vertex(_orientation0?i:j);
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| 301 | _vertices[TriInterpCoef::ijk_to_index(i, j, 0)]
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| 302 | = _edges[2]->interior_vertex(_orientation2?i:j);
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| 303 | }
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| 304 |
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| 305 | const SCVector3& p0 = vertex(0)->point();
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| 306 | const SCVector3& p1 = vertex(1)->point();
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| 307 | const SCVector3& p2 = vertex(2)->point();
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| 308 | const SCVector3& norm0 = vertex(0)->normal();
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| 309 | const SCVector3& norm1 = vertex(1)->normal();
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| 310 | const SCVector3& norm2 = vertex(2)->normal();
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| 311 |
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| 312 | for (i=0; i<=_order; i++) {
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| 313 | double I = (1.0*i)/_order;
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| 314 | for (j=0; j<=_order-i; j++) {
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| 315 | SCVector3 trialpoint;
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| 316 | SCVector3 trialnorm;
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| 317 | SCVector3 newpoint;
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| 318 | double J = (1.0*j)/_order;
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| 319 | k = _order - i - j;
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| 320 | if (!i || !j || !k) continue; // interior point check
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| 321 | double K = (1.0*k)/_order;
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| 322 | int index = TriInterpCoef::ijk_to_index(i,j,k);
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| 323 | // this get approximate vertices and normals
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| 324 | trialpoint = I*p0 + J*p1 + K*p2;
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| 325 | trialnorm = I*norm0 + J*norm1 + K*norm2;
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| 326 | // now refine that guess
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| 327 | vol->solve(trialpoint,trialnorm,isovalue,newpoint);
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| 328 | // compute the true normal
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| 329 | vol->set_x(newpoint);
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| 330 | if (vol->gradient_implemented()) {
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| 331 | vol->get_gradient(trialnorm);
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| 332 | }
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| 333 | trialnorm.normalize();
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| 334 | _vertices[index] = new Vertex(newpoint,trialnorm);
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| 335 | }
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| 336 | }
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| 337 | }
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| 338 |
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| 339 | /////////////////////////////////////////////////////////////////////////
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| 340 | // TriangleIntegrator
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| 341 |
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| 342 | static ClassDesc TriangleIntegrator_cd(
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| 343 | typeid(TriangleIntegrator),"TriangleIntegrator",1,"public DescribedClass",
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| 344 | 0, create<TriangleIntegrator>, 0);
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| 345 |
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| 346 | TriangleIntegrator::TriangleIntegrator(int order):
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| 347 | _n(order)
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| 348 | {
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| 349 | _r = new double [_n];
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| 350 | _s = new double [_n];
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| 351 | _w = new double [_n];
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| 352 | coef_ = 0;
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| 353 | }
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| 354 |
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| 355 | TriangleIntegrator::TriangleIntegrator(const Ref<KeyVal>& keyval)
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| 356 | {
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| 357 | _n = keyval->intvalue("n");
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| 358 | if (keyval->error() != KeyVal::OK) {
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| 359 | _n = 7;
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| 360 | }
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| 361 | _r = new double [_n];
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| 362 | _s = new double [_n];
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| 363 | _w = new double [_n];
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| 364 | coef_ = 0;
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| 365 | }
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| 366 |
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| 367 | TriangleIntegrator::~TriangleIntegrator()
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| 368 | {
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| 369 | delete[] _r;
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| 370 | delete[] _s;
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| 371 | delete[] _w;
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| 372 | clear_coef();
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| 373 | }
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| 374 |
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| 375 | void
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| 376 | TriangleIntegrator::set_n(int n)
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| 377 | {
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| 378 | delete[] _r;
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| 379 | delete[] _s;
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| 380 | delete[] _w;
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| 381 | _n = n;
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| 382 | _r = new double [_n];
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| 383 | _s = new double [_n];
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| 384 | _w = new double [_n];
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| 385 | clear_coef();
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| 386 | }
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| 387 |
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| 388 | void
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| 389 | TriangleIntegrator::set_w(int i,double w)
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| 390 | {
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| 391 | _w[i] = w;
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| 392 | }
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| 393 |
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| 394 | void
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| 395 | TriangleIntegrator::set_r(int i,double r)
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| 396 | {
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| 397 | _r[i] = r;
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| 398 | }
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| 399 |
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| 400 | void
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| 401 | TriangleIntegrator::set_s(int i,double s)
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| 402 | {
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| 403 | _s[i] = s;
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| 404 | }
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| 405 |
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| 406 | void
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| 407 | TriangleIntegrator::init_coef()
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| 408 | {
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| 409 | int i, j;
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| 410 |
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| 411 | clear_coef();
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| 412 |
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| 413 | coef_ = new Ref<TriInterpCoef>*[Triangle::max_order];
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| 414 | for (i=0; i<Triangle::max_order; i++) {
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| 415 | coef_[i] = new Ref<TriInterpCoef>[_n];
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| 416 | for (j=0; j<_n; j++) {
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| 417 | TriInterpCoefKey key(i+1,_r[j],_s[j]);
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| 418 | coef_[i][j] = new TriInterpCoef(key);
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| 419 | }
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| 420 | }
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| 421 | }
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| 422 |
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| 423 | void
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| 424 | TriangleIntegrator::clear_coef()
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| 425 | {
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| 426 | int i, j;
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| 427 |
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| 428 | if (coef_) {
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| 429 | for (i=0; i<Triangle::max_order; i++) {
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| 430 | for (j=0; j<_n; j++) {
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| 431 | coef_[i][j] = 0;
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| 432 | }
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| 433 | delete[] coef_[i];
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| 434 | }
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| 435 | }
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| 436 | delete[] coef_;
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| 437 | coef_ = 0;
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| 438 | }
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| 439 |
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| 440 | /////////////////////////////////////////////////////////////////////////
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| 441 | // GaussTriangleIntegrator
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| 442 |
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| 443 | static ClassDesc GaussTriangleIntegrator_cd(
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| 444 | typeid(GaussTriangleIntegrator),"GaussTriangleIntegrator",1,"public TriangleIntegrator",
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| 445 | 0, create<GaussTriangleIntegrator>, 0);
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| 446 |
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| 447 | GaussTriangleIntegrator::GaussTriangleIntegrator(const Ref<KeyVal>& keyval):
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| 448 | TriangleIntegrator(keyval)
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| 449 | {
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| 450 | ExEnv::out0() << "Created a GaussTriangleIntegrator with n = " << n() << endl;
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| 451 | init_rw(n());
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| 452 | init_coef();
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| 453 | }
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| 454 |
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| 455 | GaussTriangleIntegrator::GaussTriangleIntegrator(int order):
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| 456 | TriangleIntegrator(order)
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| 457 | {
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| 458 | init_rw(n());
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| 459 | init_coef();
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| 460 | }
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| 461 |
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| 462 | void
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| 463 | GaussTriangleIntegrator::set_n(int n)
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| 464 | {
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| 465 | TriangleIntegrator::set_n(n);
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| 466 | init_rw(n);
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| 467 | init_coef();
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| 468 | }
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| 469 |
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| 470 | void
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| 471 | GaussTriangleIntegrator::init_rw(int order)
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| 472 | {
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| 473 | if (order == 1) {
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| 474 | set_r(0, 1.0/3.0);
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| 475 | set_s(0, 1.0/3.0);
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| 476 | set_w(0, 1.0);
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| 477 | }
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| 478 | else if (order == 3) {
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| 479 | set_r(0, 1.0/6.0);
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| 480 | set_r(1, 2.0/3.0);
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| 481 | set_r(2, 1.0/6.0);
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| 482 | set_s(0, 1.0/6.0);
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| 483 | set_s(1, 1.0/6.0);
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| 484 | set_s(2, 2.0/3.0);
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| 485 | set_w(0, 1.0/3.0);
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| 486 | set_w(1, 1.0/3.0);
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| 487 | set_w(2, 1.0/3.0);
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| 488 | }
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| 489 | else if (order == 4) {
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| 490 | set_r(0, 1.0/3.0);
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| 491 | set_r(1, 1.0/5.0);
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| 492 | set_r(2, 3.0/5.0);
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| 493 | set_r(3, 1.0/5.0);
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| 494 | set_s(0, 1.0/3.0);
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| 495 | set_s(1, 1.0/5.0);
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| 496 | set_s(2, 1.0/5.0);
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| 497 | set_s(3, 3.0/5.0);
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| 498 | set_w(0, -27.0/48.0);
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| 499 | set_w(1, 25.0/48.0);
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| 500 | set_w(2, 25.0/48.0);
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| 501 | set_w(3, 25.0/48.0);
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| 502 | }
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| 503 | else if (order == 6) {
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| 504 | set_r(0, 0.091576213509771);
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| 505 | set_r(1, 0.816847572980459);
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| 506 | set_r(2, r(0));
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|---|
| 507 | set_r(3, 0.445948490915965);
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| 508 | set_r(4, 0.108103018168070);
|
|---|
| 509 | set_r(5, r(3));
|
|---|
| 510 | set_s(0, r(0));
|
|---|
| 511 | set_s(1, r(0));
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|---|
| 512 | set_s(2, r(1));
|
|---|
| 513 | set_s(3, r(3));
|
|---|
| 514 | set_s(4, r(3));
|
|---|
| 515 | set_s(5, r(4));
|
|---|
| 516 | set_w(0, 0.109951743655322);
|
|---|
| 517 | set_w(1, w(0));
|
|---|
| 518 | set_w(2, w(0));
|
|---|
| 519 | set_w(3, 0.223381589678011);
|
|---|
| 520 | set_w(4, w(3));
|
|---|
| 521 | set_w(5, w(3));
|
|---|
| 522 | }
|
|---|
| 523 | else if (order == 7) {
|
|---|
| 524 | set_r(0, 1.0/3.0);
|
|---|
| 525 | set_r(1, 0.101286507323456);
|
|---|
| 526 | set_r(2, 0.797426985353087);
|
|---|
| 527 | set_r(3, r(1));
|
|---|
| 528 | set_r(4, 0.470142064105115);
|
|---|
| 529 | set_r(5, 0.059715871789770);
|
|---|
| 530 | set_r(6, r(4));
|
|---|
| 531 | set_s(0, r(0));
|
|---|
| 532 | set_s(1, r(1));
|
|---|
| 533 | set_s(2, r(1));
|
|---|
| 534 | set_s(3, r(2));
|
|---|
| 535 | set_s(4, r(4));
|
|---|
| 536 | set_s(5, r(4));
|
|---|
| 537 | set_s(6, r(5));
|
|---|
| 538 | set_w(0, 0.225);
|
|---|
| 539 | set_w(1, 0.125939180544827);
|
|---|
| 540 | set_w(2, w(1));
|
|---|
| 541 | set_w(3, w(1));
|
|---|
| 542 | set_w(4, 0.132394152788506);
|
|---|
| 543 | set_w(5, w(4));
|
|---|
| 544 | set_w(6, w(4));
|
|---|
| 545 | }
|
|---|
| 546 | else {
|
|---|
| 547 | ExEnv::errn() << "GaussTriangleIntegrator: invalid order " << order << endl;
|
|---|
| 548 | abort();
|
|---|
| 549 | }
|
|---|
| 550 |
|
|---|
| 551 | // scale the weights by the area of the unit triangle
|
|---|
| 552 | for (int i=0; i<order; i++) {
|
|---|
| 553 | set_w(i, w(i)*0.5);
|
|---|
| 554 | }
|
|---|
| 555 | }
|
|---|
| 556 |
|
|---|
| 557 | GaussTriangleIntegrator::~GaussTriangleIntegrator()
|
|---|
| 558 | {
|
|---|
| 559 | }
|
|---|
| 560 |
|
|---|
| 561 | /////////////////////////////////////////////////////////////////////////////
|
|---|
| 562 |
|
|---|
| 563 | // Local Variables:
|
|---|
| 564 | // mode: c++
|
|---|
| 565 | // c-file-style: "CLJ"
|
|---|
| 566 | // End:
|
|---|
