 |
Mesh Oriented datABase
(version 5.5.1)
An array-based unstructured mesh library
|
|
Mesh Oriented datABase
(version 5.5.1)
An array-based unstructured mesh library
|
1 #include "moab/LocalDiscretization/LinearTri.hpp"
2 #include "moab/Forward.hpp"
3 #include <algorithm>
4 #include <cmath>
5 #include <limits>
6
7 namespace moab
8 {
9
10 const double LinearTri::corner[3][2] = { { 0, 0 }, { 1, 0 }, { 0, 1 } };
11
12 ErrorCode LinearTri::initFcn( const double* verts, const int nverts, double*& work )
13 {
14 // allocate work array as:
15 // work[0..8] = T
16 // work[9..17] = Tinv
17 // work[18] = detT
18 // work[19] = detTinv
19 if( nverts != 3 )
20 {
21 std::cout << "Invalid Triangle. Expected 3 vertices.\n";
22 return MB_FAILURE;
23 }
24
25 assert( verts );
26
27 Matrix3 J( verts[1 * 3 + 0] - verts[0 * 3 + 0], verts[2 * 3 + 0] - verts[0 * 3 + 0], 0.0,
28 verts[1 * 3 + 1] - verts[0 * 3 + 1], verts[2 * 3 + 1] - verts[0 * 3 + 1], 0.0,
29 verts[1 * 3 + 2] - verts[0 * 3 + 2], verts[2 * 3 + 2] - verts[0 * 3 + 2], 1.0 );
30 J *= 0.5;
31
32 // Update the work array
33 if( !work ) work = new double[20];
34
35 J.copyto( work );
36 J.inverse().copyto( work + Matrix3::size );
37 work[18] = J.determinant();
38 work[19] = ( work[18] < 1e-12 ? std::numeric_limits< double >::max() : 1.0 / work[18] );
39
40 return MB_SUCCESS;
41 }
42
43 ErrorCode LinearTri::evalFcn( const double* params,
44 const double* field,
45 const int /*ndim*/,
46 const int num_tuples,
47 double* /*work*/,
48 double* result )
49 {
50 assert( params && field && num_tuples > 0 );
51 // convert to [0,1]
52 double p1 = 0.5 * ( 1.0 + params[0] ), p2 = 0.5 * ( 1.0 + params[1] ), p0 = 1.0 - p1 - p2;
53
54 for( int j = 0; j < num_tuples; j++ )
55 result[j] = p0 * field[0 * num_tuples + j] + p1 * field[1 * num_tuples + j] + p2 * field[2 * num_tuples + j];
56
57 return MB_SUCCESS;
58 }
59
60 ErrorCode LinearTri::integrateFcn( const double* field,
61 const double* /*verts*/,
62 const int nverts,
63 const int /*ndim*/,
64 const int num_tuples,
65 double* work,
66 double* result )
67 {
68 assert( field && num_tuples > 0 );
69 std::fill( result, result + num_tuples, 0.0 );
70 for( int i = 0; i < nverts; ++i )
71 {
72 for( int j = 0; j < num_tuples; j++ )
73 result[j] += field[i * num_tuples + j];
74 }
75 double tmp = work[18] / 6.0;
76 for( int i = 0; i < num_tuples; i++ )
77 result[i] *= tmp;
78
79 return MB_SUCCESS;
80 }
81
82 ErrorCode LinearTri::jacobianFcn( const double*, const double*, const int, const int, double* work, double* result )
83 {
84 // jacobian is cached in work array
85 assert( work );
86 std::copy( work, work + 9, result );
87 return MB_SUCCESS;
88 }
89
90 ErrorCode LinearTri::reverseEvalFcn( EvalFcn eval,
91 JacobianFcn jacob,
92 InsideFcn ins,
93 const double* posn,
94 const double* verts,
95 const int nverts,
96 const int ndim,
97 const double iter_tol,
98 const double inside_tol,
99 double* work,
100 double* params,
101 int* is_inside )
102 {
103 assert( posn && verts );
104 return evaluate_reverse( eval, jacob, ins, posn, verts, nverts, ndim, iter_tol, inside_tol, work, params,
105 is_inside );
106 }
107
108 int LinearTri::insideFcn( const double* params, const int, const double tol )
109 {
110 return ( params[0] >= -1.0 - tol && params[1] >= -1.0 - tol && params[0] + params[1] <= 1.0 + tol );
111 }
112
113 ErrorCode LinearTri::evaluate_reverse( EvalFcn eval,
114 JacobianFcn jacob,
115 InsideFcn inside_f,
116 const double* posn,
117 const double* verts,
118 const int nverts,
119 const int ndim,
120 const double iter_tol,
121 const double inside_tol,
122 double* work,
123 double* params,
124 int* inside )
125 {
126 // TODO: should differentiate between epsilons used for
127 // Newton Raphson iteration, and epsilons used for curved boundary geometry errors
128 // right now, fix the tolerance used for NR
129 const double error_tol_sqr = iter_tol * iter_tol;
130 CartVect* cvparams = reinterpret_cast< CartVect* >( params );
131 const CartVect* cvposn = reinterpret_cast< const CartVect* >( posn );
132
133 // find best initial guess to improve convergence
134 CartVect tmp_params[] = { CartVect( -1, -1, -1 ), CartVect( 1, -1, -1 ), CartVect( -1, 1, -1 ) };
135 double resl = std::numeric_limits< double >::max();
136 CartVect new_pos, tmp_pos;
137 ErrorCode rval;
138 for( unsigned int i = 0; i < 3; i++ )
139 {
140 rval = ( *eval )( tmp_params[i].array(), verts, ndim, 3, work, tmp_pos.array() );
141 if( MB_SUCCESS != rval ) return rval;
142 double tmp_resl = ( tmp_pos - *cvposn ).length_squared();
143 if( tmp_resl < resl )
144 {
145 *cvparams = tmp_params[i];
146 new_pos = tmp_pos;
147 resl = tmp_resl;
148 }
149 }
150
151 // residual is diff between old and new pos; need to minimize that
152 CartVect res = new_pos - *cvposn;
153 Matrix3 J;
154 rval = ( *jacob )( cvparams->array(), verts, nverts, ndim, work, J[0] );
155 #ifndef NDEBUG
156 double det = J.determinant();
157 assert( det > std::numeric_limits< double >::epsilon() );
158 #endif
159 Matrix3 Ji = J.inverse();
160
161 int iters = 0;
162 // while |res| larger than tol
163 while( res % res > error_tol_sqr )
164 {
165 if( ++iters > 25 ) return MB_FAILURE;
166
167 // new params tries to eliminate residual
168 *cvparams -= Ji * res;
169
170 // get the new forward-evaluated position, and its difference from the target pt
171 rval = ( *eval )( params, verts, ndim, 3, work, new_pos.array() );
172 if( MB_SUCCESS != rval ) return rval;
173 res = new_pos - *cvposn;
174 }
175
176 if( inside ) *inside = ( *inside_f )( params, ndim, inside_tol );
177
178 return MB_SUCCESS;
179 } // Map::evaluate_reverse()
180
181 /* ErrorCode LinearTri::get_normal( int facet, double *work, double *normal)
182 {
183 ErrorCode error;
184 //Get the local vertex ids of local edge
185 int id1 = ledges[facet][0];
186 int id2 = ledges[facet][1];
187
188 //Find the normal to the face
189 double face_normal[3];
190
191
192 }*/
193
194 ErrorCode LinearTri::normalFcn( const int ientDim,
195 const int facet,
196 const int nverts,
197 const double* verts,
198 double normal[3] )
199 {
200 // assert(facet < 3 && ientDim == 1 && nverts==3);
201 if( nverts != 3 ) MB_SET_ERR( MB_FAILURE, "Incorrect vertex count for passed triangle :: expected value = 3 " );
202 if( ientDim != 1 ) MB_SET_ERR( MB_FAILURE, "Requesting normal for unsupported dimension :: expected value = 1 " );
203 if( facet > 3 || facet < 0 ) MB_SET_ERR( MB_FAILURE, "Incorrect local edge id :: expected value = one of 0-2" );
204
205 // Get the local vertex ids of local edge
206 int id0 = CN::mConnectivityMap[MBTRI][ientDim - 1].conn[facet][0];
207 int id1 = CN::mConnectivityMap[MBTRI][ientDim - 1].conn[facet][1];
208
209 // Find a vector along the edge
210 double edge[3];
211 for( int i = 0; i < 3; i++ )
212 {
213 edge[i] = verts[3 * id1 + i] - verts[3 * id0 + i];
214 }
215 // Find the normal of the face
216 double x0[3], x1[3], fnrm[3];
217 for( int i = 0; i < 3; i++ )
218 {
219 x0[i] = verts[3 * 1 + i] - verts[3 * 0 + i];
220 x1[i] = verts[3 * 2 + i] - verts[3 * 0 + i];
221 }
222 fnrm[0] = x0[1] * x1[2] - x1[1] * x0[2];
223 fnrm[1] = x1[0] * x0[2] - x0[0] * x1[2];
224 fnrm[2] = x0[0] * x1[1] - x1[0] * x0[1];
225
226 // Find the normal of the edge as the cross product of edge and face normal
227
228 double a = edge[1] * fnrm[2] - fnrm[1] * edge[2];
229 double b = edge[2] * fnrm[0] - fnrm[2] * edge[0];
230 double c = edge[0] * fnrm[1] - fnrm[0] * edge[1];
231 double nrm = sqrt( a * a + b * b + c * c );
232
233 if( nrm > std::numeric_limits< double >::epsilon() )
234 {
235 normal[0] = a / nrm;
236 normal[1] = b / nrm;
237 normal[2] = c / nrm;
238 }
239 return MB_SUCCESS;
240 }
241
242 } // namespace moab
1.9.1.