Reference documentation for deal.II version Git d3aed38b93 2021-10-28 13:33:27 +0200
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bounding_box.cc
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15 
18 
20 
21 template <int spacedim, typename Number>
22 bool
24  const double tolerance) const
25 {
26  for (unsigned int i = 0; i < spacedim; ++i)
27  {
28  // Bottom left-top right convention: the point is outside if it's smaller
29  // than the first or bigger than the second boundary point The bounding
30  // box is defined as a closed set
31  if ((p[i] < this->boundary_points.first[i] -
32  tolerance * std::abs(this->boundary_points.second[i] -
33  this->boundary_points.first[i])) ||
34  (p[i] > this->boundary_points.second[i] +
35  tolerance * std::abs(this->boundary_points.second[i] -
36  this->boundary_points.first[i])))
37  return false;
38  }
39  return true;
40 }
41 
42 
43 
44 template <int spacedim, typename Number>
45 void
47  const BoundingBox<spacedim, Number> &other_bbox)
48 {
49  for (unsigned int i = 0; i < spacedim; ++i)
50  {
51  this->boundary_points.first[i] =
52  std::min(this->boundary_points.first[i],
53  other_bbox.boundary_points.first[i]);
54  this->boundary_points.second[i] =
55  std::max(this->boundary_points.second[i],
56  other_bbox.boundary_points.second[i]);
57  }
58 }
59 
60 
61 
62 template <int spacedim, typename Number>
65  const BoundingBox<spacedim, Number> &other_bbox) const
66 {
67  if (spacedim == 1)
68  {
69  // In dimension 1 if the two bounding box are neighbors
70  // we can merge them
71  if (this->point_inside(other_bbox.boundary_points.first) ||
72  this->point_inside(other_bbox.boundary_points.second))
75  }
76  else
77  {
78  const std::array<Point<spacedim, Number>, 2> bbox1 = {
79  {this->get_boundary_points().first,
80  this->get_boundary_points().second}};
81  const std::array<Point<spacedim, Number>, 2> bbox2 = {
82  {other_bbox.get_boundary_points().first,
83  other_bbox.get_boundary_points().second}};
84 
85  // Step 1: testing if the boxes are close enough to intersect
86  for (unsigned int d = 0; d < spacedim; ++d)
87  if (bbox1[0][d] * (1 - std::numeric_limits<Number>::epsilon()) >
88  bbox2[1][d] ||
89  bbox2[0][d] * (1 - std::numeric_limits<Number>::epsilon()) >
90  bbox1[1][d])
92 
93  // The boxes intersect: we need to understand now how they intersect.
94  // We begin by computing the intersection:
95  std::array<double, spacedim> intersect_bbox_min;
96  std::array<double, spacedim> intersect_bbox_max;
97  for (unsigned int d = 0; d < spacedim; ++d)
98  {
99  intersect_bbox_min[d] = std::max(bbox1[0][d], bbox2[0][d]);
100  intersect_bbox_max[d] = std::min(bbox1[1][d], bbox2[1][d]);
101  }
102 
103  // Finding the intersection's dimension
104  int intersect_dim = spacedim;
105  for (unsigned int d = 0; d < spacedim; ++d)
106  if (std::abs(intersect_bbox_min[d] - intersect_bbox_max[d]) <=
108  (std::abs(intersect_bbox_min[d]) +
109  std::abs(intersect_bbox_max[d])))
110  --intersect_dim;
111 
112  if (intersect_dim == 0 || intersect_dim == spacedim - 2)
114 
115  // Checking the two mergeable cases: first if the boxes are aligned so
116  // that they can be merged
117  unsigned int not_align_1 = 0, not_align_2 = 0;
118  bool same_direction = true;
119  for (unsigned int d = 0; d < spacedim; ++d)
120  {
121  if (std::abs(bbox2[0][d] - bbox1[0][d]) >
123  (std::abs(bbox2[0][d]) + std::abs(bbox1[0][d])))
124  ++not_align_1;
125  if (std::abs(bbox1[1][d] - bbox2[1][d]) >
127  (std::abs(bbox1[1][d]) + std::abs(bbox2[1][d])))
128  ++not_align_2;
129  if (not_align_1 != not_align_2)
130  {
131  same_direction = false;
132  break;
133  }
134  }
135 
136  if (not_align_1 <= 1 && not_align_2 <= 1 && same_direction)
138 
139  // Second: one box is contained/equal to the other
140  if ((this->point_inside(bbox2[0]) && this->point_inside(bbox2[1])) ||
141  (other_bbox.point_inside(bbox1[0]) &&
142  other_bbox.point_inside(bbox1[1])))
144 
145  // Degenerate and mergeable cases have been found, it remains:
147  }
148 }
149 
150 
151 
152 template <int spacedim, typename Number>
153 double
155 {
156  double vol = 1.0;
157  for (unsigned int i = 0; i < spacedim; ++i)
158  vol *= (this->boundary_points.second[i] - this->boundary_points.first[i]);
159  return vol;
160 }
161 
162 
163 
164 template <int spacedim, typename Number>
165 Number
166 BoundingBox<spacedim, Number>::lower_bound(const unsigned int direction) const
167 {
168  AssertIndexRange(direction, spacedim);
169 
170  return boundary_points.first[direction];
171 }
172 
173 
174 
175 template <int spacedim, typename Number>
176 Number
177 BoundingBox<spacedim, Number>::upper_bound(const unsigned int direction) const
178 {
179  AssertIndexRange(direction, spacedim);
180 
181  return boundary_points.second[direction];
182 }
183 
184 
185 
186 template <int spacedim, typename Number>
189 {
191  for (unsigned int i = 0; i < spacedim; ++i)
192  point[i] = .5 * (boundary_points.first[i] + boundary_points.second[i]);
193 
194  return point;
195 }
196 
197 
198 
199 template <int spacedim, typename Number>
201 BoundingBox<spacedim, Number>::bounds(const unsigned int direction) const
202 {
203  AssertIndexRange(direction, spacedim);
204 
205  std::pair<Point<1, Number>, Point<1, Number>> lower_upper_bounds;
206  lower_upper_bounds.first[0] = lower_bound(direction);
207  lower_upper_bounds.second[0] = upper_bound(direction);
208 
209  return BoundingBox<1, Number>(lower_upper_bounds);
210 }
211 
212 
213 
214 template <int spacedim, typename Number>
215 Number
216 BoundingBox<spacedim, Number>::side_length(const unsigned int direction) const
217 {
218  AssertIndexRange(direction, spacedim);
219 
220  return boundary_points.second[direction] - boundary_points.first[direction];
221 }
222 
223 
224 
225 template <int spacedim, typename Number>
227 BoundingBox<spacedim, Number>::vertex(const unsigned int index) const
228 {
230 
231  const Point<spacedim> unit_cell_vertex =
233 
235  for (unsigned int i = 0; i < spacedim; ++i)
236  point[i] = boundary_points.first[i] + side_length(i) * unit_cell_vertex[i];
237 
238  return point;
239 }
240 
241 
242 
243 template <int spacedim, typename Number>
245 BoundingBox<spacedim, Number>::child(const unsigned int index) const
246 {
248 
249  // Vertex closest to child.
250  const Point<spacedim, Number> parent_vertex = vertex(index);
251  const Point<spacedim, Number> parent_center = center();
252 
253  const Point<spacedim> upper_corner_unit_cell =
256 
257  const Point<spacedim> lower_corner_unit_cell =
259 
260  std::pair<Point<spacedim, Number>, Point<spacedim, Number>>
261  child_lower_upper_corner;
262  for (unsigned int i = 0; i < spacedim; ++i)
263  {
264  const double child_side_length = side_length(i) / 2;
265 
266  const double child_center = (parent_center[i] + parent_vertex[i]) / 2;
267 
268  child_lower_upper_corner.first[i] =
269  child_center + child_side_length * (lower_corner_unit_cell[i] - .5);
270  child_lower_upper_corner.second[i] =
271  child_center + child_side_length * (upper_corner_unit_cell[i] - .5);
272  }
273 
274  return BoundingBox<spacedim, Number>(child_lower_upper_corner);
275 }
276 
277 
278 
279 template <int spacedim, typename Number>
280 BoundingBox<spacedim - 1, Number>
281 BoundingBox<spacedim, Number>::cross_section(const unsigned int direction) const
282 {
283  AssertIndexRange(direction, spacedim);
284 
285  std::pair<Point<spacedim - 1, Number>, Point<spacedim - 1, Number>>
286  cross_section_lower_upper_corner;
287  for (unsigned int d = 0; d < spacedim - 1; ++d)
288  {
289  const int index_to_write_from =
290  internal::coordinate_to_one_dim_higher<spacedim - 1>(direction, d);
291 
292  cross_section_lower_upper_corner.first[d] =
293  boundary_points.first[index_to_write_from];
294 
295  cross_section_lower_upper_corner.second[d] =
296  boundary_points.second[index_to_write_from];
297  }
298 
299  return BoundingBox<spacedim - 1, Number>(cross_section_lower_upper_corner);
300 }
301 
302 
303 
304 template <int spacedim, typename Number>
307  const Point<spacedim, Number> &point) const
308 {
309  auto unit = point;
310  const auto diag = boundary_points.second - boundary_points.first;
311  unit -= boundary_points.first;
312  for (unsigned int d = 0; d < spacedim; ++d)
313  unit[d] /= diag[d];
314  return unit;
315 }
316 
317 
318 
319 template <int spacedim, typename Number>
322  const Point<spacedim, Number> &point) const
323 {
324  auto real = boundary_points.first;
325  const auto diag = boundary_points.second - boundary_points.first;
326  for (unsigned int d = 0; d < spacedim; ++d)
327  real[d] += diag[d] * point[d];
328  return real;
329 }
330 
331 
332 
333 template <int dim, typename Number>
336 {
337  std::pair<Point<dim, Number>, Point<dim, Number>> lower_upper_corner;
338  for (unsigned int i = 0; i < dim; ++i)
339  {
340  lower_upper_corner.second[i] = 1;
341  }
342  return BoundingBox<dim, Number>(lower_upper_corner);
343 }
344 
345 
346 #include "bounding_box.inst"
Point< spacedim, Number > vertex(const unsigned int index) const
Iterator lower_bound(Iterator first, Iterator last, const T &val)
Definition: utilities.h:1112
NeighborType
Definition: bounding_box.h:32
#define AssertIndexRange(index, range)
Definition: exceptions.h:1720
static Point< dim > unit_cell_vertex(const unsigned int vertex)
void merge_with(const BoundingBox< spacedim, Number > &other_bbox)
Definition: bounding_box.cc:46
Number lower_bound(const unsigned int direction) const
Definition: point.h:110
SymmetricTensor< 2, dim, Number > epsilon(const Tensor< 2, dim, Number > &Grad_u)
Number upper_bound(const unsigned int direction) const
Point< spacedim, Number > unit_to_real(const Point< spacedim, Number > &point) const
BoundingBox< spacedim, Number > child(const unsigned int index) const
Point< spacedim, Number > center() const
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:401
std::pair< Point< spacedim, Number >, Point< spacedim, Number > > boundary_points
Definition: bounding_box.h:315
BoundingBox< spacedim - 1, Number > cross_section(const unsigned int direction) const
Point< spacedim > point(const gp_Pnt &p, const double tolerance=1e-10)
Definition: utilities.cc:185
SymmetricTensor< 2, dim, Number > d(const Tensor< 2, dim, Number > &F, const Tensor< 2, dim, Number > &dF_dt)
NeighborType get_neighbor_type(const BoundingBox< spacedim, Number > &other_bbox) const
Definition: bounding_box.cc:64
Number side_length(const unsigned int direction) const
std::pair< Point< spacedim, Number >, Point< spacedim, Number > > & get_boundary_points()
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:400
Point< spacedim, Number > real_to_unit(const Point< spacedim, Number > &point) const
Point< 3 > center
BoundingBox< 1, Number > bounds(const unsigned int direction) const
BoundingBox< dim, Number > create_unit_bounding_box()
double volume() const
bool point_inside(const Point< spacedim, Number > &p, const double tolerance=std::numeric_limits< Number >::epsilon()) const
Definition: bounding_box.cc:23