16 #ifndef dealii_geometry_info_h
17 #define dealii_geometry_info_h
37 namespace GeometryInfoHelper
45 struct Initializers<1>
47 static constexpr std::array<unsigned int, 2>
53 static constexpr std::array<unsigned int, 2>
54 unit_normal_direction()
59 static constexpr std::array<int, 2>
60 unit_normal_orientation()
65 static constexpr std::array<Tensor<1, 1>, 2>
71 static constexpr ::ndarray<Tensor<1, 1>, 2, 0>
72 unit_tangential_vectors()
74 return {{{{}}, {{}}}};
77 static constexpr std::array<unsigned int, 2>
83 static constexpr std::array<unsigned int, 2>
89 static constexpr ::ndarray<unsigned int, 2, 1>
92 return {{{{0}}, {{1}}}};
97 struct Initializers<2>
99 static constexpr std::array<unsigned int, 4>
102 return {{0, 1, 3, 2}};
105 static constexpr std::array<unsigned int, 4>
106 unit_normal_direction()
108 return {{0, 0, 1, 1}};
111 static constexpr std::array<int, 4>
112 unit_normal_orientation()
114 return {{-1, 1, -1, 1}};
117 static constexpr std::array<Tensor<1, 2>, 4>
126 static constexpr ::ndarray<Tensor<1, 2>, 4, 1>
127 unit_tangential_vectors()
135 static constexpr std::array<unsigned int, 4>
138 return {{1, 0, 3, 2}};
141 static constexpr std::array<unsigned int, 4>
144 return {{0, 2, 1, 3}};
147 static constexpr ::ndarray<unsigned int, 4, 2>
150 return {{{{0, 2}}, {{1, 2}}, {{0, 3}}, {{1, 3}}}};
155 struct Initializers<3>
157 static constexpr std::array<unsigned int, 8>
160 return {{0, 4, 5, 1, 2, 6, 7, 3}};
163 static constexpr std::array<unsigned int, 6>
164 unit_normal_direction()
166 return {{0, 0, 1, 1, 2, 2}};
169 static constexpr std::array<int, 6>
170 unit_normal_orientation()
172 return {{-1, 1, -1, 1, -1, 1}};
175 static constexpr std::array<Tensor<1, 3>, 6>
186 static constexpr ::ndarray<Tensor<1, 3>, 6, 2>
187 unit_tangential_vectors()
197 static constexpr std::array<unsigned int, 6>
200 return {{1, 0, 3, 2, 5, 4}};
203 static constexpr std::array<unsigned int, 8>
206 return {{0, 4, 2, 6, 1, 5, 3, 7}};
209 static constexpr ::ndarray<unsigned int, 8, 3>
212 return {{{{0, 2, 4}},
224 struct Initializers<4>
226 static constexpr std::array<unsigned int, 16>
247 static constexpr std::array<unsigned int, 8>
248 unit_normal_direction()
250 return {{0, 0, 1, 1, 2, 2, 3, 3}};
253 static constexpr std::array<int, 8>
254 unit_normal_orientation()
256 return {{-1, 1, -1, 1, -1, 1, -1, 1}};
259 static constexpr std::array<Tensor<1, 4>, 8>
272 static constexpr ::ndarray<Tensor<1, 4>, 8, 3>
273 unit_tangential_vectors()
301 static constexpr std::array<unsigned int, 8>
304 return {{1, 0, 3, 2, 5, 4, 7, 6}};
307 static constexpr std::array<unsigned int, 16>
328 static constexpr ::ndarray<unsigned int, 16, 4>
463 operator unsigned int()
const;
676 cut_xy = cut_x | cut_y,
751 cut_xy = cut_x | cut_y,
759 cut_xz = cut_x | cut_z,
763 cut_yz = cut_y | cut_z,
767 cut_xyz = cut_x | cut_y | cut_z,
884 template <
class Archive>
894 <<
"The refinement flags given (" << arg1
895 <<
") contain set bits that do not "
896 <<
"make sense for the space dimension of the object to which they are applied.");
903 std::uint8_t
value : (dim > 0 ? dim : 1);
1188 subface_possibility);
1201 operator std::uint8_t()
const;
1206 static constexpr std::size_t
1215 <<
"The subface case given (" << arg1 <<
") does not make sense "
1216 <<
"for the space dimension of the object to which they are applied.");
1223 std::uint8_t
value : (dim == 3 ? 4 : 1);
1287 static std::array<unsigned int, 0>
1330 static std::array<unsigned int, vertices_per_cell>
1358 const unsigned int vertex,
1359 const bool face_orientation =
true,
1360 const bool face_flip =
false,
1361 const bool face_rotation =
false);
1379 const unsigned int line,
1380 const bool face_orientation =
true,
1381 const bool face_flip =
false,
1382 const bool face_rotation =
false);
1449 static const std::array<unsigned int, vertices_per_cell>
dx_to_deal;
2120 static constexpr std::array<unsigned int, vertices_per_cell>
ucd_to_deal =
2121 internal::GeometryInfoHelper::Initializers<dim>::ucd_to_deal();
2136 static constexpr std::array<unsigned int, vertices_per_cell>
dx_to_deal =
2137 internal::GeometryInfoHelper::Initializers<dim>::dx_to_deal();
2151 internal::GeometryInfoHelper::Initializers<dim>::vertex_to_face();
2178 const unsigned int subface_no);
2187 const unsigned int face_no,
2188 const bool face_orientation =
true,
2189 const bool face_flip =
false,
2190 const bool face_rotation =
false);
2200 const unsigned int face_no,
2201 const bool face_orientation =
true,
2202 const bool face_flip =
false,
2203 const bool face_rotation =
false);
2211 const unsigned int line_no);
2268 const unsigned int face,
2269 const unsigned int subface,
2270 const bool face_orientation =
true,
2271 const bool face_flip =
false,
2272 const bool face_rotation =
false,
2314 const unsigned int vertex,
2315 const bool face_orientation =
true,
2316 const bool face_flip =
false,
2317 const bool face_rotation =
false);
2332 const unsigned int line,
2333 const bool face_orientation =
true,
2334 const bool face_flip =
false,
2335 const bool face_rotation =
false);
2348 const bool face_orientation =
true,
2349 const bool face_flip =
false,
2350 const bool face_rotation =
false);
2363 const bool face_orientation =
true,
2364 const bool face_flip =
false,
2365 const bool face_rotation =
false);
2378 const bool face_orientation =
true,
2379 const bool face_flip =
false,
2380 const bool face_rotation =
false);
2389 const bool line_orientation =
true);
2398 static std::array<unsigned int, 2>
2408 static std::array<unsigned int, 2>
2418 static std::array<unsigned int, 2>
2432 const bool face_orientation =
true,
2433 const bool face_flip =
false,
2434 const bool face_rotation =
false);
2465 const unsigned int child_index,
2476 const unsigned int child_index,
2505 template <
typename Number =
double>
2582 template <
int spacedim>
2585 #ifndef DEAL_II_CXX14_CONSTEXPR_BUG
2601 static constexpr std::array<unsigned int, faces_per_cell>
2603 internal::GeometryInfoHelper::Initializers<dim>::unit_normal_direction();
2622 internal::GeometryInfoHelper::Initializers<dim>::unit_normal_orientation();
2636 internal::GeometryInfoHelper::Initializers<dim>::unit_normal_vector();
2661 internal::GeometryInfoHelper::Initializers<dim>::opposite_face();
2669 <<
"The coordinates must satisfy 0 <= x_i <= 1, "
2670 <<
"but here we have x_i=" << arg1);
2679 <<
"RefinementCase<dim> " << arg1 <<
": face " << arg2
2680 <<
" has no subface " << arg3);
2694 const unsigned int i);
2698 const unsigned int i);
2702 const unsigned int i);
2716 : object(static_cast<Object>(object_dimension))
2720 inline GeometryPrimitive::operator
unsigned int()
const
2722 return static_cast<unsigned int>(object);
2732 :
value(subface_possibility)
2737 inline SubfaceCase<dim>::operator std::uint8_t()
const
2751 return static_cast<std::uint8_t
>(-1);
2795 inline std::array<RefinementCase<1>, 2>
2805 inline std::array<RefinementCase<2>, 4>
2817 inline std::array<RefinementCase<3>, 8>
2842 :
value(refinement_case)
2848 Assert((refinement_case &
2851 ExcInvalidRefinementCase(refinement_case));
2858 :
value(refinement_case)
2864 Assert((refinement_case &
2867 ExcInvalidRefinementCase(refinement_case));
2918 template <
class Archive>
2924 std::uint8_t uchar_value =
value;
2926 value = uchar_value;
2937 return Point<1>(
static_cast<double>(vertex));
2948 return {
static_cast<double>(vertex % 2),
static_cast<double>(vertex / 2)};
2959 return {
static_cast<double>(vertex % 2),
2960 static_cast<double>(vertex / 2 % 2),
2961 static_cast<double>(vertex / 4)};
2966 inline std::array<unsigned int, 0>
2974 inline std::array<unsigned int, 1>
2986 return {0
U, faces_per_cell};
2995 return {0
U, vertices_per_cell};
3015 Assert((p[0] >= 0) && (p[0] <= 1), ExcInvalidCoordinate(p[0]));
3017 return (p[0] <= 0.5 ? 0 : 1);
3026 Assert((p[0] >= 0) && (p[0] <= 1), ExcInvalidCoordinate(p[0]));
3027 Assert((p[1] >= 0) && (p[1] <= 1), ExcInvalidCoordinate(p[1]));
3029 return (p[0] <= 0.5 ? (p[1] <= 0.5 ? 0 : 2) : (p[1] <= 0.5 ? 1 : 3));
3038 Assert((p[0] >= 0) && (p[0] <= 1), ExcInvalidCoordinate(p[0]));
3039 Assert((p[1] >= 0) && (p[1] <= 1), ExcInvalidCoordinate(p[1]));
3040 Assert((p[2] >= 0) && (p[2] <= 1), ExcInvalidCoordinate(p[2]));
3042 return (p[0] <= 0.5 ?
3043 (p[1] <= 0.5 ? (p[2] <= 0.5 ? 0 : 4) : (p[2] <= 0.5 ? 2 : 6)) :
3044 (p[1] <= 0.5 ? (p[2] <= 0.5 ? 1 : 5) : (p[2] <= 0.5 ? 3 : 7)));
3062 const unsigned int child_index,
3070 return Point<1>(p * 2.0 - unit_cell_vertex(child_index));
3078 const unsigned int child_index,
3085 switch (refine_case)
3089 if (child_index == 1)
3094 if (child_index == 1)
3099 point -= unit_cell_vertex(child_index);
3113 const unsigned int child_index,
3125 switch (refine_case)
3129 if (child_index == 1)
3134 if (child_index == 1)
3139 if (child_index == 1)
3145 if (child_index % 2 == 1)
3147 if (child_index / 2 == 1)
3157 if (child_index / 2 == 1)
3159 if (child_index % 2 == 1)
3165 if (child_index % 2 == 1)
3167 if (child_index / 2 == 1)
3172 point -= unit_cell_vertex(child_index);
3187 const unsigned int ,
3200 const unsigned int child_index,
3208 return (p + unit_cell_vertex(child_index)) * 0.5;
3216 const unsigned int child_index,
3228 switch (refine_case)
3231 if (child_index == 1)
3236 if (child_index == 1)
3241 if (child_index == 1)
3246 if (child_index % 2 == 1)
3248 if (child_index / 2 == 1)
3258 if (child_index / 2 == 1)
3260 if (child_index % 2 == 1)
3266 if (child_index % 2 == 1)
3268 if (child_index / 2 == 1)
3274 point += unit_cell_vertex(child_index);
3289 const unsigned int child_index,
3295 switch (refine_case)
3298 if (child_index == 1)
3303 if (child_index == 1)
3308 point += unit_cell_vertex(child_index);
3324 const unsigned int ,
3345 return (p[0] >= 0.) && (p[0] <= 1.);
3354 return (p[0] >= 0.) && (p[0] <= 1.) && (p[1] >= 0.) && (p[1] <= 1.);
3363 return (p[0] >= 0.) && (p[0] <= 1.) && (p[1] >= 0.) && (p[1] <= 1.) &&
3364 (p[2] >= 0.) && (p[2] <= 1.);
3381 return (p[0] >= -
eps) && (p[0] <= 1. +
eps);
3390 const double l = -
eps, u = 1 +
eps;
3391 return (p[0] >=
l) && (p[0] <= u) && (p[1] >=
l) && (p[1] <= u);
3400 const double l = -
eps, u = 1.0 +
eps;
3401 return (p[0] >=
l) && (p[0] <= u) && (p[1] >=
l) && (p[1] <= u) &&
3402 (p[2] >=
l) && (p[2] <= u);
3410 const unsigned int vertex)
3423 const unsigned int vertex)
3425 constexpr
unsigned int cell_vertices[4][2] = {{0, 2}, {1, 3}, {0, 1}, {2, 3}};
3426 return cell_vertices[line][vertex];
3434 const unsigned int vertex)
3439 constexpr
unsigned vertices[lines_per_cell][2] = {{0, 2},
3467 const bool face_orientation,
3468 const bool face_flip,
3469 const bool face_rotation)
3491 constexpr
unsigned int vertex_translation[4][2][2][2] = {
3513 return vertex_translation[vertex][face_orientation][face_flip][face_rotation];
3535 0, 2, 2, 4, 2, 4, 4, 8};
3537 return n_children[ref_case];
3572 0, 2, 3, 3, 4, 2, 3, 3, 4, 4};
3573 return nsubs[subface_case];
3602 switch (subface_case)
3639 const unsigned int subface_no)
3642 switch (subface_case)
3677 if (subface_no == 0)
3724 const unsigned int face_no,
3729 const unsigned int dim = 2;
3751 return ref_cases[cell_refinement_case][face_no / 2];
3759 const unsigned int face_no,
3760 const bool face_orientation,
3762 const bool face_rotation)
3764 const unsigned int dim = 3;
3810 ref_cases[cell_refinement_case][face_no / 2];
3830 return (face_orientation == face_rotation) ? flip[ref_case] : ref_case;
3848 const unsigned int line_no)
3851 const unsigned int dim = 1;
3857 return cell_refinement_case;
3865 const unsigned int line_no)
3868 return face_refinement_case(cell_refinement_case, line_no);
3876 const unsigned int line_no)
3878 const unsigned int dim = 3;
3899 const unsigned int direction[lines_per_cell] = {
3900 1, 1, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2};
3902 return ((cell_refinement_case & cut_one[direction[line_no]]) ?
3932 const unsigned int dim = 1;
3943 const unsigned int face_no,
3948 const unsigned int dim = 2;
3965 const unsigned int face_no,
3966 const bool face_orientation,
3968 const bool face_rotation)
3970 const unsigned int dim = 3;
3994 (face_orientation == face_rotation) ? flip[face_refinement_case] :
3995 face_refinement_case;
4014 return face_to_cell[face_no / 2][std_face_ref];
4032 const unsigned int line_no)
4044 const unsigned int line_no)
4046 const unsigned int dim = 2;
4058 const unsigned int line_no)
4060 const unsigned int dim = 3;
4071 return ref_cases[line_no / 2];
4079 const bool face_orientation,
4080 const bool face_flip,
4081 const bool face_rotation)
4103 const unsigned int vertex_translation[4][2][2][2] = {
4125 return vertex_translation[vertex][face_orientation][face_flip][face_rotation];
4147 const bool face_orientation,
4148 const bool face_flip,
4149 const bool face_rotation)
4171 const unsigned int line_translation[4][2][2][2] = {
4193 return line_translation[line][face_orientation][face_flip][face_rotation];
4214 const bool line_orientation)
4216 return line_orientation ? vertex : (1 - vertex);
4233 inline std::array<unsigned int, 2>
4235 const unsigned int vertex)
4237 return {{vertex % 2, vertex / 2}};
4243 inline std::array<unsigned int, 2>
4245 const unsigned int vertex)
4255 inline std::array<unsigned int, 2>
4279 return {{lookup_table[i][0], lookup_table[i][1]}};
4285 inline std::array<unsigned int, 2>
4296 inline std::array<unsigned int, 2>
4298 const unsigned int vertex)
4305 return {{4 + vertex / 4, vertex % 4}};
4311 inline std::array<unsigned int, 2>
4313 const unsigned int vertex)
4325 const bool face_orientation,
4326 const bool face_flip,
4327 const bool face_rotation)
4349 const unsigned int line_translation[4][2][2][2] = {
4371 return line_translation[line][face_orientation][face_flip][face_rotation];
4392 const unsigned int face,
4393 const unsigned int subface,
4411 const unsigned int face,
4412 const unsigned int subface,
4414 const bool face_flip,
4428 constexpr
unsigned int
4434 {{0, 0}, {1, 1}, {0, 1}, {0, 1}},
4435 {{0, 1}, {0, 1}, {0, 0}, {1, 1}},
4436 {{0, 2}, {1, 3}, {0, 1}, {2, 3}}
4440 {{0, 0}, {1, 1}, {1, 0}, {1, 0}},
4441 {{1, 0}, {1, 0}, {0, 0}, {1, 1}},
4442 {{2, 0}, {3, 1}, {1, 0}, {3, 2}}
4445 return subcells[face_flip][ref_case - 1][face][subface];
4453 const unsigned int face,
4454 const unsigned int subface,
4455 const bool face_orientation,
4456 const bool face_flip,
4457 const bool face_rotation,
4460 const unsigned int dim = 3;
4465 if (!(subface == 0 &&
4503 (face_orientation == face_rotation) ? flip[face_ref_case] : face_ref_case;
4515 const unsigned int subface_exchange[4][2][2][2][4] = {
4518 {{{{0,
e,
e,
e}, {0,
e,
e,
e}}, {{0,
e,
e,
e}, {0,
e,
e,
e}}},
4519 {{{0,
e,
e,
e}, {0,
e,
e,
e}}, {{0,
e,
e,
e}, {0,
e,
e,
e}}}},
4533 {{{{0, 1,
e,
e}, {0, 1,
e,
e}}, {{1, 0,
e,
e}, {1, 0,
e,
e}}},
4534 {{{0, 1,
e,
e}, {0, 1,
e,
e}}, {{1, 0,
e,
e}, {1, 0,
e,
e}}}},
4537 {{{{0, 1,
e,
e}, {1, 0,
e,
e}}, {{1, 0,
e,
e}, {0, 1,
e,
e}}},
4538 {{{0, 1,
e,
e}, {1, 0,
e,
e}}, {{1, 0,
e,
e}, {0, 1,
e,
e}}}},
4560 const unsigned int std_subface =
4561 subface_exchange[face_ref_case][face_orientation][face_flip][face_rotation]
4573 [max_children_per_face] = {
4635 if ((std_face_ref & face_refinement_case(ref_case, face)) ==
4636 face_refinement_case(ref_case, face))
4645 const unsigned int equivalent_iso_subface[4][4] = {
4651 const unsigned int equ_std_subface =
4652 equivalent_iso_subface[std_face_ref][std_subface];
4655 return iso_children[ref_case - 1][face][equ_std_subface];
4662 ExcMessage(
"The face RefineCase is too coarse "
4663 "for the given cell RefineCase."));
4690 const unsigned int line,
4708 const unsigned int line,
4709 const bool face_orientation,
4710 const bool face_flip,
4711 const bool face_rotation)
4716 const unsigned lines[faces_per_cell][lines_per_face] = {
4723 return lines[face][real_to_standard_face_line(
4724 line, face_orientation, face_flip, face_rotation)];
4759 const unsigned int vertex,
4760 const bool face_orientation,
4761 const bool face_flip,
4762 const bool face_rotation)
4788 template <
typename Number>
4793 for (
unsigned int i = 0; i < dim; ++i)
4805 double result = 0.0;
4807 for (
unsigned int i = 0; i < dim; ++i)
4810 result =
std::max(result, p[i] - 1.);
4821 const unsigned int i)
4829 const double x = xi[0];
4842 const double x = xi[0];
4843 const double y = xi[1];
4847 return (1 - x) * (1 - y);
4860 const double x = xi[0];
4861 const double y = xi[1];
4862 const double z = xi[2];
4866 return (1 - x) * (1 - y) * (1 - z);
4868 return x * (1 - y) * (1 - z);
4870 return (1 - x) * y * (1 - z);
4872 return x * y * (1 - z);
4874 return (1 - x) * (1 - y) * z;
4876 return x * (1 - y) * z;
4878 return (1 - x) * y * z;
4896 const unsigned int i)
4916 const unsigned int i)
4920 const double x = xi[0];
4921 const double y = xi[1];
4925 return Point<2>(-(1 - y), -(1 - x));
4941 const unsigned int i)
4945 const double x = xi[0];
4946 const double y = xi[1];
4947 const double z = xi[2];
4951 return Point<3>(-(1 - y) * (1 - z),
4953 -(1 - x) * (1 - y));
4955 return Point<3>((1 - y) * (1 - z), -x * (1 - z), -x * (1 - y));
4957 return Point<3>(-y * (1 - z), (1 - x) * (1 - z), -(1 - x) * y);
4959 return Point<3>(y * (1 - z), x * (1 - z), -x * y);
4961 return Point<3>(-(1 - y) * z, -(1 - x) * z, (1 - x) * (1 - y));
4963 return Point<3>((1 - y) * z, -x * z, x * (1 - y));
4965 return Point<3>(-y * z, (1 - x) * z, (1 - x) * y);
4967 return Point<3>(y * z, x * z, x * y);
4993 namespace GeometryInfoHelper
5003 result[0] = derivative[0][1];
5004 result[1] = -derivative[0][0];
5015 return cross_product_3d(derivative[0], derivative[1]);
5027 for (
unsigned int i = 0; i < dim; ++i)
5028 jacobian[i] = derivative[i];
5037 template <
int spacedim>
5040 # ifndef DEAL_II_CXX14_CONSTEXPR_BUG
5042 Tensor<spacedim - dim, spacedim> (&forms)[vertices_per_cell])
5076 for (
unsigned int i = 0; i < vertices_per_cell; ++i)
5080 for (
unsigned int j = 0; j < vertices_per_cell; ++j)
5083 d_linear_shape_function_gradient(unit_cell_vertex(i), j);
5084 for (
unsigned int l = 0;
l < dim; ++
l)
5085 derivatives[
l] +=
vertices[j] * grad_phi_j[
l];
5088 forms[i] = internal::GeometryInfoHelper::wedge_product(derivatives);
GeometryPrimitive(const unsigned int object_dimension)
GeometryPrimitive(const Object object)
RefinementCase operator|(const RefinementCase &r) const
static std::size_t memory_consumption()
RefinementCase operator~() const
RefinementCase operator&(const RefinementCase &r) const
static std::array< RefinementCase< dim >, n_refinement_cases > all_refinement_cases()
RefinementCase(const typename RefinementPossibilities< dim >::Possibilities refinement_case)
static constexpr unsigned int n_refinement_cases
static RefinementCase cut_axis(const unsigned int i)
void serialize(Archive &ar, const unsigned int version)
RefinementCase(const std::uint8_t refinement_case)
static constexpr std::size_t memory_consumption()
SubfaceCase(const typename SubfacePossibilities< dim >::Possibilities subface_possibility)
#define DEAL_II_NAMESPACE_OPEN
#define DEAL_II_NAMESPACE_CLOSE
static ::ExceptionBase & ExcInternalError()
static ::ExceptionBase & ExcInvalidCoordinate(double arg1)
static ::ExceptionBase & ExcInvalidSubface(int arg1, int arg2, int arg3)
#define Assert(cond, exc)
static ::ExceptionBase & ExcNotImplemented()
static ::ExceptionBase & ExcInvalidSubfaceCase(int arg1)
static ::ExceptionBase & ExcImpossibleInDim(int arg1)
#define AssertIndexRange(index, range)
#define DeclException3(Exception3, type1, type2, type3, outsequence)
#define DeclException1(Exception1, type1, outsequence)
static ::ExceptionBase & ExcInvalidRefinementCase(int arg1)
static ::ExceptionBase & ExcMessage(std::string arg1)
Point< spacedim > point(const gp_Pnt &p, const double tolerance=1e-10)
SymmetricTensor< 2, dim, Number > e(const Tensor< 2, dim, Number > &F)
Tensor< 2, dim, Number > l(const Tensor< 2, dim, Number > &F, const Tensor< 2, dim, Number > &dF_dt)
static const unsigned int invalid_unsigned_int
boost::integer_range< IncrementableType > iota_view
typename internal::ndarray::HelperArray< T, Ns... >::type ndarray
#define DEAL_II_HOST_DEVICE
static unsigned int n_children(const RefinementCase< 0 > &refinement_case)
static unsigned int face_to_cell_vertices(const unsigned int face, const unsigned int vertex, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false)
static const std::array< unsigned int, vertices_per_cell > dx_to_deal
static std::array< unsigned int, vertices_per_cell > vertex_indices()
static std::array< unsigned int, 0 > face_indices()
static unsigned int face_to_cell_lines(const unsigned int face, const unsigned int line, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false)
static const std::array< unsigned int, vertices_per_cell > ucd_to_deal
static unsigned int child_cell_from_point(const Point< dim > &p)
static unsigned int standard_to_real_line_vertex(const unsigned int vertex, const bool line_orientation=true)
static constexpr std::array< unsigned int, vertices_per_cell > ucd_to_deal
static constexpr ndarray< Tensor< 1, dim >, faces_per_cell, dim - 1 > unit_tangential_vectors
static bool is_inside_unit_cell(const Point< dim > &p, const double eps)
static RefinementCase< dim > min_cell_refinement_case_for_face_refinement(const RefinementCase< dim - 1 > &face_refinement_case, const unsigned int face_no, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false)
static double distance_to_unit_cell(const Point< dim > &p)
static unsigned int child_cell_on_face(const RefinementCase< dim > &ref_case, const unsigned int face, const unsigned int subface, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false, const RefinementCase< dim - 1 > &face_refinement_case=RefinementCase< dim - 1 >::isotropic_refinement)
static constexpr unsigned int quads_per_face
static unsigned int standard_to_real_face_vertex(const unsigned int vertex, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false)
static std_cxx20::ranges::iota_view< unsigned int, unsigned int > face_indices()
static constexpr std::array< unsigned int, faces_per_cell > opposite_face
static constexpr unsigned int max_children_per_face
static unsigned int face_to_cell_vertices(const unsigned int face, const unsigned int vertex, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false)
static constexpr unsigned int vertices_per_cell
static std::array< unsigned int, 2 > standard_hex_line_to_quad_line_index(const unsigned int line)
static Point< dim > unit_cell_vertex(const unsigned int vertex)
static constexpr std::array< unsigned int, vertices_per_cell > dx_to_deal
static std_cxx20::ranges::iota_view< unsigned int, unsigned int > vertex_indices()
static constexpr unsigned int lines_per_cell
static RefinementCase< 1 > line_refinement_case(const RefinementCase< dim > &cell_refinement_case, const unsigned int line_no)
static constexpr std::array< unsigned int, faces_per_cell > unit_normal_direction
static RefinementCase< dim > min_cell_refinement_case_for_line_refinement(const unsigned int line_no)
static constexpr unsigned int faces_per_cell
static unsigned int standard_to_real_face_line(const unsigned int line, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false)
static double subface_ratio(const internal::SubfaceCase< dim > &subface_case, const unsigned int subface_no)
static constexpr unsigned int hexes_per_cell
static Point< dim > child_to_cell_coordinates(const Point< dim > &p, const unsigned int child_index, const RefinementCase< dim > refine_case=RefinementCase< dim >::isotropic_refinement)
static Point< dim > cell_to_child_coordinates(const Point< dim > &p, const unsigned int child_index, const RefinementCase< dim > refine_case=RefinementCase< dim >::isotropic_refinement)
static double d_linear_shape_function(const Point< dim > &xi, const unsigned int i)
static constexpr std::array< Tensor< 1, dim >, faces_per_cell > unit_normal_vector
static Point< dim, Number > project_to_unit_cell(const Point< dim, Number > &p)
static Tensor< 1, dim > d_linear_shape_function_gradient(const Point< dim > &xi, const unsigned int i)
static constexpr unsigned int vertices_per_face
static unsigned int real_to_standard_face_line(const unsigned int line, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false)
static unsigned int line_to_cell_vertices(const unsigned int line, const unsigned int vertex)
static bool is_inside_unit_cell(const Point< dim > &p)
static unsigned int n_children(const RefinementCase< dim > &refinement_case)
static unsigned int real_to_standard_face_vertex(const unsigned int vertex, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false)
static unsigned int face_to_cell_lines(const unsigned int face, const unsigned int line, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false)
static std::array< unsigned int, 2 > standard_quad_vertex_to_line_vertex_index(const unsigned int vertex)
static constexpr ndarray< unsigned int, vertices_per_cell, dim > vertex_to_face
static void alternating_form_at_vertices(const Point< spacedim >(&vertices)[vertices_per_cell], Tensor< spacedim - dim, spacedim >(&forms)[vertices_per_cell])
static RefinementCase< dim - 1 > face_refinement_case(const RefinementCase< dim > &cell_refinement_case, const unsigned int face_no, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false)
static constexpr std::array< int, faces_per_cell > unit_normal_orientation
static constexpr unsigned int quads_per_cell
static constexpr unsigned int max_children_per_cell
static unsigned int n_subfaces(const internal::SubfaceCase< dim > &subface_case)
static constexpr unsigned int lines_per_face
static std::array< unsigned int, 2 > standard_hex_vertex_to_quad_vertex_index(const unsigned int vertex)
constexpr DEAL_II_HOST Number determinant(const SymmetricTensor< 2, dim, Number > &)