15#ifndef dealii_geometry_info_h
16#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;
670 cut_xy = cut_x | cut_y,
743 cut_xy = cut_x | cut_y,
751 cut_xz = cut_x | cut_z,
755 cut_yz = cut_y | cut_z,
759 cut_xyz = cut_x | cut_y | cut_z,
818 operator std::uint8_t()
const;
875 template <
class Archive>
885 <<
"The refinement flags given (" << arg1
886 <<
") contain set bits that do not "
887 <<
"make sense for the space dimension of the object to which they are applied.");
894 std::uint8_t
value : (dim > 0 ? dim : 1);
1167 subface_possibility);
1180 operator std::uint8_t()
const;
1185 static constexpr std::size_t
1194 <<
"The subface case given (" << arg1 <<
") does not make sense "
1195 <<
"for the space dimension of the object to which they are applied.");
1202 std::uint8_t
value : (dim == 3 ? 4 : 1);
1266 static std::array<unsigned int, 0>
1309 static std::array<unsigned int, vertices_per_cell>
1337 const unsigned int vertex,
1338 const bool face_orientation =
true,
1339 const bool face_flip =
false,
1340 const bool face_rotation =
false);
1358 const unsigned int line,
1359 const bool face_orientation =
true,
1360 const bool face_flip =
false,
1361 const bool face_rotation =
false);
1413 static const std::array<unsigned int, vertices_per_cell>
ucd_to_deal;
1428 static const std::array<unsigned int, vertices_per_cell>
dx_to_deal;
2098 static constexpr std::array<unsigned int, vertices_per_cell>
ucd_to_deal =
2099 internal::GeometryInfoHelper::Initializers<dim>::ucd_to_deal();
2114 static constexpr std::array<unsigned int, vertices_per_cell>
dx_to_deal =
2115 internal::GeometryInfoHelper::Initializers<dim>::dx_to_deal();
2129 internal::GeometryInfoHelper::Initializers<dim>::vertex_to_face();
2156 const unsigned int subface_no);
2165 const unsigned int face_no,
2166 const bool face_orientation =
true,
2167 const bool face_flip =
false,
2168 const bool face_rotation =
false);
2178 const unsigned int face_no,
2179 const bool face_orientation =
true,
2180 const bool face_flip =
false,
2181 const bool face_rotation =
false);
2189 const unsigned int line_no);
2246 const unsigned int face,
2247 const unsigned int subface,
2248 const bool face_orientation =
true,
2249 const bool face_flip =
false,
2250 const bool face_rotation =
false,
2292 const unsigned int vertex,
2293 const bool face_orientation =
true,
2294 const bool face_flip =
false,
2295 const bool face_rotation =
false);
2310 const unsigned int line,
2311 const bool face_orientation =
true,
2312 const bool face_flip =
false,
2313 const bool face_rotation =
false);
2326 const bool face_orientation =
true,
2327 const bool face_flip =
false,
2328 const bool face_rotation =
false);
2341 const bool face_orientation =
true,
2342 const bool face_flip =
false,
2343 const bool face_rotation =
false);
2356 const bool face_orientation =
true,
2357 const bool face_flip =
false,
2358 const bool face_rotation =
false);
2367 const bool line_orientation =
true);
2376 static std::array<unsigned int, 2>
2386 static std::array<unsigned int, 2>
2396 static std::array<unsigned int, 2>
2410 const bool face_orientation =
true,
2411 const bool face_flip =
false,
2412 const bool face_rotation =
false);
2443 const unsigned int child_index,
2454 const unsigned int child_index,
2483 template <
typename Number =
double>
2560 template <
int spacedim>
2563#ifndef DEAL_II_CXX14_CONSTEXPR_BUG
2579 static constexpr std::array<unsigned int, faces_per_cell>
2581 internal::GeometryInfoHelper::Initializers<dim>::unit_normal_direction();
2600 internal::GeometryInfoHelper::Initializers<dim>::unit_normal_orientation();
2614 internal::GeometryInfoHelper::Initializers<dim>::unit_normal_vector();
2639 internal::GeometryInfoHelper::Initializers<dim>::opposite_face();
2647 <<
"The coordinates must satisfy 0 <= x_i <= 1, "
2648 <<
"but here we have x_i=" << arg1);
2657 <<
"RefinementCase<dim> " << arg1 <<
": face " << arg2
2658 <<
" has no subface " << arg3);
2672 const unsigned int i);
2676 const unsigned int i);
2680 const unsigned int i);
2694 : object(static_cast<Object>(object_dimension))
2698inline GeometryPrimitive::operator
unsigned int()
const
2700 return static_cast<unsigned int>(object);
2710 :
value(subface_possibility)
2715 inline SubfaceCase<dim>::operator std::uint8_t()
const
2729 return static_cast<std::uint8_t
>(-1);
2773inline std::array<RefinementCase<1>, 2>
2783inline std::array<RefinementCase<2>, 4>
2795inline std::array<RefinementCase<3>, 8>
2820 :
value(refinement_case)
2826 Assert((refinement_case &
2829 ExcInvalidRefinementCase(refinement_case));
2836 :
value(refinement_case)
2842 Assert((refinement_case &
2845 ExcInvalidRefinementCase(refinement_case));
2896template <
class Archive>
2902 std::uint8_t uchar_value =
value;
2904 value = uchar_value;
2915 return Point<1>(
static_cast<double>(vertex));
2926 return {
static_cast<double>(vertex % 2),
static_cast<double>(vertex / 2)};
2937 return {
static_cast<double>(vertex % 2),
2938 static_cast<double>(vertex / 2 % 2),
2939 static_cast<double>(vertex / 4)};
2944inline std::array<unsigned int, 0>
2952inline std::array<unsigned int, 1>
2965 0U, faces_per_cell);
2975 0U, vertices_per_cell);
2995 Assert((p[0] >= 0) && (p[0] <= 1), ExcInvalidCoordinate(p[0]));
2997 return (p[0] <= 0.5 ? 0 : 1);
3006 Assert((p[0] >= 0) && (p[0] <= 1), ExcInvalidCoordinate(p[0]));
3007 Assert((p[1] >= 0) && (p[1] <= 1), ExcInvalidCoordinate(p[1]));
3009 return (p[0] <= 0.5 ? (p[1] <= 0.5 ? 0 : 2) : (p[1] <= 0.5 ? 1 : 3));
3018 Assert((p[0] >= 0) && (p[0] <= 1), ExcInvalidCoordinate(p[0]));
3019 Assert((p[1] >= 0) && (p[1] <= 1), ExcInvalidCoordinate(p[1]));
3020 Assert((p[2] >= 0) && (p[2] <= 1), ExcInvalidCoordinate(p[2]));
3022 return (p[0] <= 0.5 ?
3023 (p[1] <= 0.5 ? (p[2] <= 0.5 ? 0 : 4) : (p[2] <= 0.5 ? 2 : 6)) :
3024 (p[1] <= 0.5 ? (p[2] <= 0.5 ? 1 : 5) : (p[2] <= 0.5 ? 3 : 7)));
3042 const unsigned int child_index,
3050 return Point<1>(p * 2.0 - unit_cell_vertex(child_index));
3058 const unsigned int child_index,
3065 switch (refine_case)
3069 if (child_index == 1)
3074 if (child_index == 1)
3079 point -= unit_cell_vertex(child_index);
3093 const unsigned int child_index,
3105 switch (refine_case)
3109 if (child_index == 1)
3114 if (child_index == 1)
3119 if (child_index == 1)
3125 if (child_index % 2 == 1)
3127 if (child_index / 2 == 1)
3137 if (child_index / 2 == 1)
3139 if (child_index % 2 == 1)
3145 if (child_index % 2 == 1)
3147 if (child_index / 2 == 1)
3152 point -= unit_cell_vertex(child_index);
3167 const unsigned int ,
3180 const unsigned int child_index,
3188 return (p + unit_cell_vertex(child_index)) * 0.5;
3196 const unsigned int child_index,
3208 switch (refine_case)
3211 if (child_index == 1)
3216 if (child_index == 1)
3221 if (child_index == 1)
3226 if (child_index % 2 == 1)
3228 if (child_index / 2 == 1)
3238 if (child_index / 2 == 1)
3240 if (child_index % 2 == 1)
3246 if (child_index % 2 == 1)
3248 if (child_index / 2 == 1)
3254 point += unit_cell_vertex(child_index);
3269 const unsigned int child_index,
3275 switch (refine_case)
3278 if (child_index == 1)
3283 if (child_index == 1)
3288 point += unit_cell_vertex(child_index);
3304 const unsigned int ,
3325 return (p[0] >= 0.) && (p[0] <= 1.);
3334 return (p[0] >= 0.) && (p[0] <= 1.) && (p[1] >= 0.) && (p[1] <= 1.);
3343 return (p[0] >= 0.) && (p[0] <= 1.) && (p[1] >= 0.) && (p[1] <= 1.) &&
3344 (p[2] >= 0.) && (p[2] <= 1.);
3361 return (p[0] >= -eps) && (p[0] <= 1. +
eps);
3370 const double l = -
eps, u = 1 +
eps;
3371 return (p[0] >= l) && (p[0] <= u) && (p[1] >= l) && (p[1] <= u);
3380 const double l = -
eps, u = 1.0 +
eps;
3381 return (p[0] >= l) && (p[0] <= u) && (p[1] >= l) && (p[1] <= u) &&
3382 (p[2] >= l) && (p[2] <= u);
3390 const unsigned int vertex)
3403 const unsigned int vertex)
3405 constexpr unsigned int cell_vertices[4][2] = {{0, 2}, {1, 3}, {0, 1}, {2, 3}};
3406 return cell_vertices[line][vertex];
3414 const unsigned int vertex)
3419 constexpr unsigned vertices[lines_per_cell][2] = {{0, 2},
3432 return vertices[line][vertex];
3447 const bool face_orientation,
3448 const bool face_flip,
3449 const bool face_rotation)
3471 constexpr unsigned int vertex_translation[4][2][2][2] = {
3493 return vertex_translation[vertex][face_orientation][face_flip][face_rotation];
3515 0, 2, 2, 4, 2, 4, 4, 8};
3517 return n_children[ref_case];
3552 0, 2, 3, 3, 4, 2, 3, 3, 4, 4};
3553 return nsubs[subface_case];
3582 switch (subface_case)
3619 const unsigned int subface_no)
3622 switch (subface_case)
3657 if (subface_no == 0)
3704 const unsigned int face_no,
3709 const unsigned int dim = 2;
3731 return ref_cases[cell_refinement_case][face_no / 2];
3739 const unsigned int face_no,
3740 const bool face_orientation,
3742 const bool face_rotation)
3744 const unsigned int dim = 3;
3790 ref_cases[cell_refinement_case][face_no / 2];
3810 return (face_orientation == face_rotation) ? flip[ref_case] : ref_case;
3828 const unsigned int line_no)
3831 const unsigned int dim = 1;
3837 return cell_refinement_case;
3845 const unsigned int line_no)
3848 return face_refinement_case(cell_refinement_case, line_no);
3856 const unsigned int line_no)
3858 const unsigned int dim = 3;
3879 const unsigned int direction[lines_per_cell] = {
3880 1, 1, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2};
3882 return ((cell_refinement_case & cut_one[direction[line_no]]) ?
3912 const unsigned int dim = 1;
3923 const unsigned int face_no,
3928 const unsigned int dim = 2;
3945 const unsigned int face_no,
3946 const bool face_orientation,
3948 const bool face_rotation)
3950 const unsigned int dim = 3;
3974 (face_orientation == face_rotation) ? flip[face_refinement_case] :
3975 face_refinement_case;
3994 return face_to_cell[face_no / 2][std_face_ref];
4012 const unsigned int line_no)
4024 const unsigned int line_no)
4026 const unsigned int dim = 2;
4038 const unsigned int line_no)
4040 const unsigned int dim = 3;
4051 return ref_cases[line_no / 2];
4059 const bool face_orientation,
4060 const bool face_flip,
4061 const bool face_rotation)
4083 const unsigned int vertex_translation[4][2][2][2] = {
4105 return vertex_translation[vertex][face_orientation][face_flip][face_rotation];
4127 const bool face_orientation,
4128 const bool face_flip,
4129 const bool face_rotation)
4151 const unsigned int line_translation[4][2][2][2] = {
4173 return line_translation[line][face_orientation][face_flip][face_rotation];
4194 const bool line_orientation)
4196 return line_orientation ? vertex : (1 - vertex);
4213inline std::array<unsigned int, 2>
4215 const unsigned int vertex)
4217 return {{vertex % 2, vertex / 2}};
4223inline std::array<unsigned int, 2>
4225 const unsigned int vertex)
4235inline std::array<unsigned int, 2>
4259 return {{lookup_table[i][0], lookup_table[i][1]}};
4265inline std::array<unsigned int, 2>
4276inline std::array<unsigned int, 2>
4278 const unsigned int vertex)
4285 return {{4 + vertex / 4, vertex % 4}};
4291inline std::array<unsigned int, 2>
4293 const unsigned int vertex)
4305 const bool face_orientation,
4306 const bool face_flip,
4307 const bool face_rotation)
4329 const unsigned int line_translation[4][2][2][2] = {
4351 return line_translation[line][face_orientation][face_flip][face_rotation];
4372 const unsigned int face,
4373 const unsigned int subface,
4391 const unsigned int face,
4392 const unsigned int subface,
4393 const bool face_orientation,
4408 constexpr unsigned int
4414 {{0, 0}, {1, 1}, {1, 0}, {1, 0}},
4415 {{1, 0}, {1, 0}, {0, 0}, {1, 1}},
4416 {{2, 0}, {3, 1}, {1, 0}, {3, 2}}
4420 {{0, 0}, {1, 1}, {0, 1}, {0, 1}},
4421 {{0, 1}, {0, 1}, {0, 0}, {1, 1}},
4422 {{0, 2}, {1, 3}, {0, 1}, {2, 3}}
4425 return subcells[face_orientation][ref_case - 1][face][subface];
4433 const unsigned int face,
4434 const unsigned int subface,
4435 const bool face_orientation,
4436 const bool face_flip,
4437 const bool face_rotation,
4440 const unsigned int dim = 3;
4445 if (!(subface == 0 &&
4483 (face_orientation == face_rotation) ? flip[face_ref_case] : face_ref_case;
4495 const unsigned int subface_exchange[4][2][2][2][4] = {
4498 {{{{0,
e,
e,
e}, {0,
e,
e,
e}}, {{0,
e,
e,
e}, {0,
e,
e,
e}}},
4499 {{{0,
e,
e,
e}, {0,
e,
e,
e}}, {{0,
e,
e,
e}, {0,
e,
e,
e}}}},
4513 {{{{0, 1,
e,
e}, {0, 1,
e,
e}}, {{1, 0,
e,
e}, {1, 0,
e,
e}}},
4514 {{{0, 1,
e,
e}, {0, 1,
e,
e}}, {{1, 0,
e,
e}, {1, 0,
e,
e}}}},
4517 {{{{0, 1,
e,
e}, {1, 0,
e,
e}}, {{1, 0,
e,
e}, {0, 1,
e,
e}}},
4518 {{{0, 1,
e,
e}, {1, 0,
e,
e}}, {{1, 0,
e,
e}, {0, 1,
e,
e}}}},
4540 const unsigned int std_subface =
4541 subface_exchange[face_ref_case][face_orientation][face_flip][face_rotation]
4553 [max_children_per_face] = {
4615 if ((std_face_ref & face_refinement_case(ref_case, face)) ==
4616 face_refinement_case(ref_case, face))
4625 const unsigned int equivalent_iso_subface[4][4] = {
4631 const unsigned int equ_std_subface =
4632 equivalent_iso_subface[std_face_ref][std_subface];
4635 return iso_children[ref_case - 1][face][equ_std_subface];
4642 ExcMessage(
"The face RefineCase is too coarse "
4643 "for the given cell RefineCase."));
4670 const unsigned int line,
4688 const unsigned int line,
4689 const bool face_orientation,
4690 const bool face_flip,
4691 const bool face_rotation)
4696 const unsigned lines[faces_per_cell][lines_per_face] = {
4703 return lines[face][real_to_standard_face_line(
4704 line, face_orientation, face_flip, face_rotation)];
4739 const unsigned int vertex,
4740 const bool face_orientation,
4741 const bool face_flip,
4742 const bool face_rotation)
4768template <
typename Number>
4773 for (
unsigned int i = 0; i < dim; ++i)
4785 double result = 0.0;
4787 for (
unsigned int i = 0; i < dim; ++i)
4790 result =
std::max(result, p[i] - 1.);
4801 const unsigned int i)
4809 const double x = xi[0];
4822 const double x = xi[0];
4823 const double y = xi[1];
4827 return (1 - x) * (1 - y);
4840 const double x = xi[0];
4841 const double y = xi[1];
4842 const double z = xi[2];
4846 return (1 - x) * (1 - y) * (1 - z);
4848 return x * (1 - y) * (1 - z);
4850 return (1 - x) * y * (1 - z);
4852 return x * y * (1 - z);
4854 return (1 - x) * (1 - y) * z;
4856 return x * (1 - y) * z;
4858 return (1 - x) * y * z;
4876 const unsigned int i)
4896 const unsigned int i)
4900 const double x = xi[0];
4901 const double y = xi[1];
4905 return Point<2>(-(1 - y), -(1 - x));
4921 const unsigned int i)
4925 const double x = xi[0];
4926 const double y = xi[1];
4927 const double z = xi[2];
4931 return Point<3>(-(1 - y) * (1 - z),
4933 -(1 - x) * (1 - y));
4935 return Point<3>((1 - y) * (1 - z), -x * (1 - z), -x * (1 - y));
4937 return Point<3>(-y * (1 - z), (1 - x) * (1 - z), -(1 - x) * y);
4939 return Point<3>(y * (1 - z), x * (1 - z), -x * y);
4941 return Point<3>(-(1 - y) * z, -(1 - x) * z, (1 - x) * (1 - y));
4943 return Point<3>((1 - y) * z, -x * z, x * (1 - y));
4945 return Point<3>(-y * z, (1 - x) * z, (1 - x) * y);
4947 return Point<3>(y * z, x * z, x * y);
4973 namespace GeometryInfoHelper
4983 result[0] = derivative[0][1];
4984 result[1] = -derivative[0][0];
4995 return cross_product_3d(derivative[0], derivative[1]);
5007 for (
unsigned int i = 0; i < dim; ++i)
5008 jacobian[i] = derivative[i];
5017template <
int spacedim>
5020# ifndef DEAL_II_CXX14_CONSTEXPR_BUG
5022 Tensor<spacedim - dim, spacedim> (&forms)[vertices_per_cell])
5056 for (
unsigned int i = 0; i < vertices_per_cell; ++i)
5060 for (
unsigned int j = 0; j < vertices_per_cell; ++j)
5063 d_linear_shape_function_gradient(unit_cell_vertex(i), j);
5064 for (
unsigned int l = 0;
l < dim; ++
l)
5065 derivatives[l] += vertices[j] * grad_phi_j[l];
5068 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
RefinementCase(const typename RefinementPossibilities< dim >::Possibilities refinement_case)
static constexpr unsigned int n_refinement_cases
static RefinementCase cut_axis(const unsigned int i)
static std::array< RefinementCase< dim >, n_refinement_cases > all_refinement_cases()
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_HOST_DEVICE
#define DEAL_II_NAMESPACE_CLOSE
#define DEAL_II_ASSERT_UNREACHABLE()
#define DEAL_II_NOT_IMPLEMENTED()
#define Assert(cond, exc)
static ::ExceptionBase & ExcImpossibleInDim(int arg1)
static ::ExceptionBase & ExcInvalidCoordinate(double arg1)
static ::ExceptionBase & ExcInvalidSubface(int arg1, int arg2, int arg3)
static ::ExceptionBase & ExcInvalidRefinementCase(int arg1)
#define AssertIndexRange(index, range)
static ::ExceptionBase & ExcInternalError()
#define DeclException3(Exception3, type1, type2, type3, outsequence)
#define DeclException1(Exception1, type1, outsequence)
static ::ExceptionBase & ExcMessage(std::string arg1)
static ::ExceptionBase & ExcInvalidSubfaceCase(int 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)
constexpr unsigned int invalid_unsigned_int
boost::integer_range< IncrementableType > iota_view
::VectorizedArray< Number, width > min(const ::VectorizedArray< Number, width > &, const ::VectorizedArray< Number, width > &)
::VectorizedArray< Number, width > max(const ::VectorizedArray< Number, width > &, const ::VectorizedArray< Number, width > &)
typename internal::ndarray::HelperArray< T, Ns... >::type ndarray
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 std::array< unsigned int, 0 > face_indices()
static std::array< unsigned int, vertices_per_cell > vertex_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 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 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 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 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 RefinementCase< dim > min_cell_refinement_case_for_line_refinement(const unsigned int line_no)
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 constexpr std::array< unsigned int, vertices_per_cell > dx_to_deal
static constexpr unsigned int lines_per_cell
static constexpr std::array< unsigned int, faces_per_cell > unit_normal_direction
static std::array< unsigned int, 2 > standard_hex_line_to_quad_line_index(const unsigned int line)
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 std_cxx20::ranges::iota_view< unsigned int, unsigned int > face_indices()
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, Number > project_to_unit_cell(const Point< dim, Number > &p)
static RefinementCase< 1 > line_refinement_case(const RefinementCase< dim > &cell_refinement_case, const unsigned int line_no)
static std::array< unsigned int, 2 > standard_hex_vertex_to_quad_vertex_index(const unsigned int vertex)
static std::array< unsigned int, 2 > standard_quad_vertex_to_line_vertex_index(const unsigned int vertex)
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 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 std_cxx20::ranges::iota_view< unsigned int, unsigned int > vertex_indices()
static bool is_inside_unit_cell(const Point< dim > &p)
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 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 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 constexpr ndarray< unsigned int, vertices_per_cell, dim > vertex_to_face
static Tensor< 1, dim > d_linear_shape_function_gradient(const Point< dim > &xi, const unsigned int i)
static void alternating_form_at_vertices(const Point< spacedim >(&vertices)[vertices_per_cell], Tensor< spacedim - dim, spacedim >(&forms)[vertices_per_cell])
static Point< dim > unit_cell_vertex(const unsigned int vertex)
static constexpr std::array< int, faces_per_cell > unit_normal_orientation
static constexpr unsigned int quads_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 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
DEAL_II_HOST constexpr Number determinant(const SymmetricTensor< 2, dim, Number > &)