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CGAL 6.1 - 3D Mesh Generation
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CGAL 6.1 - 3D Mesh Generation
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The concept MeshTriangulationTraits_3 describes the requirements for the geometric traits class of the underlying regular triangulation used during a mesh generation process.
RegularTriangulationTraits_3 Kernel In addition to the requirements described for the traits class RegularTriangulationTraits_3, the geometric traits class of a regular triangulation used in mesh generation must fulfill the following requirements.
Types | |
| typedef unspecified_type | FT |
| Numerical type. | |
| typedef unspecified_type | Vector_3 |
| The vector type. | |
| typedef unspecified_type | Sphere_3 |
| The sphere type. | |
| typedef unspecified_type | Iso_cuboid_3 |
| The isocuboid type. | |
| typedef unspecified_type | Aff_transformation_3 |
| The affine transformation type. | |
| typedef unspecified_type | Do_intersect_3 |
| A predicate object that must provide the function operator: | |
| typedef unspecified_type | Equal_3 |
| A predicate object that must provide the function operator: | |
| typedef unspecified_type | Is_degenerate_3 |
| A predicate object that must provide the function operators: | |
| typedef unspecified_type | Collinear_3 |
| A predicate object that must provide the function operator: | |
| typedef unspecified_type | Compare_weighted_squared_radius_3 |
| A constructor object that must provide the function operators: | |
| typedef unspecified_type | Compute_approximate_dihedral_angle_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Compute_area_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Compute_power_distance_to_power_sphere_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Compute_squared_area_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Compute_squared_distance_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Compute_squared_length_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Compute_squared_radius_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Compute_squared_radius_smallest_orthogonal_sphere_3 |
| A constructor object that must provide the function operators: | |
| typedef unspecified_type | Compute_volume_3 |
| A constructor object that must provide the function operators: | |
| typedef unspecified_type | Compute_weight_3 |
| A constructor object that must provide the function operators: | |
| typedef unspecified_type | Construct_base_vector_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Construct_orthogonal_vector_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Construct_center_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Construct_weighted_circumcenter_3 |
| A constructor object that must provide the function operators: | |
| typedef unspecified_type | Construct_centroid_3 |
| A constructor object that must provide the function operators: | |
| typedef unspecified_type | Construct_midpoint_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Construct_normal_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Construct_sphere_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Construct_tetrahedron_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Construct_translated_point_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Construct_vector_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Construct_opposite_vector_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Construct_scaled_vector_3 |
| A constructor object that must provide the function operator: | |
| typedef unspecified_type | Intersect_3 |
| A constructor object that must provide the function operators: | |
Operations | |
The following functions give access to the predicate and construction objects: | |
| Do_intersect_3 | do_intersect_3_object () |
| Equal_3 | equal_3_object () |
| Is_degenerate_3 | equal_3_object () |
| Compare_weighted_squared_radius_3 | compare_weighted_squared_radius_3_object () |
| Compute_approximate_dihedral_angle_3 | compute_approximate_dihedral_angle_3_object () |
| Compute_area_3 | compute_area_3_object () |
| Compute_power_distance_to_power_sphere_3 | compute_power_distance_to_power_sphere_3_object () |
| Compute_squared_area_3 | compute_squared_area_3_object () |
| Compute_squared_distance_3 | compute_squared_distance_3_object () |
| Compute_squared_length_3 | compute_squared_length_3_object () |
| Compute_squared_radius_3 | compute_squared_radius_3_object () |
| Compute_squared_radius_smallest_orthogonal_sphere_3 | compute_squared_radius_smallest_orthogonal_sphere_3_object () |
| Compute_volume_3 | compute_volume_3_object () |
| Compute_weight_3 | compute_weight_3_object () |
| Construct_base_vector_3 | construct_base_vector_3_object () |
| Construct_orthogonal_vector_3 | construct_orthogonal_vector_3_object () |
| Construct_center_3 | construct_center_3_object () |
| Construct_midpoint_3 | construct_midpoint_3_object () |
| Construct_normal_3 | construct_normal_3_object () |
| Construct_sphere_3 | construct_sphere_3_object () |
| Construct_tetrahedron_3 | construct_tetrahedron_3_object () |
| Construct_translated_point_3 | construct_translated_point_3_object () |
| Construct_vector_3 | construct_vector_3_object () |
| Construct_scaled_vector_3 | construct_scaled_vector_3_object () |
| Construct_opposite_vector_3 | construct_opposite_vector_3_object () |
| Intersect_3 | intersect_3_object () |
A predicate object that must provide the function operator:
bool operator()(Point_3 p, Point_3 q, Point_3 r)
which returns true iff p, q, and r are collinear.
A constructor object that must provide the function operators:
bool operator()(Point_3 p, FT w)
bool operator()(Point_3 p, Point_3 q, FT w)
bool operator()(Point_3 p, Point_3 q, Point_3 r, FT w)
bool operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s, FT w)
which compare the weight of the smallest sphere orthogonal to the input weighted point(s) with the input weight.
A constructor object that must provide the function operator:
FT operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s)
which returns an approximation of the signed dihedral angle in the tetrahedron pqrs of edge pq. The sign is negative if orientation(p,q,r,s) is CGAL::NEGATIVE and positive otherwise. The angle is given in degrees.
A constructor object that must provide the function operator:
FT operator()(Point_3 p, Point_3 q, Point_3 r)
which returns the area of the triangle p, q, r.
A constructor object that must provide the function operator:
FT operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s, Point_3 t)
which returns the squared radius of the sphere centered in t and orthogonal to the sphere orthogonal to p, q, r, and s.
A constructor object that must provide the function operator:
FT operator()(Triangle_3 t)
which returns the squared area of the triangle t.
A constructor object that must provide the function operator:
FT operator()(Point_3 p, Point_3 q)
which returns the squared distance between two points p and q.
A constructor object that must provide the function operator:
FT operator()(Vector_3 v)
which returns the squared length of v.
A constructor object that must provide the function operator:
FT operator()(Sphere_3 s)
which returns the squared radius of the sphere s.
| typedef unspecified_type MeshTriangulationTraits_3::Compute_squared_radius_smallest_orthogonal_sphere_3 |
A constructor object that must provide the function operators:
FT operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s)
FT operator()(Point_3 p, Point_3 q, Point_3 r)
FT operator()(Point_3 p, Point_3 q)
which returns the squared radius of the smallest sphere orthogonal to the argument(s).
A constructor object that must provide the function operators:
FT operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s)
FT operator()(Tetrahedron_3 t)
which respectively return the volume of the tetrahedron formed by the points p, q, r, and s and of the tetrahedron t.
A constructor object that must provide the function operators:
FT operator()(Weighted_point_3 p)
which returns the weight of the weighted point p.
A constructor object that must provide the function operator:
Vector_3 operator()(Plane_3 p, int index),
which returns:
index == 1: a vector b1 that is orthogonal to the normal n to plane h;index == 2: a vector b2 that is orthogonal to n and b1 and such that for an arbitrary point p on the plane h, the orientation of p, p + b1, p + b2, and p + n is positive. A constructor object that must provide the function operator:
Point_3 operator()(Sphere_3 q),
which returns the center of the sphere s.
A constructor object that must provide the function operators:
Point_3 operator()(Point_3 p, Point_3 q, Point_3 r),
Point_3 operator()(Tetrahedron_3 t),
which respectively return the centroid of the points p, q, and r, and the centroid of the tetrahedron t.
A constructor object that must provide the function operator:
Point_3 operator()(Point_3 p, Point_3 q),
which returns the midpoint of the segment pq.
A constructor object that must provide the function operator:
Vector_3 operator()(Point_3 p, Point_3 q, Point_3 r),
which returns the normal of the vectors q-p and r-p.
A constructor object that must provide the function operator:
Vector_3 operator()(Vector_3 v)
which returns -v.
A constructor object that must provide the function operator:
Vector_3 operator()(Plane_3 p),
which returns a vector that is orthogonal to the plane p and directed to the positive side of p.
A constructor object that must provide the function operator:
Vector_3 operator()(Vector_3 v, FT scale)
which returns the vector v scaled by a factor scale.
A constructor object that must provide the function operator:
Sphere_3 operator()(Point_3 p, Point_3 q),
which returns the smallest sphere which passes through the points p and q.
A constructor object that must provide the function operator:
Tetrahedron_3 operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s),
which returns the tetrahedron with vertices p, q, r, and s.
A constructor object that must provide the function operator:
Point_3 operator()(Point_3 p, Vector_3 v),
which returns the point obtained by translating p by the vector v.
A constructor object that must provide the function operator:
Vector_3 operator()(Point_3 p, Point_3 q),
which returns a vector from two points.
A constructor object that must provide the function operators:
Point_3 operator()(Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s),
Point_3 operator()(Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s),
Point_3 operator()(Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s),
which return the center of the smallest orthogonal sphere to the input weighted points.
A predicate object that must provide the function operator:
bool operator()(Sphere_3 s1, Sphere_3 s2)
which returns true iff the spheres s1 and s2 intersect.
A predicate object that must provide the function operator:
bool operator()(Point_3 p, Point_3 q)
which returns true iff p and q are equal.
Numerical type.
Must be a model of FieldNumberType and FieldWithSqrt, and constructible from a double.
A constructor object that must provide the function operators:
std::optional< std::variant< T... > > operator()(Segment_3 s, Plane_3 p)
std::optional< std::variant< T... > > operator()(Ray_3 r, Iso_cuboid i)
std::optional< std::variant< T... > > operator()(Segment_3 s, Iso_cuboid i)
which returns the intersection region of two geometrical objects.
A predicate object that must provide the function operators:
bool operator()(Segment_3 s)
bool operator()(Ray_3 s)
which return true iff the object is degenerate.
1.9.6