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CGAL 6.0 - 3D Triangulations
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SpatialSortingTraits_3 The concept TriangulationTraits_3 is the first template parameter of the class CGAL::Triangulation_3. It defines the geometric objects (points, segments, triangles and tetrahedra) forming the triangulation together with a few geometric predicates and constructions on these objects: lexicographical comparison, orientation in case of coplanar points and orientation in space.
Kernel CGAL::Triangulation_3 Types | |
| typedef unspecified_type | Point_3 |
| The point type. | |
| typedef unspecified_type | Segment_3 |
| The segment type. | |
| typedef unspecified_type | Triangle_3 |
| The triangle type. | |
| typedef unspecified_type | Tetrahedron_3 |
| The tetrahedron type. | |
| typedef unspecified_type | Construct_point_3 |
| A constructor object that must provide the function operator. | |
| typedef unspecified_type | Construct_segment_3 |
| A constructor object that must provide the function operator. | |
| typedef unspecified_type | Construct_triangle_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 | Compare_xyz_3 |
| A predicate object that must provide the function operator. | |
| typedef unspecified_type | Coplanar_orientation_3 |
| A predicate object that must provide the function operator. | |
| typedef unspecified_type | Orientation_3 |
| A predicate object that must provide the function operator. | |
Creation | |
| Triangulation_traits_3 () | |
| Default constructor. | |
| Triangulation_traits_3 (const Triangulation_traits_3 &tr) | |
| Copy constructor. | |
Operations | |
The following functions give access to the predicate and construction objects: | |
| Construct_point_3 | construct_point_3_object () |
| Construct_segment_3 | construct_segment_3_object () |
| Construct_triangle_3 | construct_triangle_3_object () |
| Construct_tetrahedron_3 | construct_tetrahedron_3_object () |
| Compare_xyz_3 | compare_xyz_3_object () |
| Coplanar_orientation_3 | coplanar_orientation_3_object () |
| Orientation_3 | orientation_3_object () |
A predicate object that must provide the function operator.
Comparison_result operator()(Point_3 p, Point_3 q),
which returns EQUAL if the two points are equal. Otherwise it must return a consistent order for any two points chosen in a same line.
A constructor object that must provide the function operator.
Point_3 operator()(Point_3 p),
which simply returns p.
p to avoid useless copies.CGAL::Triangulation_3 internally manipulates points with a Point type that is not always Point_3. A constructor object that must provide the function operator.
Segment_3 operator()(Point_3 p, Point_3 q),
which constructs a segment from two points.
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 constructs a tetrahedron from four points.
A constructor object that must provide the function operator.
Triangle_3 operator()(Point_3 p, Point_3 q, Point_3 r ),
which constructs a triangle from three points.
A predicate object that must provide the function operator.
Orientation operator()(Point_3 p, Point_3 q, Point_3 r),
which returns COLLINEAR if the points are collinear. Otherwise it must return a consistent orientation for any three points chosen in a same plane.
A predicate object that must provide the function operator.
Orientation operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s),
which returns POSITIVE, if s lies on the positive side of the oriented plane h defined by p, q, and r, returns NEGATIVE if s lies on the negative side of h, and returns COPLANAR if s lies on h.
The point type.
It must be DefaultConstructible, CopyConstructible and Assignable.