CGAL 5.1.5 - 3D Triangulations
|
The concept TriangulationTraits_3
is the first template parameter of the class 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. More... | |
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. More... | |
typedef unspecified_type | Construct_segment_3 |
A constructor object that must provide the function operator. More... | |
typedef unspecified_type | Construct_triangle_3 |
A constructor object that must provide the function operator. More... | |
typedef unspecified_type | Construct_tetrahedron_3 |
A constructor object that must provide the function operator. More... | |
typedef unspecified_type | Compare_xyz_3 |
A predicate object that must provide the function operator. More... | |
typedef unspecified_type | Coplanar_orientation_3 |
A predicate object that must provide the function operator. More... | |
typedef unspecified_type | Orientation_3 |
A predicate object that must provide the function operator. More... | |
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
.