CGAL 6.1.2 - Kinetic Space Partition: KineticSpacePartitionTraits_3 Concept Reference

CGAL 6.1.2 - Kinetic Space Partition

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KineticSpacePartitionTraits_3 Concept Reference
Reference Manual » Concepts

## Definition

A concept that describes the set of types required by the `CGAL::Kinetic_space_partition_3`.

Has models
  All models of the concept `Kernel`

See also
  `CGAL::Kinetic_space_partition_3`

## Types
typedef unspecified_type | Point_3
| The 3D point type.
typedef unspecified_type | Point_2
| The 2D point type.
typedef unspecified_type | Vector_3
| The 3D vector type.
typedef unspecified_type | Line_2
| The 2D line type.
typedef unspecified_type | Direction_2
| The 2D direction type.
typedef unspecified_type | Plane_3
| The plane type.
typedef unspecified_type | Vector_2
| The 2D vector type.
typedef unspecified_type | Segment_2
| The 2D segment type.
typedef unspecified_type | Tetrahedron_3
| The 3d tetrahedron type.
typedef unspecified_type | Transform_3
| The 3d transformation type.
typedef unspecified_type | FT
| The number type of the Cartesian coordinates.
typedef unspecified_type | Construct_point_3
| Function object type that provides `Point_3 operator()(Origin p)` returning the point with 0, 0, 0 as Cartesian coordinates and `Point_3 operator()(FT x, FT y, FT z)` returning the point with `x`, `y` and `z` as Cartesian coordinates.
typedef unspecified_type | Construct_vector_3
| Function object type that provides `Vector_3 operator()(Point_3 p1, Point_3 p2)` and `Vector_3 operator()(Origin p1, Point_3 p2)` returning the vector `p1p2`, `Vector_3 operator()(NULL_VECTOR)` returning the null vector, and `Vector_3 operator()(Line_3 l)` returning a vector having the same direction as `l`
typedef unspecified_type | Construct_line_2
| Function object type that provides `Line_2 operator()(Point_2 p, Vector_2 d)` returning the line going through `p` in the direction of `d`.
typedef unspecified_type | Construct_point_on_2
| Function object type that provides `Point_2 operator()(Line_2 l, int i)` returning an arbitrary point on `l`.
typedef unspecified_type | Construct_point_2
| Function object type that provides `Point_2 operator()(FT x, FT y)` returning the 2D point with `x` and `y` as Cartesian coordinates.
typedef unspecified_type | Construct_vector_2
| Function object type that provides `Vector_2 operator()(Point_2 p1, Point_2 p2)` returning the vector `p1p2`, `Vector_2 operator()(NULL_VECTOR)` returning the null vector.
typedef unspecified_type | ConstructTetrahedron_3
| Function object type that provides `Tetrahedron_3 operator(Point_3 p, Point_3 q, Point_3 r, Point_3 s)` returning the tetrahedron with the points `p`, `q`, `r` and `s`.
typedef unspecified_type | Compute_x_3
| Function object type that provides `FT operator()(Point_3 p)` and `FT operator()(Vector_3 v)` returning the `x` coordinate of a point and a vector respectively.
typedef unspecified_type | Compute_y_3
| Function object type that provides `FT operator()(Point_3 p)` and `FT operator()(Vector_3 v)` returning the `y` coordinate of a point and a vector respectively.
typedef unspecified_type | Compute_z_3
| Function object type that provides `FT operator()(Point_3 p)` and `FT operator()(Vector_3 v)` returning the `z` coordinate of a point and a vector respectively.
typedef unspecified_type | Compute_x_2
| Function object type that provides `FT operator()(Point_2 p)` and `FT operator()(Vector_2 v)` returning the `x` coordinate of a point and a vector respectively.
typedef unspecified_type | Compute_y_2
| Function object type that provides `FT operator()(Point_2 p)` and `FT operator()(Vector_2 v)` returning the `y` coordinate of a point and a vector respectively.
typedef unspecified_type | Compute_squared_length_2
| Function object type that provides `FT operator()(Vector_2 v)` returning the squared length of `v`.
typedef unspecified_type | Compute_scalar_product_3
| Function object type that provides `FT operator()(Vector_3 v1, Vector_3 v2)` returning the scalar product of `v1` and `v2`.
typedef unspecified_type | Construct_sum_of_vectors_3
| Function object type that provides `Vector_3 operator() (Vector_3 v1, Vector_3 v2)` returning the `v1+v2`.
typedef unspecified_type | Construct_orthogonal_vector_3
| Function object type that provides `Vector_3 operator()(Plane_3 p)` returns a vector that is orthogonal to the plane `p` and directed to the positive side of `p`.
typedef unspecified_type | Construct_plane_3
| Function object type that provides `Plane_3 operator()(Point_3 p, Point_3 q, Point_3 r)` creates a plane passing through the points `p`, `q` and `r` and `Plane_3 operator()(Point_3 p, Vector_3 v)` introduces a plane that passes through point `p` and that is orthogonal to `V`.
typedef unspecified_type | Construct_projected_point_3
| Function object type that provides `Vector_3 operator()(Plane_3 h, Point_3 p)` returns the orthogonal projection of `p` onto `h`.
typedef unspecified_type | Collinear_3
| Function object type that provides `bool operator()(Point_3 p, Point_3 q, Point_3 r)` returning true if the points `p`, `q`, and `r` are collinear and false otherwise.
typedef unspecified_type | Oriented_side_3
| Function object type that provides `Oriented_size operator()(Plane_3 h, Point_3 p)` returns `CGAL::ON_ORIENTED_BOUNDARY`, `CGAL::ON_NEGATIVE_SIDE`, or `CGAL::ON_POSITIVE_SIDE`, depending on the position of `p` relative to the oriented plane `h`.

## Access to Function Objects
Construct_point_3 | construct_point_3_object ()
Construct_vector_3 | construct_vector_3_object ()
Construct_line_2 | construct_line_2_object ()
Construct_point_on_3 | construct_point_on_3_object ()
Construct_point_2 | construct_point_2_object ()
Construct_vector_2 | construct_vector_2_object ()
Construct_tetrahedron_3 | construct_tetrahedron_3_object ()
Compute_x_3 | compute_x_3_object ()
Compute_y_3 | compute_y_3_object ()
Compute_z_3 | compute_z_3_object ()
Compute_x_2 | compute_x_2_object ()
Compute_y_2 | compute_y_2_object ()
Compute_squared_length_2 | compute_squared_length_2_object ()
Construct_sum_of_vectors_3 | construct_sum_of_vectors_3_object ()
Construct_projected_point_3 | construct_projected_point_3_object ()
Compute_scalar_product_3 | compute_scalar_product_3_object ()
Collinear_3 | collinear_3_object ()
Oriented_side_3 | oriented_side_3_object ()

## Member Typedef Documentation

## ◆ Construct_point_on_2

typedef unspecified_type KineticSpacePartitionTraits_3::Construct_point_on_2

Function object type that provides `Point_2 operator()(Line_2 l, int i)` returning an arbitrary point on `l`.

`i` is not used and can be of any value.