CGAL 5.4.1 - 3D Mesh Generation
|
The concept BisectionGeometricTraits_3
describes a geometric traits class that provides the basic types and operations to implement a model of MeshDomain_3
based solely on intersection detections. Points in the non-empty intersections are herein computed by bisection.
Such traits class is relevant when intersection detections can be performed efficiently. For instance, when bounding surfaces are implicitly described by a function (such as an isosurface of a 3D function from \( \mathbb{R}^3\) to \( \mathbb{R}\)), the do-intersect predicate with a segment is computed by evaluations of the function values at both end points of the segment.
Operations | |
The following functions give access to the predicate and construction objects: | |
Compute_scalar_product_3 | compute_scalar_product_3_object () |
Compute_squared_distance_3 | compute_squared_distance_3_object () |
Compute_squared_radius_3 | compute_squared_radius_3_object () |
Construct_center_3 | construct_center_3_object () |
Construct_midpoint_3 | construct_midpoint_3_object () |
Construct_point_on_3 | construct_point_on_3_object () |
Construct_scaled_vector_3 | construct_scaled_vector_3_object () |
Construct_segment_3 | construct_segment_3_object () |
Construct_translated_point_3 | construct_translated_point_3_object () |
Construct_vector_3 | construct_vector_3_object () |
Has_on_bounded_side_3 | has_on_bounded_side_3_object () |
Model of Kernel::ComputeScalarProduct_3
.
That function object must provide the operator:
FT operator()(Vector_3 v, Vector_3 w)
which returns the scalar (inner) product of the two vectors v
and w
. Model of Kernel::ComputeSquaredDistance_3
.
That function object must provide the operator:
FT operator()(Point_3, Point_3)
which returns the squared distance between two points. Model of Kernel::ComputeSquaredRadius_3
.
That function object must provide the operator:
FT operator()(Sphere_3 s)
which returns the squared radius of s
. Model of Kernel::ConstructCenter_3
.
That function object must provide the operator:
Point_3 operator()(Sphere_3 s)
which returns the center of the sphere s
. Model of Kernel::ConstructMidpoint_3
.
That function object must provide the operator:
Point_3 operator()(Point_3 p, Point_3 q)
which computes the midpoint of the segment pq
. Model of Kernel::ConstructPoint_3
.
That function object must provide the following operators:
Point_3 operator()(Line_3 l,int i)
which returns an arbitrary point on l
. It holds point(i) == point(j)
, iff i==j
. Furthermore, is directed from point(i)
to point(j)
, for all i
< j
.Point_3 operator()(Ray_3 r,int i)
which returns a point on r
. point(0)
is the source, point(i)
, with \( i>0\), is different from the source. Point_3 operator()(Segment_3 s,int i)
which returns either source or target of s
: point(0)
returns the source of s
, point(1)
returns the target of s
. Parameter i
is taken modulo 2, which gives easy access to the other end point. Model of Kernel::ConstructScaledVector_3
`.
That function object must provide the operator:
Vector_3 operator()(Vector_3 v, FT scale)
which returns the vector v
scaled by a factor scale
. Model of Kernel::ConstructSegment_3
.
That function object must provide the operator:
Segment_3 operator()(Point_3 p, Point_3 q)
which returns a segment with source p
and target q
, directed from the source to the target. Model of Kernel::ConstructTranslatedPoint_3
.
That function object must provide the operator:
Point_3 operator()(Point_3 p, Vector_3 v)
which returns the point obtained by translating p
by the vector v
. Model of Kernel::ConstructVertex_3
.
That function object must provide the operator:
Vector_3 operator()(Point_3 a, Point_3 b)
which returns the vector b-a
. Numerical type.
Must be a model of FieldNumberType
and FieldWithSqrt
, and constructible from a double
.
Model of Kernel::HasOnBoundedSide_3
.
That function object must provide the operator:
bool operator()(Sphere_3 s, Point_3 p)
which returns true iff p
lies on the bounded side of `s. The point type.
Must have a constructor Point_3(FT, FT, FT)
.