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CGAL 5.4.1 - 3D Mesh Generation
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CGAL 5.4.1 - 3D Mesh Generation
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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).
1.8.13