CGAL 6.0.1 - 2D Straight Skeleton and Polygon Offsetting
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StraightSkeletonBuilderTraits_2 Concept Reference

Definition

Refines
DefaultConstructible
CopyConstructible

The concept StraightSkeletonBuilderTraits_2 describes the requirements for the geometric traits class required by the algorithm class CGAL::Straight_skeleton_builder_2.

Has models
CGAL::Straight_skeleton_builder_traits_2<K>

Kernel Types

typedef unspecified_type Kernel
 A model of the Kernel concept.
 
typedef unspecified_type FT
 A model of the FieldWithSqrt concept provided by the kernel.
 
typedef unspecified_type Point_2
 A model of the Kernel::Point_2 concept.
 
typedef unspecified_type Segment_2
 A model of the Kernel::Segment_2 concept.
 
typedef unspecified_type Vector_2
 A model of the Kernel::Vector_2 concept.
 
typedef unspecified_type Direction_2
 A model of the Kernel::Direction_2 concept.
 
typedef CGAL::Trisegment_2< KernelTrisegment_2
 
typedef CGAL::Trisegment_2_ptr< Trisegment_2Trisegment_2_ptr
 

Predicates and Constructors Types

typedef unspecified_type Do_ss_event_exist_2
 A predicate object type.
 
typedef unspecified_type Compare_ss_event_times_2
 A predicate object type.
 
typedef unspecified_type Are_ss_events_simultaneous_2
 A predicate object type.
 
typedef unspecified_type Construct_ss_event_time_and_point_2
 A construction object type.
 
typedef unspecified_type Construct_ss_trisegment_2
 A construction object type.
 
typedef unspecified_type Is_edge_facing_ss_node_2
 A predicate object type.
 
typedef unspecified_type Oriented_side_of_event_point_wrt_bisector_2
 A predicate object type.
 

Predicates and Constructors Functors

Are_ss_events_simultaneous_2 are_ss_events_simultaneous_2_object () const
 
Compare_ss_event_times_2 compare_ss_event_times_2_object () const
 
Do_ss_event_exist_2 do_ss_event_exist_2_object () const
 
Is_edge_facing_ss_node_2 is_edge_facing_ss_node_2_object () const
 
Oriented_side_of_event_point_wrt_bisector_2 oriented_side_of_event_point_wrt_bisector_2_object () const
 
Construct_ss_event_time_and_point_2 construct_ss_event_time_and_point_2_object () const
 
Construct_ss_trisegment_2 construct_ss_trisegment_2_object () const
 

Member Typedef Documentation

◆ Are_ss_events_simultaneous_2

A predicate object type.

Must provide bool operator()( const Trisegment_2_ptr& l, const Trisegment_2_ptr& r),

which determines if the events given by l and r are coincident in time and space; that is, both triples of offset lines intersect at the same point and at the same Euclidean distance from their sources.

Precondition
l and r must be edge-triples corresponding to events that actually exist (as determined by the predicate Do_ss_event_exist_2).

◆ Compare_ss_event_times_2

A predicate object type.

Must provide

CGAL::Comparison_result operator()(const Trisegment_2_ptr& l, const Trisegment_2_ptr& r) const,

which compares the times for the events determined by the edge-triples l and r.

The time of an event given by an edge triple (which defines three oriented lines) is the Euclidean distance t at which the corresponding offset lines at t intersect in a single point.

Precondition
l and r must be edge-triples corresponding to events that actually exist (as determined by the predicate Do_ss_event_exist_2).

◆ Construct_ss_event_time_and_point_2

A construction object type.

Must provide

std::optional< std::tuple<FT, Point_2> > operator()( const Trisegment_2_ptr& e),

which returns the Euclidean distance t >= 0 and the intersection point at which the corresponding three offset lines at t intersect if they do.

If the values cannot be computed, not even approximately (because of overflow for instance), an empty optional must be returned.

◆ Construct_ss_trisegment_2

A construction object type.

Must provide Trisegment_2_ptr operator()( const Segment_2& e0, const FT& w0, const Segment_2& e1, const FT& w1, const Segment_2& e2, const FT& w2 ) const,

which returns an intrusive pointer to an object containing the three oriented lines defined by the three input edges.

◆ Do_ss_event_exist_2

A predicate object type.

Must provide

bool operator()( const Trisegment_2_ptr& tri_segment, std::optional<FT> max_time ) const,

which determines if, given the three oriented lines defined by the three input edges, there exists a Euclidean distance t >= 0 and t <= max_time for which the corresponding three offset lines at t (parallel lines at a Euclidean distance of t) intersect in a single point.

Precondition
Each edge in the triple must properly define an oriented line, that is, its points cannot be coincident.

◆ FT

A model of the FieldWithSqrt concept provided by the kernel.

This type is used to represent the event time stored in the skeleton nodes.

◆ Is_edge_facing_ss_node_2

A predicate object type.

Must provide

bool operator()( const Point_2& contour_node, const Segment_2& opposite_edge ) const,

and

bool operator()( const Trisegment_2_ptr& skeleton_node, const Segment_2& opposite_edge ) const,

which return whether the point (either defined directly as a Point_2 if it is a contour node, or indirectly by its edge triple if it is a skeleton node) lies in the halfplane to the left of the directed edge opposite_edge.

Precondition
skeleton_node must be an edge-triple corresponding to an event that actually exists (as determined by the predicate Do_ss_event_exist_2).

◆ Oriented_side_of_event_point_wrt_bisector_2

A predicate object type.

Must provide

CGAL::Oriented_side operator()( const Trisegment_2_ptr& e, const Segment_2& e0, const FT& w0, const Segment_2& e1, const FT& w1, const Trisegment_2_ptr& e01_event, bool e0_is_primary) const,

which returns the oriented side of the event point described by the edge triple e w.r.t. the (positive) bisector [e0,e1].

Precondition
skeleton_node must be an edge-triple corresponding to an event that actually exists (as determined by the predicate Do_ss_event_exist_2).