\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.12.2 - 2D Envelopes
EnvelopeDiagramVertex Concept Reference

Definition

A vertex record in an envelope diagram. It is always associated with a point on the lower (upper) envelope of a non-empty set of curves. A vertex is also associated with a set of \( x\)-monotone curves that induce the envelope over this point. It is incident to two edges, one lying to its left and the other to its right.

See also
EnvelopeDiagram_1
EnvelopeDiagramEdge

Types

typedef unspecified_type Size
 the size type (convertible to size_t).
 
typedef unspecified_type Edge
 the corresponding diagram-edge type.
 
typedef unspecified_type Point_2
 the point type associated with the vertex.
 
typedef unspecified_type X_monotone_curve_2
 the \( x\)-monotone curve type.
 

Creation

 EnvelopeDiagramVertex ()
 default constructor.
 
 EnvelopeDiagramVertex (const EnvelopeDiagramVertex &other)
 copy constructor.
 
 EnvelopeDiagramVertex (const Point_2 &p)
 constructs a vertex associated with the given point p.
 

Access Functions

const Point_2point () const
 returns the point associated with v.
 
Size number_of_curves () const
 returns the number of \( x\)-monotone curves associated with v.
 
Curve_const_iterator curves_begin () const
 returns an iterator for the first \( x\)-monotone curve associated with v.
 
Curve_const_iterator curves_end () const
 returns a past-the-end iterator for the \( x\)-monotone curves associated with v.
 
Edge_const_handle left () const
 returns the edge lying to v's left.
 
Edge_const_handle right () const
 returns the edge lying to v's right.
 

Modifiers

void set_point (const Point_2 &p)
 associates the point p with v.
 
void clear_curves ()
 clears the set of curves associated with v.
 
void add_curve (const X_monotone_curve_2 &cv)
 adds the \( x\)-monotone curve cv to the set of curves associated with v.
 
void add_curves (Curve_const_iterator begin, Curve_const_iterator end)
 adds the given range of \( x\)-monotone curves to the set of curves associated with v.
 
void set_left (Edge_const_handle e)
 sets the edge lying to the left of v to be e.
 
void set_right (Edge_const_handle e)
 sets the edge lying to the right of v to be e.