CGAL 4.7 - 2D Circular Geometry Kernel: CircularKernel::ConstructCircularArc_2 Concept Reference

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - 2D Circular Geometry Kernel

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CircularKernel::ConstructCircularArc_2 Concept Reference
Geometric Concepts

## Definition

## Operations

A model of this concept must provide:
CircularKernel::Circular_arc_2 | operator() (const CircularKernel::Circle_2 &c)
| Constructs an arc from a full circle.
CircularKernel::Circular_arc_2 | operator() (const CircularKernel::Circle_2 &c, const CircularKernel::Circular_arc_point_2 &p1, const CircularKernel::Circular_arc_point_2 &p2)
| Construct the circular arc supported by `c`, whose source is `p1` and whose target is `p2` when traversing the circle in counterclockwise direction. More...
CircularKernel::Circular_arc_2 | operator() (const CircularKernel::Circle_2 &c, const CircularKernel::Circle_2 &c1, bool b1, const CircularKernel::Circle_2 &c2, bool b2)

Constructs the unique circular arc whose supporting circle is `c`, and whose source is the intersection of `c` and `c1` with index `b1`, and whose target is the intersection of `c` and `c2` of index `b2`, where intersections are ordered lexicographically, and when traversing the circle in counterclockwise direction. More...

CircularKernel::Circular_arc_2 | operator() (const CircularKernel::Circle_2 &c, const CircularKernel::Line_2 &l1, bool b1, const CircularKernel::Line_2 &l2, bool b2)
| Same, for intersections defined by lines instead of circles.
CircularKernel::Circular_arc_2 | operator() (const CircularKernel::Point_2 &p, const CircularKernel::Point_2 &q, const CircularKernel::Point_2 &r)
| Constructs an arc that is supported by the circle of type `CircularKernel::Circle_2` passing through the points `p`, `q` and `r`. More...

## Member Function Documentation

CircularKernel::Circular_arc_2 CircularKernel::ConstructCircularArc_2::operator() | ( | const CircularKernel::Circle_2 & | c,
|  | const CircularKernel::Circular_arc_point_2 & | p1,
|  | const CircularKernel::Circular_arc_point_2 & | p2
| ) |  |

Construct the circular arc supported by `c`, whose source is `p1` and whose target is `p2` when traversing the circle in counterclockwise direction.

Precondition
  `p1` and `p2` lie on `c`.

CircularKernel::Circular_arc_2 CircularKernel::ConstructCircularArc_2::operator() | ( | const CircularKernel::Circle_2 & | c,
|  | const CircularKernel::Circle_2 & | c1,
|  | bool | b1,
|  | const CircularKernel::Circle_2 & | c2,
|  | bool | b2
| ) |  |

Constructs the unique circular arc whose supporting circle is `c`, and whose source is the intersection of `c` and `c1` with index `b1`, and whose target is the intersection of `c` and `c2` of index `b2`, where intersections are ordered lexicographically, and when traversing the circle in counterclockwise direction.

Precondition
  `c` intersects both `c1` and `c2`, and the arc defined by the intersections has non-zero length.

CircularKernel::Circular_arc_2 CircularKernel::ConstructCircularArc_2::operator() | ( | const CircularKernel::Point_2 & | p,
|  | const CircularKernel::Point_2 & | q,
|  | const CircularKernel::Point_2 & | r
| ) |  |

Constructs an arc that is supported by the circle of type `CircularKernel::Circle_2` passing through the points `p`, `q` and `r`.

The source and target are respectively `p` and `r`, when traversing the supporting circle in the counterclockwise direction. Note that, depending on the orientation of the point triple `(p,q,r)`, `q` may not lie on the arc.

Precondition
  `p`, `q`, and `r` are not collinear.