CGAL 4.14 - 2D and 3D Linear Geometry Kernel
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#include <CGAL/Circle_2.h>
An object c
of type Circle_2
is a circle in the two-dimensional Euclidean plane \( \E^2\).
The circle is oriented, i.e. its boundary has clockwise or counterclockwise orientation. The boundary splits \( \E^2\) into a positive and a negative side, where the positive side is to the left of the boundary. The boundary also splits \( \E^2\) into a bounded and an unbounded side. Note that the circle can be degenerated, i.e. the squared radius may be zero.
Creation | |
Circle_2 (const Point_2< Kernel > ¢er, const Kernel::FT &squared_radius, const Orientation &ori=COUNTERCLOCKWISE) | |
introduces a variable c of type Circle_2 . More... | |
Circle_2 (const Point_2< Kernel > &p, const Point_2< Kernel > &q, const Point_2< Kernel > &r) | |
introduces a variable c of type Circle_2 . More... | |
Circle_2 (const Point_2< Kernel > &p, const Point_2< Kernel > &q, const Orientation &ori=COUNTERCLOCKWISE) | |
introduces a variable c of type Circle_2 . More... | |
Circle_2 (const Point_2< Kernel > ¢er, const Orientation &ori=COUNTERCLOCKWISE) | |
introduces a variable c of type Circle_2 . More... | |
Access Functions | |
const Point_2< Kernel > & | center () const |
returns the center of c . | |
const Kernel::FT & | squared_radius () const |
returns the squared radius of c . | |
Orientation | orientation () const |
returns the orientation of c . | |
bool | operator== (const Circle_2< Kernel > &circle2) const |
returns true , iff c and circle2 are equal, i.e. if they have the same center, same squared radius and same orientation. | |
bool | operator!= (const Circle_2< Kernel > &circle2) const |
returns true , iff c and circle2 are not equal. | |
Predicates | |
bool | is_degenerate () const |
returns true , iff c is degenerate, i.e. if c has squared radius zero. | |
Oriented_side | oriented_side (const Point_2< Kernel > &p) const |
returns either the constant ON_ORIENTED_BOUNDARY, ON_POSITIVE_SIDE, or ON_NEGATIVE_SIDE, iff p lies on the boundary, properly on the positive side, or properly on the negative side of c , resp. | |
Bounded_side | bounded_side (const Point_2< Kernel > &p) const |
returns ON_BOUNDED_SIDE, ON_BOUNDARY, or ON_UNBOUNDED_SIDE iff p lies properly inside, on the boundary, or properly outside of c , resp. | |
bool | has_on_positive_side (const Point_2< Kernel > &p) const |
bool | has_on_negative_side (const Point_2< Kernel > &p) const |
bool | has_on_boundary (const Point_2< Kernel > &p) const |
bool | has_on_bounded_side (const Point_2< Kernel > &p) const |
bool | has_on_unbounded_side (const Point_2< Kernel > &p) const |
Miscellaneous | |
Circle_2< Kernel > | opposite () const |
returns the circle with the same center and squared radius as c but with opposite orientation. | |
Circle_2< Kernel > | orthogonal_transform (Aff_transformation_2< Kernel > const &at) const |
returns the circle obtained by applying \( at\) on c . More... | |
Bbox_2 | bbox () const |
returns a bounding box containing c . | |
CGAL::Circle_2< Kernel >::Circle_2 | ( | const Point_2< Kernel > & | center, |
const Kernel::FT & | squared_radius, | ||
const Orientation & | ori = COUNTERCLOCKWISE |
||
) |
introduces a variable c
of type Circle_2
.
It is initialized to the circle with center center
, squared radius squared_radius
and orientation ori
.
ori
\( \neq\) COLLINEAR
, and further, squared_radius
\( \geq\) 0. CGAL::Circle_2< Kernel >::Circle_2 | ( | const Point_2< Kernel > & | p, |
const Point_2< Kernel > & | q, | ||
const Point_2< Kernel > & | r | ||
) |
introduces a variable c
of type Circle_2
.
It is initialized to the unique circle which passes through the points p
, q
and r
. The orientation of the circle is the orientation of the point triple p
, q
, r
.
p
, q
, and r
are not collinear. CGAL::Circle_2< Kernel >::Circle_2 | ( | const Point_2< Kernel > & | p, |
const Point_2< Kernel > & | q, | ||
const Orientation & | ori = COUNTERCLOCKWISE |
||
) |
introduces a variable c
of type Circle_2
.
It is initialized to the circle with diameter \( \overline{pq}\) and orientation ori
.
ori
\( \neq\) COLLINEAR
. CGAL::Circle_2< Kernel >::Circle_2 | ( | const Point_2< Kernel > & | center, |
const Orientation & | ori = COUNTERCLOCKWISE |
||
) |
introduces a variable c
of type Circle_2
.
It is initialized to the circle with center center
, squared radius zero and orientation ori
.
ori
\( \neq\) COLLINEAR
. c.is_degenerate()
= true
. Circle_2<Kernel> CGAL::Circle_2< Kernel >::orthogonal_transform | ( | Aff_transformation_2< Kernel > const & | at | ) | const |
returns the circle obtained by applying \( at\) on c
.
at
is an orthogonal transformation.