CGAL 5.5.2 - Bounding Volumes
|
An object circle
of the class Circle
is a circle in the two-dimensional Euclidean plane \( \E^2\). Its boundary splits the plane into a bounded and an unbounded side. By definition, an empty circle
has no boundary and no bounded side, i.e. its unbounded side equals the whole plane \( \E^2\). A circle
containing exactly one point \( p\) has no bounded side, its boundary is \( \{p\}\), and its unbounded side equals \( \E^2 \setminus \{p\}\).
Types | |
typedef unspecified_type | Point |
Point type. | |
typedef unspecified_type | Distance |
Distance type. More... | |
Creation | |
void | set () |
sets circle to the empty circle. | |
void | set (const Point &p) |
sets circle to the circle containing exactly p . | |
void | set (const Point &p, const Point &q) |
sets circle to the circle with diameter equal to the segment connecting p and q . More... | |
void | set (const Point &p, const Point &q, const Point &r) |
sets circle to the circle through p , q , and r . More... | |
Predicates | |
bool | has_on_unbounded_side (const Point &p) const |
returns true , iff p lies properly outside of circle . | |
CGAL::Bounded_side | bounded_side (const Point &p) const |
returns CGAL::ON_BOUNDED_SIDE , CGAL::ON_BOUNDARY , or CGAL::ON_UNBOUNDED_SIDE iff p lies properly inside, on the boundary, or properly outside of circle , resp. More... | |
bool | has_on_bounded_side (const Point &p) const |
returns true , iff p lies properly inside circle . More... | |
bool | has_on_boundary (const Point &p) const |
returns true , iff p lies on the boundary of circle . More... | |
bool | is_empty () const |
returns true , iff circle is empty (this implies degeneracy). More... | |
bool | is_degenerate () const |
returns true , iff circle is degenerate, i.e. if circle is empty or equal to a single point. More... | |
Additional Operations for Checking | |
bool | operator== (const Circle &circle2) const |
returns true , iff circle and circle2 are equal. More... | |
Point | center () const |
returns the center of circle . More... | |
Distance | squared_radius () const |
returns the squared radius of circle . More... | |
I/O | |
std::ostream & | operator<< (std::ostream &os, const Circle &circle) |
writes circle to output stream os . | |
typedef unspecified_type Circle::Distance |
Distance type.
The function squared_radius()
(see below) returns an object of this type.
is_valid()
of Min_circle_2
is used. CGAL::Bounded_side Circle::bounded_side | ( | const Point & | p | ) | const |
returns CGAL::ON_BOUNDED_SIDE
, CGAL::ON_BOUNDARY
, or CGAL::ON_UNBOUNDED_SIDE
iff p
lies properly inside, on the boundary, or properly outside of circle
, resp.
Min_circle_2
is used. Point Circle::center | ( | ) | const |
returns the center of circle
.
is_valid()
of Min_circle_2
is used. bool Circle::has_on_boundary | ( | const Point & | p | ) | const |
returns true
, iff p
lies on the boundary of circle
.
Min_circle_2
is used. bool Circle::has_on_bounded_side | ( | const Point & | p | ) | const |
returns true
, iff p
lies properly inside circle
.
Min_circle_2
is used. bool Circle::is_degenerate | ( | ) | const |
returns true
, iff circle
is degenerate, i.e. if circle
is empty or equal to a single point.
Min_circle_2
is used. bool Circle::is_empty | ( | ) | const |
returns true
, iff circle
is empty (this implies degeneracy).
Min_circle_2
is used. bool Circle::operator== | ( | const Circle & | circle2 | ) | const |
returns true
, iff circle
and circle2
are equal.
is_valid()
of Min_circle_2
is used. sets circle
to the circle with diameter equal to the segment connecting p
and q
.
The algorithm guarantees that set()
is never called with two equal points.
sets circle
to the circle through p
, q
, and r
.
The algorithm guarantees that set()
is never called with three collinear points.
Distance Circle::squared_radius | ( | ) | const |
returns the squared radius of circle
.
is_valid()
of Min_circle_2
is used.