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CGAL 6.0 - Bounding Volumes
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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. | |
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. | |
| void | set (const Point &p, const Point &q, const Point &r) |
sets circle to the circle through p, q, and r. | |
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. | |
| bool | has_on_bounded_side (const Point &p) const |
returns true, iff p lies properly inside circle. | |
| bool | has_on_boundary (const Point &p) const |
returns true, iff p lies on the boundary of circle. | |
| bool | is_empty () const |
returns true, iff circle is empty (this implies degeneracy). | |
| bool | is_degenerate () const |
returns true, iff circle is degenerate, i.e. if circle is empty or equal to a single point. | |
Additional Operations for Checking | |
| bool | operator== (const Circle &circle2) const |
returns true, iff circle and circle2 are equal. | |
| Point | center () const |
returns the center of circle. | |
| Distance | squared_radius () const |
returns the squared radius of circle. | |
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.