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CGAL 5.6 - 2D and 3D Linear Geometry Kernel
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CGAL 5.6 - 2D and 3D Linear Geometry Kernel
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#include <CGAL/Sphere_3.h>
An object of type Sphere_3 is a sphere in the three-dimensional Euclidean space \( \E^3\).
The sphere is oriented, i.e. its boundary has clockwise or counterclockwise orientation. The boundary splits \( \E^3\) into a positive and a negative side, where the positive side is to the left of the boundary. The boundary also splits \( \E^3\) into a bounded and an unbounded side. Note that the sphere can be degenerated, i.e. the squared radius may be zero.
Hashable if Kernel is a cartesian kernel and if Kernel::FT is Hashable
Creation | |
| Sphere_3 (const Point_3< Kernel > ¢er, const Kernel::FT &squared_radius, const Orientation &orientation=COUNTERCLOCKWISE) | |
introduces a variable c of type Sphere_3. More... | |
| Sphere_3 (const Point_3< Kernel > &p, const Point_3< Kernel > &q, const Point_3< Kernel > &r, const Point_3< Kernel > &s) | |
introduces a variable c of type Sphere_3. More... | |
| Sphere_3 (const Point_3< Kernel > &p, const Point_3< Kernel > &q, const Point_3< Kernel > &r, const Orientation &o=COUNTERCLOCKWISE) | |
introduces a variable c of type Sphere_3. More... | |
| Sphere_3 (const Point_3< Kernel > &p, const Point_3< Kernel > &q, const Orientation &o=COUNTERCLOCKWISE) | |
introduces a variable c of type Sphere_3. More... | |
| Sphere_3 (const Point_3< Kernel > ¢er, const Orientation &orientation=COUNTERCLOCKWISE) | |
introduces a variable c of type Sphere_3. More... | |
| Sphere_3 (const Circle_3< Kernel > &c) | |
introduces a variable c of type Sphere_3. More... | |
Access Functions | |
| const Point_3< Kernel > & | center () const |
returns the center of c. | |
| Kernel::FT const & | squared_radius () const |
returns the squared radius of c. | |
| Orientation const & | orientation () const |
returns the orientation of c. | |
| bool | operator== (const Sphere_3< Kernel > &sphere2) const |
returns true, iff c and sphere2 are equal, i.e. if they have the same center, same squared radius and same orientation. | |
| bool | operator!= (const Sphere_3< Kernel > &sphere2) const |
returns true, iff c and sphere2 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_3< 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_3< 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_3< Kernel > &p) const |
| bool | has_on_negative_side (const Point_3< Kernel > &p) const |
| bool | has_on_boundary (const Point_3< Kernel > &p) const |
| bool | has_on_bounded_side (const Point_3< Kernel > &p) const |
| bool | has_on_unbounded_side (const Point_3< Kernel > &p) const |
| bool | has_on (const Point_3< Kernel > &p) const |
| bool | has_on (const Circle_3< Kernel > &p) const |
Miscellaneous | |
| Sphere_3< Kernel > | opposite () const |
returns the sphere with the same center and squared radius as c but with opposite orientation. | |
| Sphere_3< Kernel > | orthogonal_transform (Aff_transformation_3< Kernel > const &at) const |
returns the sphere obtained by applying at on c. More... | |
| Bbox_3 | bbox () const |
returns a bounding box containing c. | |
| CGAL::Sphere_3< Kernel >::Sphere_3 | ( | const Point_3< Kernel > & | center, |
| const Kernel::FT & | squared_radius, | ||
| const Orientation & | orientation = COUNTERCLOCKWISE |
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| ) |
introduces a variable c of type Sphere_3.
It is initialized to the sphere with center center, squared radius squared_radius and orientation orientation.
orientation != COPLANAR and squared_radius >= 0. | CGAL::Sphere_3< Kernel >::Sphere_3 | ( | const Point_3< Kernel > & | p, |
| const Point_3< Kernel > & | q, | ||
| const Point_3< Kernel > & | r, | ||
| const Point_3< Kernel > & | s | ||
| ) |
introduces a variable c of type Sphere_3.
It is initialized to the unique sphere which passes through the points p, q, r and s. The orientation of the sphere is the orientation of the point quadruple p, q, r, s.
p, q, r, and s are not coplanar. | CGAL::Sphere_3< Kernel >::Sphere_3 | ( | const Point_3< Kernel > & | p, |
| const Point_3< Kernel > & | q, | ||
| const Point_3< Kernel > & | r, | ||
| const Orientation & | o = COUNTERCLOCKWISE |
||
| ) |
introduces a variable c of type Sphere_3.
It is initialized to the smallest sphere which passes through the points p, q, and r. The orientation of the sphere is o.
o != COPLANAR. | CGAL::Sphere_3< Kernel >::Sphere_3 | ( | const Point_3< Kernel > & | p, |
| const Point_3< Kernel > & | q, | ||
| const Orientation & | o = COUNTERCLOCKWISE |
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| ) |
introduces a variable c of type Sphere_3.
It is initialized to the smallest sphere which passes through the points p and q. The orientation of the sphere is o.
o != COPLANAR. | CGAL::Sphere_3< Kernel >::Sphere_3 | ( | const Point_3< Kernel > & | center, |
| const Orientation & | orientation = COUNTERCLOCKWISE |
||
| ) |
introduces a variable c of type Sphere_3.
It is initialized to the sphere with center center, squared radius zero and orientation orientation.
orientation != COPLANAR. c.is_degenerate() = true. | CGAL::Sphere_3< Kernel >::Sphere_3 | ( | const Circle_3< Kernel > & | c | ) |
introduces a variable c of type Sphere_3.
It is initialized to the diametral sphere of the circle.
| Sphere_3<Kernel> CGAL::Sphere_3< Kernel >::orthogonal_transform | ( | Aff_transformation_3< Kernel > const & | at | ) | const |
returns the sphere obtained by applying at on c.
at is an orthogonal transformation. 
1.8.13