CGAL 4.14 - 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.
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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) |
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 |
||
) |
CGAL::Sphere_3< Kernel >::Sphere_3 | ( | const Point_3< Kernel > & | p, |
const Point_3< Kernel > & | q, | ||
const Orientation & | o = COUNTERCLOCKWISE |
||
) |
CGAL::Sphere_3< Kernel >::Sphere_3 | ( | const Point_3< Kernel > & | center, |
const Orientation & | orientation = COUNTERCLOCKWISE |
||
) |
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.