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An object of type Sphere_3<Kernel> is a sphere in the
three-dimensional Euclidean space 
3. The sphere is oriented, i.e.
its boundary has clockwise or counterclockwise orientation. The
boundary splits 3 into a positive and a negative side, where the
positive side is to the left of the boundary. The boundary also
splits 3 into a bounded and an unbounded side. Note that the
sphere can be degenerated, i.e. the squared radius may be zero.
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introduces a variable c of type Sphere_3<Kernel>.
It is initialized to the sphere with center center,
squared radius squared_radius and orientation
orientation.
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| Sphere_3<Kernel> c ( Point_3<Kernel> const& p, Point_3<Kernel> const& q, Point_3<Kernel> const& r, Point_3<Kernel> const& s); | |||||
introduces a variable c of type Sphere_3<Kernel>.
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.
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| Sphere_3<Kernel> c ( Point_3<Kernel> const& p, Point_3<Kernel> const& q, Point_3<Kernel> const& r, Orientation o = COUNTERCLOCKWISE); | |||||
introduces a variable c of type Sphere_3<Kernel>.
It is initialized to the smallest sphere which passes through
the points p, q, and r. The orientation of
the sphere is o.
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| Sphere_3<Kernel> c ( Point_3<Kernel> const& p, Point_3<Kernel> const& q, Orientation o = COUNTERCLOCKWISE); | |||||
introduces a variable c of type Sphere_3<Kernel>.
It is initialized to the smallest sphere which passes through
the points p and q. The orientation of
the sphere is o.
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| Sphere_3<Kernel> c ( Point_3<Kernel> const& center, Orientation const& orientation = COUNTERCLOCKWISE); | |||||
introduces a variable c of type Sphere_3<Kernel>.
It is initialized to the sphere with center center, squared
radius zero and orientation orientation.
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| Sphere_3<Kernel> c ( Circle_3<Kernel> const& c); | |||||
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introduces a variable c of type Sphere_3<Kernel>.
It is initialized to the diametral sphere of the circle.
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| Point_3<Kernel> const& | c.center () const | returns the center of c. |
| Kernel::FT const& | c.squared_radius () const | returns the squared radius of c. |
| Orientation const& | c.orientation () const | returns the orientation of c. |
| bool | c.operator == ( const& 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 | c.operator != ( const& sphere2) const | |
| returns true, iff c and sphere2 are not equal. | ||
| bool | c.is_degenerate () const | returns true, iff c is degenerate, i.e. if c has squared radius zero. |
| Oriented_side | c.oriented_side ( Point_3<Kernel> const& 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 | c.bounded_side ( Point_3<Kernel> const& 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 | c.has_on_positive_side ( Point_3<Kernel> p) const | |
| bool | c.has_on_negative_side ( Point_3<Kernel> p) const | |
| bool | c.has_on_boundary ( Point_3<Kernel> p) const | |
| bool | c.has_on_bounded_side ( Point_3<Kernel> p) const | |
| bool | c.has_on_unbounded_side ( Point_3<Kernel> p) const | |
| bool | c.has_on ( Point_3<Kernel> p) const | |
| bool | c.has_on ( Circle_3<Kernel> p) const | |
| Sphere_3<Kernel> | c.opposite () const | returns the sphere with the same center and squared radius as c but with opposite orientation. | ||
| Sphere_3<Kernel> | c.orthogonal_transform ( Aff_transformation_3<Kernel> const& at) const | |||
returns the sphere obtained by applying at on c.
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| Bbox_3 | c.bbox () const | returns a bounding box containing c. | ||