Sphere_d<Kernel>

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CGAL::Sphere_d<Kernel>

Definition

An instance S of the data type Sphere_d is an oriented sphere in some d-dimensional space. A sphere is defined by d+1 points (class Point_d<Kernel>). We use A to denote the array of the defining points. A set A of defining points is legal if either the points are affinely independent or if the points are all equal. Only a legal set of points defines a sphere in the geometric sense and hence many operations on spheres require the set of defining points to be legal. The orientation of S is equal to the orientation of the defining points, i.e., orientation(A).

Types

Sphere_d<Kernel>::LA
	the linear algebra layer.

Sphere_d<Kernel>::point_iterator
	a read-only iterator for points defining the sphere.

Creation

Sphere_d<Kernel> S;

introduces a variable S of type Sphere_d<Kernel>.

template <class ForwardIterator>

Sphere_d<Kernel> S ( int d, ForwardIterator first, ForwardIterator last);

introduces a variable S of type Sphere_d<Kernel>. S is initialized to the sphere through the points in A = tuple [first,last).

Precondition:

A consists of d+1 d-dimensional points.

Requirement:

The value type of ForwardIterator is Point_d<Kernel>.

Operations

int

S.dimension ()

returns the dimension of the ambient space.

Point_d<Kernel>

S.point ( int i)

returns the ith defining point.

Precondition:

0 ≤ i ≤ dim.

point_iterator

S.points_begin ()

returns an iterator pointing to the first defining point.

point_iterator

S.points_end ()

returns an iterator pointing beyond the last defining point.

bool

S.is_degenerate ()

returns true iff the defining points are not full dimensional.

bool

S.is_legal ()

returns true iff the set of defining points is legal. A set of defining points is legal iff their orientation is non-zero or if they are all equal.

Point_d<Kernel>

S.center ()

returns the center of S.

Precondition:

S is legal.

S.squared_radius ()

returns the squared radius of the sphere.

Precondition:

S is legal.

Orientation

S.orientation ()

returns the orientation of S.

Oriented_side

S.oriented_side ( Point_d<Kernel> p)

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 sphere, resp.

Precondition: