#include <sphere.hpp>

Detailed Description

This class defines a sphere. It also computes coordinate transformations between cartesian $ (x, y, z) $ and spherical $(r, \theta, \phi)$ coordinates. The spherical coordinates are valid in the ranges:

$0 \le r < \infty$
$0 \le \theta < \pi$
$0 \le \phi < 2\pi$

The coordinates are related as follows: $\phi$ is the angle in the xy plane starting with 0. from the positive x axis, $\theta$ is measured against the positive z axis.

\      | Z
\theta|
\    |    .
\   |   .
\  |  .
\ | .
\|.
---------------+---------.---------
/|\       .          Y
/phi\     .
/  |  \   .
/   |   \ .
/.........\
/     |
X /

Author: Benjamin S. Kirk, Daniel Dreyer, 2002-2003; Christophe Prud'homme, 2005

Date: 2002-2003

Inheritance diagram for Feel::Sphere:

Public Member Functions
Constructors, destructor
	Sphere ()

	Sphere (Sphere const &s)

	Sphere (const Point &c, const double r)

	~Sphere ()

Accessors
double	radius () const

const Point &	center () const

Mutators
void	setCenter (Point const &p)

void	setRadius (double r)

Methods
void	createFromCenterRadius (const Point &c, const double r)

bool	intersects (const Sphere &other_sphere) const

bool	aboveSurface (const Point &p) const

bool	belowSurface (const Point &p) const

bool	onSurface (const Point &p) const

Point	closestPoint (const Point &p) const

Point	unitNormal (const Point &p) const

Point	surfaceCoords (const Point &cart) const

Point	worldCoords (const Point &sph) const

Public Member Functions inherited from Feel::Surface
	Surface ()

	Surface (const Surface &)

virtual	~Surface ()

Member Function Documentation

bool Feel::Sphere::aboveSurface ( const Point & p ) const

inlinevirtual

Returns: true if the point p is above the surface, false otherwise.

Implements Feel::Surface.

References center(), and radius().

bool Feel::Sphere::belowSurface ( const Point & p ) const

inlinevirtual

Returns: true if the point p is below the surface, false otherwise.

Implements Feel::Surface.

References aboveSurface().

const Point& Feel::Sphere::center ( ) const

inline

Returns: the center of the sphere.

Point Feel::Sphere::closestPoint ( const Point & p ) const

inlinevirtual

Returns: the closest point on the surface to point p.

Implements Feel::Surface.

References center(), Feel::Geo0D< Dim, T >::node(), radius(), and unitNormal().

void Feel::Sphere::createFromCenterRadius	(	const Point &	c,
		const double	r
	)

inline

Defines a sphere of radius r centered at c.

References setCenter(), and setRadius().

bool Feel::Sphere::intersects ( const Sphere & other_sphere ) const

inline

Returns: true if other_sphere intersects this sphere, false otherwise.

References center(), and radius().

bool Feel::Sphere::onSurface ( const Point & p ) const

inlinevirtual

Returns: true if the point p is on the surface, false otherwise. Note that the definition of on the surface really means "very close" to account for roundoff error.

Implements Feel::Surface.

References center(), and radius().

double Feel::Sphere::radius ( ) const

inline

Returns the radius of the sphere.

void Feel::Sphere::setCenter ( Point const & p )

inline

set the center.

void Feel::Sphere::setRadius ( double r )

inline

set the radius

Point Feel::Sphere::surfaceCoords ( const Point & cart ) const