Feel::Sphere Class Reference

This class defines a sphere. More...

Inheritance diagram for Feel::Sphere:

Collaboration diagram for Feel::Sphere:

Methods
void	createFromCenterRadius (const Point &c, const double r)
	Defines a sphere of radius r centered at c.
bool	intersects (const Sphere &other_sphere) const
bool	aboveSurface (const Point &p) const override
bool	belowSurface (const Point &p) const override
bool	onSurface (const Point &p) const override
Point	closestPoint (const Point &p) const override
Point	unitNormal (const Point &p) const override
Point	surfaceCoords (const Point &cart) const override
Point	worldCoords (const Point &sph) const override

Constructors, destructor
	Sphere ()
	Sphere (Sphere const &s)
	Sphere (const Point &c, const double r)
	~Sphere () override

Accessors
double	radius () const
	Returns the radius of the sphere.
const Point &	center () const

Mutators
void	setCenter (Point const &p)
	set the center.
void	setRadius (double r)
	set the radius

Additional Inherited Members
Public Member Functions inherited from Feel::Surface
	Surface ()
	Constructor. More...
	Surface (const Surface &)
	Copy-constructor.
virtual	~Surface ()
	Destructor.

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

Member Function Documentation

aboveSurface()

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

overridevirtual

Returns

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

Implements Feel::Surface.

References center(), and radius().

Referenced by belowSurface().

belowSurface()

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

overridevirtual

Returns

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

Implements Feel::Surface.

References aboveSurface().

center()

const Point & Feel::Sphere::center

(

)

const

Returns

the center of the sphere.

Referenced by aboveSurface(), closestPoint(), intersects(), onSurface(), unitNormal(), and worldCoords().

closestPoint()

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

overridevirtual

Returns

the closest point on the surface to point p.

Implements Feel::Surface.

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

intersects()

bool Feel::Sphere::intersects

(

const Sphere &

other_sphere

)

const

Returns

true if other_sphere intersects this sphere, false otherwise.

References center(), and radius().

onSurface()

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

overridevirtual

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().

surfaceCoords()

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

overridevirtual

Returns

the spherical coordinates for the cartesian coordinates cart.

Reimplemented from Feel::Surface.

References Feel::Geo0D< Dim, T, IndexT >::node().

unitNormal()

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

overridevirtual

Returns

a unit vector normal to the surface at point p.

Implements Feel::Surface.

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

Referenced by closestPoint().

worldCoords()

Point Feel::Sphere::worldCoords ( const Point &  sph ) const

overridevirtual

Returns

the cartesian coordinates for the spherical coordinates sph.

Reimplemented from Feel::Surface.

References center().