A geometric object representing a sphere. More...

#include <sphere.h>

Inheritance diagram for libMesh::Sphere:

Public Member Functions
	Sphere ()

	Sphere (const Point &c, const Real r)

	Sphere (const Point &, const Point &, const Point &, const Point &)

	Sphere (const Sphere &other_sphere)

	~Sphere ()

void	create_from_center_radius (const Point &c, const Real r)

bool	intersects (const Sphere &other_sphere) const

Real	distance (const Sphere &other_sphere) const

virtual bool	above_surface (const Point &p) const override

virtual bool	below_surface (const Point &p) const override

virtual bool	on_surface (const Point &p) const override

virtual Point	closest_point (const Point &p) const override

virtual Point	unit_normal (const Point &p) const override

Real	radius () const

Real &	radius ()

const Point &	center () const

Point &	center ()

virtual Point	surface_coords (const Point &cart) const override

virtual Point	world_coords (const Point &sph) const override

Private Attributes
Point	_cent

Real	_rad

Detailed Description

A geometric object representing a sphere.

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

Date: 2002-2007

Definition at line 72 of file sphere.h.

Constructor & Destructor Documentation

◆ Sphere() [1/4]

libMesh::Sphere::Sphere ( )

Dummy Constructor.

Definition at line 36 of file sphere.C.

                 :
   _rad(-1.)
 {
 }

◆ Sphere() [2/4]

libMesh::Sphere::Sphere	(	const Point &	c,
		const Real	r
	)

Constructs a sphere of radius r centered at c.

Definition at line 43 of file sphere.C.

References create_from_center_radius().

 {
   libmesh_assert_greater (r, 0.);
 
   this->create_from_center_radius (c, r);
 }

◆ Sphere() [3/4]

libMesh::Sphere::Sphere	(	const Point &	pa,
		const Point &	pb,
		const Point &	pc,
		const Point &	pd
	)

Constructs a sphere connecting four points.

Definition at line 62 of file sphere.C.

References std::abs(), create_from_center_radius(), libMesh::TypeTensor< T >::det(), libMesh::TypeVector< T >::norm_sq(), and libMesh::Real.

 {
   Point pad = pa - pd;
   Point pbd = pb - pd;
   Point pcd = pc - pd;
 
   TensorValue<Real> T(pad,pbd,pcd);
 
   Real D = T.det();
 
   // The points had better not be coplanar
   libmesh_assert_greater (std::abs(D), 1e-12);
 
   Real e = 0.5*(pa.norm_sq() - pd.norm_sq());
   Real f = 0.5*(pb.norm_sq() - pd.norm_sq());
   Real g = 0.5*(pc.norm_sq() - pd.norm_sq());
 
   TensorValue<Real> T1(e,pad(1),pad(2),
                        f,pbd(1),pbd(2),
                        g,pcd(1),pcd(2));
   Real sx = T1.det()/D;
 
   TensorValue<Real> T2(pad(0),e,pad(2),
                        pbd(0),f,pbd(2),
                        pcd(0),g,pcd(2));
   Real sy = T2.det()/D;
 
   TensorValue<Real> T3(pad(0),pad(1),e,
                        pbd(0),pbd(1),f,
                        pcd(0),pcd(1),g);
   Real sz = T3.det()/D;
 
   Point c(sx,sy,sz);
   Real r = (c-pa).norm();
 
   this->create_from_center_radius(c,r);
 }

◆ Sphere() [4/4]

libMesh::Sphere::Sphere ( const Sphere & other_sphere )

Copy-constructor.

Definition at line 53 of file sphere.C.

References center(), create_from_center_radius(), and radius().

                                            :
   Surface()
 {
   this->create_from_center_radius (other_sphere.center(),
                                    other_sphere.radius());
 }

◆ ~Sphere()

libMesh::Sphere::~Sphere ( )

Destructor. Does nothing at the moment.

Definition at line 105 of file sphere.C.

106 {

107 }

Member Function Documentation

◆ above_surface()

bool libMesh::Sphere::above_surface ( const Point & p ) const

overridevirtual

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

Implements libMesh::Surface.

Definition at line 140 of file sphere.C.

References center(), libMesh::TypeVector< T >::norm(), and radius().

Referenced by below_surface().

 {
   libmesh_assert_greater (this->radius(), 0.);
 
   // create a vector from the center to the point.
   const Point w = p - this->center();
 
   if (w.norm() > this->radius())
     return true;
 
   return false;
 }

◆ below_surface()

bool libMesh::Sphere::below_surface ( const Point & p ) const

overridevirtual

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

Implements libMesh::Surface.

Definition at line 155 of file sphere.C.

References above_surface(), and radius().

 {
   libmesh_assert_greater (this->radius(), 0.);
 
   return ( !this->above_surface (p) );
 }

◆ center() [1/2]

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

inline

Returns: The center of the sphere.

Definition at line 163 of file sphere.h.

References _cent.

Referenced by above_surface(), closest_point(), create_from_center_radius(), distance(), on_surface(), Sphere(), surface_coords(), unit_normal(), and world_coords().

163 { return _cent; }

libMesh::Sphere::_cent

Point _cent

Definition: sphere.h:188

◆ center() [2/2]

Point& libMesh::Sphere::center ( )

inline

Returns: The center of the sphere.

Definition at line 168 of file sphere.h.

References _cent.

168 { return _cent; }

libMesh::Sphere::_cent

Point _cent

Definition: sphere.h:188

◆ closest_point()

Point libMesh::Sphere::closest_point ( const Point & p ) const

overridevirtual

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

Implements libMesh::Surface.

Definition at line 181 of file sphere.C.

References center(), radius(), and unit_normal().

 {
   libmesh_assert_greater (this->radius(), 0.);
 
   // get the normal from the surface in the direction
   // of p
   Point normal = this->unit_normal (p);
 
   // The closest point on the sphere is in the direction
   // of the normal a distance r from the center.
   const Point cp = this->center() + normal*this->radius();
 
   return cp;
 }

◆ create_from_center_radius()

void libMesh::Sphere::create_from_center_radius	(	const Point &	c,
		const Real	r
	)

Defines a sphere of radius r centered at c.

Definition at line 111 of file sphere.C.

References center(), and radius().

Referenced by Sphere().

 {
   this->center() = c;
   this->radius() = r;
 
   libmesh_assert_greater (this->radius(), 0.);
 }

◆ distance()

Real libMesh::Sphere::distance ( const Sphere & other_sphere ) const

Returns: The distance between the surface of this sphere and another sphere.

Definition at line 128 of file sphere.C.

References center(), radius(), and libMesh::Real.

Referenced by intersects().

 {
   libmesh_assert_greater ( this->radius(), 0. );
   libmesh_assert_greater ( other_sphere.radius(), 0. );
 
   const Real the_distance = (this->center() - other_sphere.center()).norm();
 
   return the_distance - (this->radius() + other_sphere.radius());
 }

◆ intersects()

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

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

Definition at line 121 of file sphere.C.

References distance().

 {
   return distance(other_sphere) < 0 ? true : false;
 }

◆ on_surface()

bool libMesh::Sphere::on_surface ( const Point & p ) const

overridevirtual

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

Note: The definition of "on the surface" really means "very close" to account for roundoff error.

Implements libMesh::Surface.

Definition at line 164 of file sphere.C.

References std::abs(), center(), libMesh::TypeVector< T >::norm(), and radius().

 {
   libmesh_assert_greater (this->radius(), 0.);
 
   // Create a vector from the center to the point.
   const Point w = p - this->center();
 
   // if the size of that vector is the same as the radius() then
   // the point is on the surface.
   if (std::abs(w.norm() - this->radius()) < 1.e-10)
     return true;
 
   return false;
 }

◆ radius() [1/2]

Real libMesh::Sphere::radius ( ) const

inline

Returns: The radius of the sphere.

Definition at line 153 of file sphere.h.

References _rad.

Referenced by above_surface(), below_surface(), closest_point(), create_from_center_radius(), distance(), on_surface(), Sphere(), and unit_normal().

153 { return _rad; }

libMesh::Sphere::_rad

Real _rad

Definition: sphere.h:193

◆ radius() [2/2]

Real& libMesh::Sphere::radius ( )

inline

Returns: The radius of the sphere as a writable reference.

Definition at line 158 of file sphere.h.

References _rad.

158 { return _rad; }

libMesh::Sphere::_rad

Real _rad

Definition: sphere.h:193

◆ surface_coords()

Point libMesh::Sphere::surface_coords ( const Point & cart ) const

inlineoverridevirtual

Returns: The spherical coordinates for the cartesian coordinates cart.

Reimplemented from libMesh::Surface.

Definition at line 201 of file sphere.h.

References center(), libMesh::TypeVector< T >::norm(), libMesh::pi, and libMesh::Real.

 {
   // constant translation in the origin
   const Point c (cart-this->center());
 
   // phi: special care, so that it gives 0..2pi results
   const Real phi = std::atan2(c(1), c(0));
 
   return Point(/* radius */ c.norm(),
                /* theta  */ std::atan2( std::sqrt( c(0)*c(0) + c(1)*c(1) ), c(2) ),
                /* phi    */ ( (phi < 0)  ?  2.*libMesh::pi+phi  :  phi ) );
 }

◆ unit_normal()

Point libMesh::Sphere::unit_normal ( const Point & p ) const

overridevirtual

Returns: A unit vector normal to the surface at point p.

Implements libMesh::Surface.

Definition at line 198 of file sphere.C.

References center(), radius(), and libMesh::TypeVector< T >::unit().

Referenced by closest_point().

 {
   libmesh_assert_greater (this->radius(), 0.);
 
   libmesh_assert_not_equal_to (p, this->center());
 
   // Create a vector from the center to the point
   Point n = p - this->center();
 
   return n.unit();
 }

◆ world_coords()

Point libMesh::Sphere::world_coords ( const Point & sph ) const

inlineoverridevirtual

Returns: The cartesian coordinates for the spherical coordinates sph.

Reimplemented from libMesh::Surface.

Definition at line 217 of file sphere.h.

References center(), and libMesh::Real.

 {
   const Real r     = sph(0);
   const Real theta = sph(1);
   const Real phi   = sph(2);
 
   // constant translation out of the origin
   return Point (/* x */ r*std::sin(theta)*std::cos(phi) + this->center()(0),
                 /* y */ r*std::sin(theta)*std::sin(phi) + this->center()(1),
                 /* z */ r*std::cos(theta)               + this->center()(2));
 }

Member Data Documentation

◆ _cent

Point libMesh::Sphere::_cent

private

The center of the sphere.

Definition at line 188 of file sphere.h.

Referenced by center().

◆ _rad

Real libMesh::Sphere::_rad

private

The radius of the sphere.

Definition at line 193 of file sphere.h.

Referenced by radius().

The documentation for this class was generated from the following files:

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Sphere() [1/4]

◆ Sphere() [2/4]

◆ Sphere() [3/4]

◆ Sphere() [4/4]

◆ ~Sphere()

Member Function Documentation

◆ above_surface()

◆ below_surface()

◆ center() [1/2]

◆ center() [2/2]

◆ closest_point()

◆ create_from_center_radius()

◆ distance()

◆ intersects()

◆ on_surface()

◆ radius() [1/2]

◆ radius() [2/2]

◆ surface_coords()

◆ unit_normal()

◆ world_coords()

Member Data Documentation

◆ _cent

◆ _rad