libMesh::Sphere Class Reference

This class defines a sphere. More...

#include <sphere.h>

Inheritance diagram for libMesh::Sphere:

Public Member Functions
	Sphere ()
	Dummy Constructor. More...
	Sphere (const Point &c, const Real r)
	Constructs a sphere of radius r centered at c. More...
	Sphere (const Point &, const Point &, const Point &, const Point &)
	Constructs a sphere connecting four points. More...
	Sphere (const Sphere &other_sphere)
	Copy-constructor. More...
	~Sphere ()
	Destructor. More...
void	create_from_center_radius (const Point &c, const Real r)
	Defines a sphere of radius r centered at c. More...
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
	The center of the sphere. More...
Real	_rad
	The radius of the sphere. More...

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

Date

2002-2007

A geometric object representing a sphere.

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.

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

References create_from_center_radius().

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.

{
#if LIBMESH_DIM > 2
  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);
#else // LIBMESH_DIM > 2
  libmesh_ignore(pa, pb, pc, pd);
  libmesh_not_implemented();
#endif
}

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

Sphere() [4/4]

libMesh::Sphere::Sphere

(

const Sphere &

other_sphere

)

Copy-constructor.

Definition at line 53 of file sphere.C.

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

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

~Sphere()

libMesh::Sphere::~Sphere

(

)

Destructor.

Does nothing at the moment.

Definition at line 110 of file sphere.C.

{
}

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 145 of file sphere.C.

{
  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;
}

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

Referenced by below_surface().

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 160 of file sphere.C.

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

References above_surface(), and radius().

center() [1/2]

Point& libMesh::Sphere::center ( )

inline

Returns

The center of the sphere.

Definition at line 168 of file sphere.h.

{ return _cent; }

References _cent.

center() [2/2]

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

inline

Returns

The center of the sphere.

Definition at line 163 of file sphere.h.

{ return _cent; }

References _cent.

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

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 186 of file sphere.C.

{
  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;
}

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

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 116 of file sphere.C.

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

References center(), and radius().

Referenced by Sphere().

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 133 of file sphere.C.

{
  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());
}

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

Referenced by intersects().

intersects()

bool libMesh::Sphere::intersects

(

const Sphere &

other_sphere

)

const

Returns

true if other_sphere intersects this sphere, false otherwise.

Definition at line 126 of file sphere.C.

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

References distance().

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 169 of file sphere.C.

{
  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;
}

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

radius() [1/2]

Real& libMesh::Sphere::radius ( )

inline

Returns

The radius of the sphere as a writable reference.

Definition at line 158 of file sphere.h.

{ return _rad; }

References _rad.

radius() [2/2]

Real libMesh::Sphere::radius ( ) const

inline

Returns

The radius of the sphere.

Definition at line 153 of file sphere.h.

{ return _rad; }

References _rad.

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

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.

{
#if LIBMESH_DIM > 2
  // 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 ) );
#else
  libmesh_ignore(cart);
  libmesh_not_implemented();
#endif
}

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

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 203 of file sphere.C.

{
  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();
}

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

Referenced by closest_point().

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 222 of file sphere.h.

{
  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));
}

References center(), and libMesh::Real.

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:

• include/geom/sphere.h
• src/geom/sphere.C