#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
bool	above_surface (const Point &p) const
bool	below_surface (const Point &p) const
bool	on_surface (const Point &p) const
Point	closest_point (const Point &p) const
Point	unit_normal (const Point &p) const
Real	radius () const
Real &	radius ()
const Point &	center () const
Point &	center ()
Point	surface_coords (const Point &cart) const
Point	world_coords (const Point &sph) const
Private Attributes
Point	_cent
Real	_rad

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

Definition at line 72 of file sphere.h.

Constructor & Destructor Documentation

libMesh::Sphere::Sphere ( )

Dummy Constructor.

Definition at line 36 of file sphere.C.

                :
  _rad(-1.)
{
}

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);
}

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::Real, and libMesh::TypeVector< T >::size_sq().

{
  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.size_sq() - pd.size_sq());
  Real f = 0.5*(pb.size_sq() - pd.size_sq());
  Real g = 0.5*(pc.size_sq() - pd.size_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).size();

  this->create_from_center_radius(c,r);
}

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());
}

libMesh::Sphere::~Sphere ( )

Destructor. Does nothing at the moment.

Definition at line 105 of file sphere.C.

{
}

Member Function Documentation

bool libMesh::Sphere::above_surface ( const Point & p ) const [virtual]

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(), radius(), and libMesh::TypeVector< T >::size().

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.size() > this->radius())
    return true;

  return false;
}

bool libMesh::Sphere::below_surface ( const Point & p ) const [virtual]

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) );
}

const Point& libMesh::Sphere::center ( ) const [inline]

Returns:: the center of the sphere.

Definition at line 162 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().

{ return _cent; }

Point& libMesh::Sphere::center ( ) [inline]

Returns:: the center of the sphere.

Definition at line 167 of file sphere.h.

References _cent.

{ return _cent; }

Point libMesh::Sphere::closest_point ( const Point & p ) const [virtual]

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;
}

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.);
}

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()).size();

  return the_distance - (this->radius() + other_sphere.radius());
}

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;
}

bool libMesh::Sphere::on_surface ( const Point & p ) const [virtual]

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 libMesh::Surface.

Definition at line 164 of file sphere.C.

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

{
  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.size() - this->radius()) < 1.e-10)
    return true;

  return false;
}

Real libMesh::Sphere::radius ( ) const [inline]

Returns the radius of the sphere.

Definition at line 152 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().

{ return _rad; }

Real& libMesh::Sphere::radius ( ) [inline]

Returns the radius of the sphere as a writeable reference.

Definition at line 157 of file sphere.h.

References _rad.

{ return _rad; }

Point libMesh::Sphere::surface_coords ( const Point & cart ) const [inline, virtual]

Returns:: the spherical coordinates for the cartesian coordinates cart.

Reimplemented from libMesh::Surface.

Definition at line 201 of file sphere.h.

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

{
  // 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.size(),
               /* theta  */ std::atan2( std::sqrt( c(0)*c(0) + c(1)*c(1) ), c(2) ),
               /* phi    */ ( (phi < 0)  ?  2.*libMesh::pi+phi  :  phi ) );
}

Point libMesh::Sphere::unit_normal ( const Point & p ) const [virtual]

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();
}

Point libMesh::Sphere::world_coords ( const Point & sph ) const [inline, virtual]

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

Point libMesh::Sphere::_cent [private]

The center of the sphere.

Definition at line 188 of file sphere.h.

Referenced by center().

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

Member Function Documentation

Member Data Documentation