libMesh::Plane Class Reference

This class defines a plane. More...

#include <plane.h>

Inheritance diagram for libMesh::Plane:

Public Member Functions
	Plane ()
	Dummy Constructor.
	Plane (const Point &p, const Point &n)
	Constructs a plane containing point p with normal n.
	Plane (const Point &p0, const Point &p1, const Point &p2)
	Constructs a plane containing the three points.
	Plane (const Plane &other_plane)
	Copy-constructor.
	~Plane ()
	Destructor.
void	create_from_point_normal (const Point &p, const Point &n)
	Defines a plane containing point p with normal n.
void	create_from_three_points (const Point &p0, const Point &p1, const Point &p2)
	Defines a plane intersecting the three points p0, p1, and p2.
void	xy_plane (const Real zpos=0.)
	Creates an XY plane located at z=zpos.
void	xz_plane (const Real ypos=0.)
	Creates an XZ plane located at y=ypos.
void	yz_plane (const Real xpos=0.)
	Creates an YZ plane located at x=xpos.
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
const Point &	get_planar_point () const
virtual Point	surface_coords (const Point &world_coords) const
virtual Point	world_coords (const Point &surf_coords) const

Private Member Functions
const Point &	normal () const

Private Attributes
Point	_point
	The plane is defined by a point and a normal.
Point	_normal

Detailed Description

This class defines a plane.

Author

Benjamin S. Kirk

Date

2002

A geometric object representing a planar surface.

Definition at line 36 of file plane.h.

Constructor & Destructor Documentation

Plane() [1/4]

libMesh::Plane::Plane ( )

default

Dummy Constructor.

Plane() [2/4]

libMesh::Plane::Plane	(	const Point &	p,
		const Point &	n
	)

Constructs a plane containing point p with normal n.

Definition at line 34 of file plane.C.

{
  this->create_from_point_normal (p, n);
}

References create_from_point_normal().

Plane() [3/4]

libMesh::Plane::Plane	(	const Point &	p0,
		const Point &	p1,
		const Point &	p2
	)

Constructs a plane containing the three points.

The normal is determined in a counter-clockwise sense. See the create_from_three_points method for more details.

Definition at line 42 of file plane.C.

{
  this->create_from_three_points (p0, p1, p2);
}

References create_from_three_points().

Plane() [4/4]

libMesh::Plane::Plane

(

const Plane &

other_plane

)

Copy-constructor.

Definition at line 51 of file plane.C.

                                       :
  Surface()
{
  this->create_from_point_normal(other_plane._point,
                                 other_plane._normal);
}

References _normal, _point, and create_from_point_normal().

~Plane()

libMesh::Plane::~Plane ( )

default

Destructor.

Does nothing at the moment.

Member Function Documentation

above_surface()

bool libMesh::Plane::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 121 of file plane.C.

{
  // Create a vector from the surface to point p;
  const Point w = p - _point;
 
  // The point is above the surface if the projection
  // of that vector onto the normal is positive
  const Real proj = w*this->normal();
 
  if (proj > 0.)
    return true;
 
  return false;
}

References _point, normal(), and libMesh::Real.

Referenced by below_surface().

below_surface()

bool libMesh::Plane::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 138 of file plane.C.

{
  return ( !this->above_surface (p) );
}

References above_surface().

closest_point()

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

overridevirtual

Returns

The closest point on the surface to point p.

Implements libMesh::Surface.

Definition at line 163 of file plane.C.

{
  // Create a vector from the surface to point p;
  const Point w = p - _point;
 
  // The closest point in the plane to point p
  // is in the negative normal direction
  // a distance w (dot) p.
  const Point cp = p - this->normal()*(w*this->normal());
 
  return cp;
}

References _point, and normal().

create_from_point_normal()

void libMesh::Plane::create_from_point_normal	(	const Point &	p,
		const Point &	n
	)

Defines a plane containing point p with normal n.

Definition at line 64 of file plane.C.

{
  _normal = n.unit();
  _point  = p;
}

References _normal, _point, and libMesh::TypeVector< T >::unit().

Referenced by Plane(), and Plane().

create_from_three_points()

void libMesh::Plane::create_from_three_points	(	const Point &	p0,
		const Point &	p1,
		const Point &	p2
	)

Defines a plane intersecting the three points p0, p1, and p2.

The normal is constructed in a counter-clockwise sense, i.e. (p1-p0)x(p2-p0);

Definition at line 72 of file plane.C.

{
  // Just use p0 for the point.
  _point = p0;
 
  const Point e0 = p1 - p0;
  const Point e1 = p2 - p0;
  const Point n  = e0.cross(e1);
 
  _normal = n.unit();
}

References _normal, _point, libMesh::TypeVector< T >::cross(), and libMesh::TypeVector< T >::unit().

Referenced by Plane().

get_planar_point()

const Point & libMesh::Plane::get_planar_point

(

)

const

Returns

A point on the plane useful for determining position.

Definition at line 183 of file plane.C.

{
  return _point;
}

References _point.

normal()

const Point & libMesh::Plane::normal ( ) const

inlineprivate

Returns

The normal for the plane.

Definition at line 139 of file plane.h.

{ return _normal; }

References _normal.

Referenced by above_surface(), closest_point(), and on_surface().

on_surface()

bool libMesh::Plane::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 145 of file plane.C.

{
  // Create a vector from the surface to point p;
  const Point w = p - _point;
 
  // If the projection of that vector onto the
  // plane's normal is 0 then the point is in
  // the plane.
  const Real proj = w * this->normal();
 
  if (std::abs(proj) < 1.e-10)
    return true;
 
  return false;
}

References _point, normal(), and libMesh::Real.

surface_coords()

virtual Point libMesh::Surface::surface_coords ( const Point &  world_coords ) const

inlinevirtualinherited

Returns

The Point world_coords in the surface's coordinate system. world_coords is in the world coordinate system. This method is not purely virtual, because there may be surfaces that do not have their own coordinate system. These simply do not have to override this method.

Reimplemented in libMesh::Sphere.

Definition at line 101 of file surface.h.

{ return world_coords; }

References libMesh::Surface::world_coords().

unit_normal()

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

overridevirtual

Returns

A unit vector normal to the surface at point p.

Implements libMesh::Surface.

Definition at line 178 of file plane.C.

{
  return _normal;
}

References _normal.

world_coords()

virtual Point libMesh::Surface::world_coords ( const Point &  surf_coords ) const

inlinevirtualinherited

Returns

The world (cartesian) coordinates for the surface coordinates surf_coords. This method is not purely virtual, because there may be surfaces that do not have an own coordinate system. These simply do not have to override this method.

Reimplemented in libMesh::Sphere.

Definition at line 110 of file surface.h.

{ return surf_coords; }

Referenced by libMesh::Surface::surface_coords().

xy_plane()

void libMesh::Plane::xy_plane

(

const Real

zpos = 0.

)

Creates an XY plane located at z=zpos.

Definition at line 88 of file plane.C.

{
  const Point p (0., 0., zpos);
  const Point n (0., 0., 1.);
 
  _point  = p;
  _normal = n;
}

References _normal, and _point.

xz_plane()

void libMesh::Plane::xz_plane

(

const Real

ypos = 0.

)

Creates an XZ plane located at y=ypos.

Definition at line 99 of file plane.C.

{
  const Point p (0., ypos, 0.);
  const Point n (0., 1., 0.);
 
  _point  = p;
  _normal = n;
}

References _normal, and _point.

yz_plane()

void libMesh::Plane::yz_plane

(

const Real

xpos = 0.

)

Creates an YZ plane located at x=xpos.

Definition at line 110 of file plane.C.

{
  const Point p (xpos, 0., 0.);
  const Point n (1., 0., 0.);
 
  _point  = p;
  _normal = n;
}

References _normal, and _point.

Member Data Documentation

_normal

Point libMesh::Plane::_normal

private

Definition at line 145 of file plane.h.

Referenced by create_from_point_normal(), create_from_three_points(), normal(), Plane(), unit_normal(), xy_plane(), xz_plane(), and yz_plane().

_point

Point libMesh::Plane::_point

private

The plane is defined by a point and a normal.

Definition at line 144 of file plane.h.

Referenced by above_surface(), closest_point(), create_from_point_normal(), create_from_three_points(), get_planar_point(), on_surface(), Plane(), xy_plane(), xz_plane(), and yz_plane().

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

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