Plane< T, N > Class Template Reference

A geometric plane or hyperplane. More...

#include <geomc/shape/Plane.h>

Inheritance diagram for Plane< T, N >:

Public Member Functions
	Plane ()
	Plane (Vec< T, N > n)
	Plane (Vec< T, N > n, Vec< T, N > pt)
T	distance (const Vec< T, N > p) const
T	sdf (Vec< T, N > p) const
bool	contains (const Vec< T, N > p) const
template<typename ConvexShape >
bool	contains (const ConvexShape &shape) const
Vec< T, N >	project (Vec< T, N > p) const
Vec< T, N >	origin () const
void	apply (const AffineTransform< T, N > &xf)
void	apply_inverse (const AffineTransform< T, N > &xf)
template<typename ConvexShape >
bool	intersects (const ConvexShape &shape) const
bool	intersects (const Sphere< T, N > &s) const
bool	intersects (const Vec< T, N > *hull, index_t npts) const
Plane< T, N > &	operator*= (const AffineTransform< T, N > &tx)
Plane< T, N > &	operator/= (const AffineTransform< T, N > &tx)

Static Public Member Functions
static Plane	from_basis (const Vec< T, N > bases[N-1])
static Plane	from_basis (const Vec< T, N > bases[N-1], Vec< T, N > p)
static Plane	from_simplex (const Vec< T, N > points[N])

Public Attributes
Vec< T, N >	normal
	Normal direction, unit length.
T	d
	Distance along the unit normal from the origin to the plane surface.

Friends
Plane< T, N >	operator* (const AffineTransform< T, N > &tx, Plane< T, N > p)
Plane< T, N >	operator/ (Plane< T, N > p, const AffineTransform< T, N > &tx)

Detailed Description

template<typename T, index_t N>
class geom::Plane< T, N >

A geometric plane or hyperplane.

A Euclidean subspace of R^N with dimension N-1.

Constructor & Destructor Documentation

Plane() [1/3]

Plane ( )

inline

Construct a plane with a normal along +x, crossing the origin.

Plane() [2/3]

Plane ( Vec< T, N >  n )

inline

Construct a plane with normal n.

Parameters

n	Normal direction.

Plane() [3/3]

Plane ( Vec< T, N >  n, Vec< T, N >  pt  )

inline

Construct a plane with normal n passing through the point pt.

Parameters

n	Normal direction.
pt	A point on the plane.

Member Function Documentation

apply()

void apply ( const AffineTransform< T, N > &  xf )

inline

Geometrically transform this plane by xf.

Parameters

xf	An affine transformation.

apply_inverse()

void apply_inverse ( const AffineTransform< T, N > &  xf )

inline

Un-transform this plane by xf.

Parameters

xf	An affine transformation.

contains() [1/2]

bool contains ( const ConvexShape &  shape ) const

inline

Half-space test.

Returns

true if shape is completely on or below the surface of the plane (i.e. on the side opposite the normal); false otherwise.

contains() [2/2]

bool contains ( const Vec< T, N >  p ) const

inline

Half-space test.

Returns

true if p is on or below the surface of the plane (i.e. on the side opposite the normal); false otherwise.

distance()

T distance ( const Vec< T, N >  p ) const

inline

Returns

The distance from p along the normal direction to the surface of the plane. Negative if p is on the backfacing side of the plane.

from_basis() [1/2]

static Plane from_basis ( const Vec< T, N >  bases[N-1] )

inlinestatic

Construct a plane spanning the given basis vectors.

Parameters

bases

An array of N-1 bases.

Returns

A plane whose normal is orthogonal to all the given bases.

from_basis() [2/2]

static Plane from_basis ( const Vec< T, N >  bases[N-1], Vec< T, N >  p  )

inlinestatic

Construct a plane spanning the given basis vectors through the given point.

Parameters

bases	An array of N-1 bases.
p	Point through which to construct the plane.

Returns

A plane whose normal is orthogonal to all the given bases.

from_simplex()

static Plane from_simplex ( const Vec< T, N >  points[N] )

inlinestatic

Construct a plane spanning the points on the given simplex (i.e. line segment, triangle, tetrahedron, etc; as appropriate for the dimension).

Parameters

points

The N vertecies of a simplex.

Returns

A plane on which the given simplex lies.

intersects() [1/3]

bool intersects ( const ConvexShape &  shape ) const

inline

Convex shape intersection test.

Returns

true if and only if this plane passes through shape.

intersects() [2/3]

bool intersects ( const Sphere< T, N > &  s ) const

inline

Sphere interesection test.

Returns

true if and only if this plane passes through s.

intersects() [3/3]

bool intersects ( const Vec< T, N > *  hull, index_t  npts  ) const

inline

Convex hull intersection test.

Parameters

hull	A list of points whose convex hull is to be tested.
npts	Number of points in the list.

Returns

true if this plane intersects the convex hull of hull, false otherwise,

operator*=()

Plane< T, N > & operator*= ( const AffineTransform< T, N > &  tx )

inline

Affine transformation.

Parameters

tx	An affine transformation to apply to this plane.

operator/=()

Plane< T, N > & operator/= ( const AffineTransform< T, N > &  tx )

inline

Inverse affine transformation.

Parameters

tx	An affine transformation to un-apply to this plane.

origin()

Vec< T, N > origin ( ) const

inline

Returns

The point on the plane closest to the origin.

project()

Vec< T, N > project ( Vec< T, N >  p ) const

inline

Returns

p projected onto the plane.

sdf()

T sdf ( Vec< T, N >  p ) const

inline

Return the signed distance to the surface of the shape.

Friends And Related Function Documentation

operator*

Plane< T, N > operator* ( const AffineTransform< T, N > &  tx, Plane< T, N >  p  )

friend

Affine transformation.

Parameters

tx	An affine transformation.
p	A plane.

Returns

A new plane representing p transformed by at.

operator/

Plane< T, N > operator/ ( Plane< T, N >  p, const AffineTransform< T, N > &  tx  )

friend

Inverse affine transformation.

Parameters

p	A plane.
tx	An affine transformation.

Returns

A new plane representing p un-transformed by at.

---

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

• geomc/shape/Plane.h