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)

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

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

template<typename ConvexShape>
bool	contains (const ConvexShape &shape) const

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

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

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)

bool	operator== (const Plane< T, N > &other) const

Vec< T, N >	origin () const

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

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

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
T	d
	Distance along the unit normal from the origin to the plane surface.

Vec< T, N >	normal
	Normal direction, unit length.

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]

template<typename T, index_t N>

Plane ( )

inline

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

◆ Plane() [2/3]

template<typename T, index_t N>

Plane ( Vec< T, N > n )

inline

Construct a plane with normal n.

Parameters

n	Normal direction.

◆ Plane() [3/3]

template<typename T, index_t N>

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()

template<typename T, index_t N>

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

inline

Geometrically transform this plane by xf.

Parameters

xf	An affine transformation.

◆ apply_inverse()

template<typename T, index_t N>

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

inline

Un-transform this plane by xf.

Parameters

xf	An affine transformation.

◆ contains() [1/2]

template<typename T, index_t N>

template<typename ConvexShape>

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]

template<typename T, index_t N>

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()

template<typename T, index_t N>

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]

template<typename T, index_t N>

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]

template<typename T, index_t N>

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()

template<typename T, index_t N>

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]

template<typename T, index_t N>

template<typename ConvexShape>

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]

template<typename T, index_t N>

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]

template<typename T, index_t N>

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*=()

template<typename T, index_t N>

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

inline

Affine transformation.

Parameters

tx	An affine transformation to apply to this plane.

◆ operator/=()

template<typename T, index_t N>

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()

template<typename T, index_t N>

Vec< T, N > origin ( ) const

inline

Returns: The point on the plane closest to the origin.

◆ project()

template<typename T, index_t N>

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

inline

Returns: p projected onto the plane.

◆ sdf()

template<typename T, index_t N>

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

inline

Return the signed distance to the surface of the shape.

Friends And Related Symbol Documentation

◆ operator*

template<typename T, index_t N>

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/

template<typename T, index_t N>

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

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Plane() [1/3]

◆ Plane() [2/3]

◆ Plane() [3/3]

Member Function Documentation

◆ apply()

◆ apply_inverse()

◆ contains() [1/2]

◆ contains() [2/2]

◆ distance()

◆ from_basis() [1/2]

◆ from_basis() [2/2]

◆ from_simplex()

◆ intersects() [1/3]

◆ intersects() [2/3]

◆ intersects() [3/3]

◆ operator*=()

◆ operator/=()

◆ origin()

◆ project()

◆ sdf()

Friends And Related Symbol Documentation

◆ operator*

◆ operator/