A hyperplane ((N - 1)-flat) in N-dimensional space, where N is any positive (non-zero) integer and T is a field. More...

#include <HyperplaneN.hpp>

Inheritance diagram for HyperplaneN< N, T >:

Public Types
typedef HyperplaneN< N, T >	HyperplaneT
	N-dimensional hyperplane. More...

typedef Vector< N, T >	VectorT
	N-dimensional vector. More...

Public Member Functions
template<typename U >
HyperplaneN< N, U >	cast () const
	Cast the hyperplane to a different scalar type. More...

VectorT	closestPoint (VectorT const &p) const
	Get the point on the hyperplane closest to a given point. More...

T	distance (VectorT const &p) const
	Get the (unsigned) distance of a given point from the hyperplane. More...

void	flip ()
	Flip the hyperplane so that the normal points the other way. More...

Vector< N+1, T >	getEquation () const
	Get the coefficients {a_i} of the hyperplane equation a_0 * x_0 + a_1 * x_1 + ... More...

VectorT const &	getNormal () const
	Get the unit normal vector of the hyperplane. More...

VectorT	getPoint () const
	Get a point on the hyperplane. More...

	HyperplaneN ()
	Default constructor. More...

bool	negativeHalfSpaceContains (VectorT const &p) const
	Check if the negative half space (the side of the hyperplane not containing the normal) contains a given point. More...

bool	positiveHalfSpaceContains (VectorT const &p) const
	Check if the positive half space (the side of the hyperplane containing the normal) contains a given point. More...

RayIntersectionN< N, T >	rayIntersection (RayN< N, T > const &ray, T max_time=-1) const
	Get the intersection of a ray with the object, including the hit time and the normal at the intersection point. More...

T	rayIntersectionTime (RayN< N, T > const &ray, T max_time=-1) const
	Get the time taken for a ray to intersect the object, or a negative value if there was no intersection in the forward direction. More...

bool	rayIntersects (RayN< N, T > const &ray, T max_time=-1) const
	Check if a ray intersects the object in the forward direction. More...

VectorT	reflect (VectorT const &p) const
	Reflect a point in the hyperplane. More...

T	signedDistance (VectorT const &p) const
	Get the signed distance of a given point from the hyperplane. More...

T	squaredDistance (VectorT const &p) const
	Get the square of the distance of the hyperplane from a given point. More...

std::string	toString () const
	Get a textual description of the hyperplane. More...

Static Public Member Functions
static HyperplaneT	fromDistanceAndNormal (T dist_, VectorT const &normal_, bool normalize=true)
	Construct a hyperplane from its signed distance from the origin, and its normal vector (need not be a unit vector). More...

static HyperplaneT	fromNPoints (Array< VectorT > const &points)
	Construct a hyperplane from N points on it. More...

static HyperplaneT	fromPointAndNormal (VectorT const &point_, VectorT const &normal_, bool normalize=true)
	Construct a hyperplane from a point on it, and its normal vector (need not be a unit vector). More...

Protected Attributes
T	dist
	The signed distance of the hyperplane from the origin. More...

VectorT	normal
	The unit normal vector of the hyperplane. More...

Detailed Description

template<int N, typename T = Real>
class Thea::HyperplaneN< N, T >

A hyperplane ((N - 1)-flat) in N-dimensional space, where N is any positive (non-zero) integer and T is a field.

Definition at line 27 of file HyperplaneN.hpp.

Member Typedef Documentation

typedef HyperplaneN<N, T> HyperplaneT

inherited

N-dimensional hyperplane.

Definition at line 41 of file HyperplaneN.hpp.

typedef Vector<N, T> VectorT

inherited

N-dimensional vector.

Definition at line 42 of file HyperplaneN.hpp.

Constructor & Destructor Documentation

HyperplaneN ( )

Default constructor.

Definition at line 235 of file HyperplaneN.hpp.

Member Function Documentation

HyperplaneN<N, U> cast ( ) const

inherited

Cast the hyperplane to a different scalar type.

Definition at line 102 of file HyperplaneN.hpp.

VectorT closestPoint ( VectorT const & p ) const

inherited

Get the point on the hyperplane closest to a given point.

Definition at line 157 of file HyperplaneN.hpp.

T distance ( VectorT const & p ) const

inherited

Get the (unsigned) distance of a given point from the hyperplane.

Definition at line 136 of file HyperplaneN.hpp.

void flip ( )

inherited

Flip the hyperplane so that the normal points the other way.

Definition at line 129 of file HyperplaneN.hpp.

static HyperplaneT fromDistanceAndNormal	(	T	dist_,
		VectorT const &	normal_,
		bool	normalize = `true`
	)

staticinherited

Construct a hyperplane from its signed distance from the origin, and its normal vector (need not be a unit vector).

The normalize argument suppresses rescaling of the normal to unit length if set to false.

Definition at line 53 of file HyperplaneN.hpp.

static HyperplaneT fromNPoints ( Array< VectorT > const & points )

staticinherited

Construct a hyperplane from N points on it.

Definition at line 76 of file HyperplaneN.hpp.

static HyperplaneT fromPointAndNormal	(	VectorT const &	point_,
		VectorT const &	normal_,
		bool	normalize = `true`
	)

staticinherited

Construct a hyperplane from a point on it, and its normal vector (need not be a unit vector).

The normalize argument suppresses rescaling of the normal to unit length if set to false.

Definition at line 66 of file HyperplaneN.hpp.

Vector<N + 1, T> getEquation ( ) const

inherited

Get the coefficients {a_i} of the hyperplane equation a_0 * x_0 + a_1 * x_1 + ...

a_{N - 1} * x_{N - 1} + a_N * 1 = 0.

Definition at line 116 of file HyperplaneN.hpp.

VectorT const& getNormal ( ) const

inherited

Get the unit normal vector of the hyperplane.

Definition at line 111 of file HyperplaneN.hpp.

VectorT getPoint ( ) const

inherited

Get a point on the hyperplane.

Definition at line 108 of file HyperplaneN.hpp.

bool negativeHalfSpaceContains ( VectorT const & p ) const

inherited

Check if the negative half space (the side of the hyperplane not containing the normal) contains a given point.

Returns true if the point lies on the hyperplane.

Definition at line 175 of file HyperplaneN.hpp.

bool positiveHalfSpaceContains ( VectorT const & p ) const

inherited

Check if the positive half space (the side of the hyperplane containing the normal) contains a given point.

Returns true if the point lies on the hyperplane.

Definition at line 166 of file HyperplaneN.hpp.

RayIntersectionN<N, T> rayIntersection	(	RayN< N, T > const &	ray,
		T	max_time = `-1`
	)		const

virtualinherited

Get the intersection of a ray with the object, including the hit time and the normal at the intersection point.

A negative time is returned if there was no intersection in the forward direction. If the normal cannot be computed, the zero vector is returned.

Parameters

ray	The ray to test for intersection.
max_time	Maximum allowable hit time, ignored if negative.

Note: The returned normal need not have unit length.

Reimplemented from RayIntersectableN< N, T >.

Definition at line 204 of file HyperplaneN.hpp.

T rayIntersectionTime	(	RayN< N, T > const &	ray,
		T	max_time = `-1`
	)		const

virtualinherited

Get the time taken for a ray to intersect the object, or a negative value if there was no intersection in the forward direction.

All subclasses must reimplement this method. If the return value is negative, it should be at least

Parameters

ray	The ray to test for intersection.
max_time	Maximum allowable hit time, ignored if negative.

Implements RayIntersectableN< N, T >.

Definition at line 191 of file HyperplaneN.hpp.

bool rayIntersects	(	RayN< N, T > const &	ray,
		T	max_time = `-1`
	)		const

virtualinherited

Check if a ray intersects the object in the forward direction.

Parameters

ray	The ray to test for intersection.
max_time	Maximum allowable hit time, ignored if negative.

Reimplemented from RayIntersectableN< N, T >.

Definition at line 186 of file HyperplaneN.hpp.

VectorT reflect ( VectorT const & p ) const

inherited

Reflect a point in the hyperplane.

Definition at line 181 of file HyperplaneN.hpp.

T signedDistance ( VectorT const & p ) const

inherited

Get the signed distance of a given point from the hyperplane.

This is positive if the point is on the side of the hyperplane containing the normal, and negative if the point is on the other side.

Definition at line 145 of file HyperplaneN.hpp.

T squaredDistance ( VectorT const & p ) const

inherited

Get the square of the distance of the hyperplane from a given point.

Definition at line 151 of file HyperplaneN.hpp.

std::string toString ( ) const

inherited

Get a textual description of the hyperplane.

Definition at line 214 of file HyperplaneN.hpp.

Member Data Documentation

T dist

protectedinherited

The signed distance of the hyperplane from the origin.

Definition at line 223 of file HyperplaneN.hpp.

VectorT normal

protectedinherited

The unit normal vector of the hyperplane.

Definition at line 222 of file HyperplaneN.hpp.

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

HyperplaneN.hpp

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

template<int N, typename T = Real> class Thea::HyperplaneN< N, T >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<int N, typename T = Real>
class Thea::HyperplaneN< N, T >