This class implements a plane in 3D space. More...

Inheritance diagram for Ocean::PlaneT3< T >:

Public Types
typedef T	Type
	Definition of the used data type. More...

Public Member Functions
	PlaneT3 ()=default
	Creates an invalid plane. More...

	PlaneT3 (const VectorT3< T > &point, const VectorT3< T > &normal)
	Creates a plane by an intersection point and a normal. More...

	PlaneT3 (const VectorT3< T > &point0, const VectorT3< T > &point1, const VectorT3< T > &point2)
	Creates a plane by three points lying in the plane. More...

	PlaneT3 (const VectorT3< T > &normal, const T distance)
	Creates a plane by the plane's normal and the distance between origin and plane. More...

	PlaneT3 (const T yaw, const T pitch, const T distance)
	Creates a plane by the plane's normal and the distance between origin and plane. More...

	PlaneT3 (const HomogenousMatrixT4< T > &transformation)
	Creates a plane by a transformation where the z-axis defined the plane's normal and the origin or the transformation defines a point on the plane. More...

bool	isInPlane (const VectorT3< T > &point, const T epsilon=NumericT< T >::eps()) const
	Returns whether a point is in the plane. More...

T	signedDistance (const VectorT3< T > &point) const
	Returns the distance between a given point and this plane. More...

VectorT3< T >	projectOnPlane (const VectorT3< T > &point) const
	Projects a given point onto the plane. More...

VectorT3< T >	reflect (const VectorT3< T > &direction)
	Reflects a given vector in the plane. More...

const VectorT3< T > &	normal () const
	Returns the normal of the plane. More...

const T &	distance () const
	Returns the distance between plane and origin. More...

void	decomposeNormal (T &yaw, T &pitch) const
	Calculates the yaw and pitch angle of the plane's normal. More...

PlaneT3< T >	transform (const HomogenousMatrixT4< T > &iTransformation) const
	Transforms this plane so that it corresponds to a new coordinate system. More...

bool	transformation (const VectorT3< T > &pointOnPlane, const VectorT3< T > &upVector, HomogenousMatrixT4< T > &matrix) const
	Determines a transformation having the origin in a given point on the plane, with z-axis corresponding to the normal of the plane and with y-axis corresponding to a given (projected) up-vector. More...

void	setNormal (const VectorT3< T > &normal)
	Sets the normal of this plane. More...

void	setDistance (const T distance)
	Sets the distance between plane and origin. More...

VectorT3< T >	pointOnPlane () const
	Returns a point on the plane. More...

bool	intersection (const LineT3< T > &ray, VectorT3< T > &point) const
	Calculates the intersection between this plane and a given ray. More...

bool	intersection (const PlaneT3< T > &plane, LineT3< T > &line) const
	Calculates the intersection between this plane and a second plane. More...

bool	isValid () const
	Returns whether this plane is valid. More...

bool	isEqual (const PlaneT3< T > &plane, const T eps=NumericT< T >::eps()) const
	Returns whether two plane objects represent the same plane up to a specified epsilon. More...

	operator bool () const
	Returns whether the plane has a normal with non-zero length. More...

PlaneT3< T >	operator- () const
	Returns an inverted plane of this plane having an inverted normal direction (and adjusted distance). More...

bool	operator== (const PlaneT3< T > &right) const
	Returns whether two plane objects represent the same plane. More...

bool	operator!= (const PlaneT3< T > &right) const
	Returns whether two plane objects do not represent the same plane. More...

Protected Attributes
VectorT3< T >	normal_ = VectorT3<T>(0, 0, 0)
	Normal of the plane. More...

T	distance_ = T(0)
	Distance of the plane. More...

Detailed Description

template<typename T>
class Ocean::PlaneT3< T >

This class implements a plane in 3D space.

The plane is defined by:
(x - p)n = 0, xn - pn = 0, xn - d = 0,
with Intersection point p, normal n and distance d.

Template Parameters

T	Data type used to represent the plane

See also: Plane3, PlaneF3, PlaneD3.

Member Typedef Documentation

◆ Type

template<typename T >

typedef T Ocean::PlaneT3< T >::Type

Definition of the used data type.

Constructor & Destructor Documentation

◆ PlaneT3() [1/6]

template<typename T >

Ocean::PlaneT3< T >::PlaneT3 ( )

default

Creates an invalid plane.

◆ PlaneT3() [2/6]

template<typename T >

Ocean::PlaneT3< T >::PlaneT3	(	const VectorT3< T > &	point,
		const VectorT3< T > &	normal
	)

Creates a plane by an intersection point and a normal.

Parameters

point	Intersection point of the plane
normal	Unit vector perpendicular to the plane

◆ PlaneT3() [3/6]

template<typename T >

Ocean::PlaneT3< T >::PlaneT3	(	const VectorT3< T > &	point0,
		const VectorT3< T > &	point1,
		const VectorT3< T > &	point2
	)

Creates a plane by three points lying in the plane.

To create a valid plane three individual non-collinear points must be provided.
However, due to performance reasons this constructor accepts any kind of 3D object points but may create an invalid plane.
Thus, check whether the plane is valid after creation.

Parameters

point0	First intersection point
point1	Second intersection point
point2	Third intersection point

See also: isValid().

◆ PlaneT3() [4/6]

template<typename T >

Ocean::PlaneT3< T >::PlaneT3	(	const VectorT3< T > &	normal,
		const T	distance
	)

Creates a plane by the plane's normal and the distance between origin and plane.

Parameters

normal	Plane normal, must have length 1
distance	The signed distance between origin and plane, with range (-infinity, infinity)

◆ PlaneT3() [5/6]

template<typename T >

Ocean::PlaneT3< T >::PlaneT3	(	const T	yaw,
		const T	pitch,
		const T	distance
	)

Creates a plane by the plane's normal and the distance between origin and plane.

The plane's normal is provided in yaw and pitch angles from an Euler rotation.
The default normal (with yaw and pitch zero) looks along the negative z-axis.

Parameters

yaw	The yaw angle of the plane's normal, in radian
pitch	The pitch angle of the plane's normal, in radian
distance	The distance between origin and plane

◆ PlaneT3() [6/6]

template<typename T >

Ocean::PlaneT3< T >::PlaneT3 ( const HomogenousMatrixT4< T > & transformation )

explicit

Creates a plane by a transformation where the z-axis defined the plane's normal and the origin or the transformation defines a point on the plane.

The z-axis will be normalized before it is assigned as normal of the plane.

Parameters

transformation The transformation from which a plane will be defined

Member Function Documentation

◆ decomposeNormal()

template<typename T >

void Ocean::PlaneT3< T >::decomposeNormal	(	T &	yaw,
		T &	pitch
	)		const

inline

Calculates the yaw and pitch angle of the plane's normal.

The angles are related to an Euler rotation while the default normal (with angles zero) looks along the negative z-axis.

Parameters

yaw	Resulting yaw angle, in radian
pitch	Resulting pitch angle, in radian

◆ distance()

template<typename T >

const T & Ocean::PlaneT3< T >::distance

inline

Returns the distance between plane and origin.

Returns: Plane distance

◆ intersection() [1/2]

template<typename T >

bool Ocean::PlaneT3< T >::intersection	(	const LineT3< T > &	ray,
		VectorT3< T > &	point
	)		const

Calculates the intersection between this plane and a given ray.

Parameters

ray	The ray for which the intersection will be calculated, must be valid
point	Resulting intersection point

Returns: True, if the ray has an intersection with this plane

intersection point: ray.point() + t * ray.direction() t = (plane.distance() - plane.normal() * ray.point()) / (plane.normal() * ray.direction())

◆ intersection() [2/2]

template<typename T >

bool Ocean::PlaneT3< T >::intersection	(	const PlaneT3< T > &	plane,
		LineT3< T > &	line
	)		const

Calculates the intersection between this plane and a second plane.

Parameters

plane	The second plane for which the intersection will be calculated, must be valid
line	Resulting intersection line

Returns: True, if the second plane has an intersection with this plane (if both planes are not parallel)

◆ isEqual()

template<typename T >

bool Ocean::PlaneT3< T >::isEqual	(	const PlaneT3< T > &	plane,
		const T	eps = `NumericT<T>::eps()`
	)		const

inline

Returns whether two plane objects represent the same plane up to a specified epsilon.

Two planes are identical if their normal vector and distance value is identical or inverted.

Parameters

plane	The second plane to compare
eps	The epsilon value to be used, with range [0, infinity)

Returns: True, if so

◆ isInPlane()

template<typename T >

bool Ocean::PlaneT3< T >::isInPlane	(	const VectorT3< T > &	point,
		const T	epsilon = `NumericT<T>::eps()`
	)		const

Returns whether a point is in the plane.

Parameters

point	The point to check
epsilon	The epsilon value defining the accuracy threshold, with range [0, infinity)

Returns: True, if so

◆ isValid()

template<typename T >

bool Ocean::PlaneT3< T >::isValid

Returns whether this plane is valid.

A valid plane has a normal with length 1.

Returns: True, if so

◆ normal()

template<typename T >

const VectorT3< T > & Ocean::PlaneT3< T >::normal

inline

Returns the normal of the plane.

Returns: Plane normal

◆ operator bool()

template<typename T >

Ocean::PlaneT3< T >::operator bool

inlineexplicit

Returns whether the plane has a normal with non-zero length.

Beware: A plane with non-zero length normal may be invalid, however.

Returns: True, if so

◆ operator!=()

template<typename T >

bool Ocean::PlaneT3< T >::operator!= ( const PlaneT3< T > & right ) const

inline

Returns whether two plane objects do not represent the same plane.

Parameters

right Second plane to compare

Returns: True, if so

◆ operator-()

template<typename T >

PlaneT3< T > Ocean::PlaneT3< T >::operator-

inline

Returns an inverted plane of this plane having an inverted normal direction (and adjusted distance).

Returns: The inverted plane

◆ operator==()

template<typename T >

bool Ocean::PlaneT3< T >::operator== ( const PlaneT3< T > & right ) const

inline

Returns whether two plane objects represent the same plane.

Two planes are identical if their normal vector and distance value is identical or inverted.

Parameters

right Second plane to compare

Returns: True, if so

◆ pointOnPlane()

template<typename T >

VectorT3< T > Ocean::PlaneT3< T >::pointOnPlane

inline

Returns a point on the plane.

Returns: Point on plane

◆ projectOnPlane()

template<typename T >

VectorT3< T > Ocean::PlaneT3< T >::projectOnPlane ( const VectorT3< T > & point ) const

Projects a given point onto the plane.

Parameters

point The point that will be projected

Returns: The projected point

◆ reflect()

template<typename T >

VectorT3< T > Ocean::PlaneT3< T >::reflect ( const VectorT3< T > & direction )

Reflects a given vector in the plane.

The given vector should point towards the plane.

Parameters

direction The direction vector being reflected

Returns: The reflected vector

◆ setDistance()

template<typename T >

void Ocean::PlaneT3< T >::setDistance ( const T distance )

inline

Sets the distance between plane and origin.

Parameters

distance Plane distance to be set

◆ setNormal()

template<typename T >

void Ocean::PlaneT3< T >::setNormal ( const VectorT3< T > & normal )

inline

Sets the normal of this plane.

Parameters

normal The normal to be set, must have length 1.

◆ signedDistance()

template<typename T >

T Ocean::PlaneT3< T >::signedDistance ( const VectorT3< T > & point ) const

Returns the distance between a given point and this plane.

The distance will be positive for points on the side of the plane that its normal pointing to and negative on the other.

Parameters

point The point for which the distance will be determined

Returns: Distance between plane and point, with range (-infinity, infinity)

◆ transform()

template<typename T >

PlaneT3< T > Ocean::PlaneT3< T >::transform ( const HomogenousMatrixT4< T > & iTransformation ) const

Transforms this plane so that it corresponds to a new coordinate system.

Parameters

iTransformation The inverse of a new coordinate system (defining the transformation from points defined in the coordinate system of this current plane to points defined in the new coordinate system)

Returns: Resulting new plane for the given (inverted) coordinate system

◆ transformation()

template<typename T >

bool Ocean::PlaneT3< T >::transformation	(	const VectorT3< T > &	pointOnPlane,
		const VectorT3< T > &	upVector,
		HomogenousMatrixT4< T > &	matrix
	)		const

Determines a transformation having the origin in a given point on the plane, with z-axis corresponding to the normal of the plane and with y-axis corresponding to a given (projected) up-vector.

Parameters

pointOnPlane	A 3D point on this 3D plane at which the origin of the transformation will be located
upVector	An up-vector starting at the given point on the 3D plane, the vector will be projected onto the plane and normalized to define the y-axis of the transformation, can be e.g., the viewing direction of the camera, must not be parallel to the plane's normal
matrix	The resulting matrix defining the transformation

Returns: True, if succeeded

Field Documentation

◆ distance_

template<typename T >

T Ocean::PlaneT3< T >::distance_ = T(0)

protected

Distance of the plane.

◆ normal_

template<typename T >

VectorT3<T> Ocean::PlaneT3< T >::normal_ = VectorT3<T>(0, 0, 0)

protected

Normal of the plane.

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

Plane3.h

Public Types

Public Member Functions

Protected Attributes

Detailed Description

template<typename T> class Ocean::PlaneT3< T >

Member Typedef Documentation

◆ Type

Constructor & Destructor Documentation

◆ PlaneT3() [1/6]

◆ PlaneT3() [2/6]

◆ PlaneT3() [3/6]

◆ PlaneT3() [4/6]

◆ PlaneT3() [5/6]

◆ PlaneT3() [6/6]

Member Function Documentation

◆ decomposeNormal()

◆ distance()

◆ intersection() [1/2]

◆ intersection() [2/2]

◆ isEqual()

◆ isInPlane()

◆ isValid()

◆ normal()

◆ operator bool()

◆ operator!=()

◆ operator-()

◆ operator==()

◆ pointOnPlane()

◆ projectOnPlane()

◆ reflect()

◆ setDistance()

◆ setNormal()

◆ signedDistance()

◆ transform()

◆ transformation()

Field Documentation

◆ distance_

◆ normal_

template<typename T>
class Ocean::PlaneT3< T >