#include <CUPlane.h>

Public Types
enum class	Side { INCIDENT , BACK , FRONT }

Public Member Functions
	Plane ()

	Plane (const Vec3 normal, float dist=0)

	Plane (const Vec3 normal, const Vec3 point)

	Plane (const Vec3 point1, const Vec3 point2, const Vec3 point3)

	Plane (float a, float b, float c, float d)

	Plane (const Plane &plane)

	~Plane ()

Plane &	operator= (const Plane &plane)

Plane &	operator= (const Vec3 normal)

Plane &	set (const Vec3 normal, float dist=0)

Plane &	set (const Vec3 normal, const Vec3 point)

Plane &	set (const Vec3 point1, const Vec3 point2, const Vec3 point3)

Plane &	set (float a, float b, float c, float d)

Plane &	set (const Plane &plane)

Plane &	multiply (const Mat4 &mat)

Plane &	operator*= (const Mat4 &mat)

const Plane	operator* (const Mat4 &mat) const

float	distance (const Vec3 point) const

float	getIntersection (const Ray &ray) const

bool	contains (const Vec3 point, float variance=CU_MATH_EPSILON) const

Side	sideOf (const Vec3 point) const

Side	sideOf (float x, float y, float z) const

bool	isFrontFacing (const Vec3 direction) const

bool	operator== (const Plane &p) const

bool	operator!= (const Plane &p) const

bool	equals (const Plane &p, float variance=CU_MATH_EPSILON) const

std::string	toString (bool verbose=false) const

	operator std::string () const

Static Public Member Functions
static Plane *	multiply (const Plane &plane, const Mat4 &mat, Plane *dst)

static float	intersection (const Plane &plane, const Ray &ray)

Public Attributes
Vec3	normal

float	offset

Static Public Attributes
static const Plane	XY

static const Plane	XZ

static const Plane	YZ

Detailed Description

This class ia a plane defined via a normal and the distance from the origin.

The normal must be a unit vector. However, we allow direct access to the normal and do not check this invariant.

Member Enumeration Documentation

◆ Side

enum class cugl::Plane::Side

strong

This enum specifies on which side a point lies respective to the plane.

Enumerator
INCIDENT	The point is on the plane
BACK	The point is on the side opposite the normal
FRONT	The point is on the side with the normal

Constructor & Destructor Documentation

◆ Plane() [1/6]

cugl::Plane::Plane ( )

inline

Creates the XY plane.

◆ Plane() [2/6]

cugl::Plane::Plane	(	const Vec3	normal,
		float	dist = `0`
	)

inline

Creates a new plane with the given normal and distance to the origin.

Parameters

normal	The plane normal
dist	The distance to the origin

◆ Plane() [3/6]

cugl::Plane::Plane	(	const Vec3	normal,
		const Vec3	point
	)

inline

Creates a new plane based on the normal and a point on the plane.

Parameters

normal	The normal
point	The point on the plane

◆ Plane() [4/6]

cugl::Plane::Plane	(	const Vec3	point1,
		const Vec3	point2,
		const Vec3	point3
	)

inline

Creates a new plane containing the three given points.

The normal is calculated via a cross product between (point1-point2)x(point2-point3)

Parameters

point1	The first point
point2	The second point
point3	The third point

◆ Plane() [5/6]

cugl::Plane::Plane	(	float	a,
		float	b,
		float	c,
		float	d
	)

inline

Creates a new plane from the given equation coefficients.

The equation of the plane is ax + by + cz = d.

Parameters

a	The x coefficient
b	The y coefficient
c	The z coefficient
d	The constant factor

◆ Plane() [6/6]

cugl::Plane::Plane ( const Plane & plane )

inline

Creates a copy of the given plane.

Parameters

plane The plane to copy,

◆ ~Plane()

cugl::Plane::~Plane ( )

inline

Destroys this plane, releasing all resources

Member Function Documentation

◆ contains()

bool cugl::Plane::contains	(	const Vec3	point,
		float	variance = `CU_MATH_EPSILON`
	)		const

inline

Returns true if this plane contains the given point within tolerance.

The tolerance bounds the point distance.

Parameters

point	The point to check
variance	The comparison tolerance.

Returns: true if this plane contains the given point within tolerance.

◆ distance()

float cugl::Plane::distance ( const Vec3 point ) const

inline

Return the signed distance between the plane and the given point.

The distance is signed, so that a point on the same side as the normal will have positive distance, while a point on the back side will have negative distance.

Returns: the signed distance between the plane and the given point.

◆ equals()

bool cugl::Plane::equals	(	const Plane &	p,
		float	variance = `CU_MATH_EPSILON`
	)		const

inline

Returns true if the planes are within tolerance of each other.

The tolerance bounds the normal and distance separately.

Parameters

p	The plane to compare against.
variance	The comparison tolerance.

Returns: true if the rays are within tolerance of each other.

◆ getIntersection()

float cugl::Plane::getIntersection ( const Ray & ray ) const

inline

Returns the intersection parameter of the ray with this plane.

If the value is negative, the intersection is in the reverse direction of the ray.

Parameters

ray	The ray to check

Returns: the intersection of the ray with this plane.

◆ intersection()

static float cugl::Plane::intersection	(	const Plane &	plane,
		const Ray &	ray
	)

static

Computes the intersection paramter the ray with the plane.

If the value is negative, the intersection is in the reverse direction of the ray.

Parameters

plane	The plane to check
ray	The ray to check

Returns: the intersection paramter the ray with the plane.

◆ isFrontFacing()

bool cugl::Plane::isFrontFacing ( const Vec3 direction ) const

inline

Returns whether the plane is facing the direction vector.

In this method, you should think of the direction vector as the direction a camera looks in. This method will return true if the front side of the plane determined by its normal faces the camera.

Parameters

direction The direction

Returns: whether the plane is facing the direction vector.

◆ multiply() [1/2]

Plane & cugl::Plane::multiply ( const Mat4 & mat )

inline

Multiplies this plane by the given matrix.

The multiplication transforms the plane. That is, if point p is on the original plane, p*M is on the newly created plane. To transform a plane by a matrix, we mutliply the vector (a,b,c,d) by the inverse of mat, where ax + by + cz = d is the equation of the plane.

Parameters

mat	The transform matrix

Returns: A reference to this (modified) Plane for chaining.

◆ multiply() [2/2]

static Plane * cugl::Plane::multiply	(	const Plane &	plane,
		const Mat4 &	mat,
		Plane *	dst
	)

static

Multiplies the plane by the given matrix and assigns it to dst.

The multiplication transforms the plane. That is, if point p is on the original plane, p*M is on the newly created plane. To transform a plane by a matrix, we mutliply the vector (a,b,c,d) by the inverse of mat, where ax + by + cz = d is the equation of the plane.

Parameters

plane	The plane to transform
mat	The transform matrix
dst	A plane to store the result in

Returns: A reference to dst for chaining

◆ operator std::string()

cugl::Plane::operator std::string ( ) const

inline

Cast from Ray to a string.

◆ operator!=()

bool cugl::Plane::operator!= ( const Plane & p ) const

inline

Returns true if this plane is not equal to the given plane.

Comparison is exact, which may be unreliable given that the attributes are floats.

Parameters

p	The plane to compare against.

Returns: True if this plane is not equal to the given plane.

◆ operator*()

const Plane cugl::Plane::operator* ( const Mat4 & mat ) const

inline

Return a copy of this plane transformed by the given matrix.

The multiplication transforms the plane. That is, if point p is on the original plane, p*M is on the newly created plane. To transform a plane by a matrix, we mutliply the vector (a,b,c,d) by the inverse of mat, where ax + by + cz = d is the equation of the plane.

Parameters

mat	The transform matrix

Returns: a copy of this plane transformed by the given matrix.

◆ operator*=()

Plane & cugl::Plane::operator*= ( const Mat4 & mat )

inline

Multiplies this plane by the given matrix.

The multiplication transforms the plane. That is, if point p is on the original plane, p*M is on the newly created plane. To transform a plane by a matrix, we mutliply the vector (a,b,c,d) by the inverse of mat, where ax + by + cz = d is the equation of the plane.

Parameters

mat	The transform matrix

Returns: A reference to this (modified) Plane for chaining.

◆ operator=() [1/2]

Plane & cugl::Plane::operator= ( const Plane & plane )

inline

Sets this plane to be a copy of the given plane.

Parameters

plane The plane to copy,

Returns: A reference to this (modified) Plane for chaining.

◆ operator=() [2/2]

Plane & cugl::Plane::operator= ( const Vec3 normal )

inline

Sets this plane to have the given normal.

After assignment, this plane will intersect the origin.

Parameters

normal The plane normal

Returns: A reference to this (modified) Plane for chaining.

◆ operator==()

bool cugl::Plane::operator== ( const Plane & p ) const

inline

Returns true if this plane is equal to the given plane.

Comparison is exact, which may be unreliable given that the attributes are floats.

Parameters

p	The plane to compare against.

Returns: True if this plane is equal to the given plane.

◆ set() [1/5]

Plane & cugl::Plane::set ( const Plane & plane )

inline

Sets this plane to be a copy of the given plane.

Parameters

plane The plane to copy,

Returns: A reference to this (modified) Plane for chaining.

◆ set() [2/5]

Plane & cugl::Plane::set	(	const Vec3	normal,
		const Vec3	point
	)

Sets this plane to have the given normal and contain the given point.

Parameters

normal	The normal
point	The point on the plane

Returns: A reference to this (modified) Plane for chaining.

◆ set() [3/5]

Plane & cugl::Plane::set	(	const Vec3	normal,
		float	dist = `0`
	)

Sets this plane to have the given normal and distance to the origin.

Parameters

normal	The plane normal
dist	The distance to the origin

Returns: A reference to this (modified) Plane for chaining.

◆ set() [4/5]

Plane & cugl::Plane::set	(	const Vec3	point1,
		const Vec3	point2,
		const Vec3	point3
	)

Creates a new plane to one containing the three given points.

The normal is calculated via a cross product between (point1-point2)x(point2-point3)

Parameters

point1	The first point
point2	The second point
point3	The third point

Returns: A reference to this (modified) Plane for chaining.

◆ set() [5/5]

Plane & cugl::Plane::set	(	float	a,
		float	b,
		float	c,
		float	d
	)

Sets this plane to have the given equation coefficients.

The equation of the plane is ax + by + cz = d.

Parameters

a	The x coefficient
b	The y coefficient
c	The z coefficient
d	The constant factor

◆ sideOf() [1/2]

Side cugl::Plane::sideOf ( const Vec3 point ) const

inline

Returns which side the given point lies relative to normal.

Side::FRONT refers to the side the plane normal points to.

Parameters

point The point to check

Returns: which side the given point lies relative to normal.

◆ sideOf() [2/2]

Side cugl::Plane::sideOf	(	float	x,
		float	y,
		float	z
	)		const

inline

Returns which side the given point lies relative to normal.

Side::FRONT refers to the side the plane normal points to.

Parameters

x	The x-coordinate of the point
y	The x-coordinate of the point
z	The x-coordinate of the point

Returns: which side the given point lies relative to normal.

◆ toString()

std::string cugl::Plane::toString ( bool verbose = false ) const

Returns a string representation of this plane for debugging purposes.

The plane will be represented by its equation ax+by+cz = d.

If verbose is true, the string will include class information. This allows us to unambiguously identify the class.

Parameters

verbose Whether to include class information

Returns: a string representation of this ray for debugging purposes.

Member Data Documentation

◆ normal

Vec3 cugl::Plane::normal

The plane normal (should be a unit vector)

◆ offset

float cugl::Plane::offset

The distance of the plane from the origin

◆ XY

const Plane cugl::Plane::XY

static

The xy plane (normal is z-axis)

◆ XZ

const Plane cugl::Plane::XZ

static

The xz plane (normal is y-axis)

◆ YZ

const Plane cugl::Plane::YZ

static

The yz plane (normal is x-axis)

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

cugl/include/cugl/math/CUPlane.h

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Member Enumeration Documentation

◆ Side

Constructor & Destructor Documentation

◆ Plane() [1/6]

◆ Plane() [2/6]

◆ Plane() [3/6]

◆ Plane() [4/6]

◆ Plane() [5/6]

◆ Plane() [6/6]

◆ ~Plane()

Member Function Documentation

◆ contains()

◆ distance()

◆ equals()

◆ getIntersection()

◆ intersection()

◆ isFrontFacing()

◆ multiply() [1/2]

◆ multiply() [2/2]

◆ operator std::string()

◆ operator!=()

◆ operator*()

◆ operator*=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ set() [1/5]

◆ set() [2/5]

◆ set() [3/5]

◆ set() [4/5]

◆ set() [5/5]

◆ sideOf() [1/2]

◆ sideOf() [2/2]

◆ toString()

Member Data Documentation

◆ normal

◆ offset

◆ XY

◆ XZ

◆ YZ