U4DEngine::U4DPlane Class Reference

The U4DPlane class implements a mathematical representation of a 3D plane. More...

Public Member Functions
	U4DPlane ()
	Constructor which creates a 3D plane with zero normal vector and zero distance from point to plane.
	U4DPlane (U4DPoint3n &uPoint1, U4DPoint3n &uPoint2, U4DPoint3n &uPoint3)
	Constructor which creates a 3D plane given three noncollinear points (ordered CCW). This constructor in essence computes the plane equation.
	U4DPlane (U4DVector3n &uNormal, float uDistance)
	Constructor which creates a 3D plane given a normal vector and the distance from a point to plane.
	U4DPlane (U4DVector3n &uNormal, U4DPoint3n &uPoint)
	Constructor which creates a 3D plane given a normal vector and a 3D point in space.
	~U4DPlane ()
	Destructor of the class.
	U4DPlane (const U4DPlane &a)
	Copy constructor for a 3D plane object.
U4DPlane &	operator= (const U4DPlane &a)
	Copy constructor for a 3D plane object. More...
U4DPoint3n	closestPointToPlane (U4DPoint3n &uPoint)
	Method which computes the closest 3D point to a plane. More...
float	magnitudeOfPointToPlane (U4DPoint3n &uPoint)
	Method which computes the magnitude(distance) of a 3D point to a plane. More...
float	magnitudeSquareOfPointToPlane (U4DPoint3n &uPoint)
	Method which computes the square magnitude(distance) of a 3D point to a plane. That is, it does not compute the square root of the magnitude. More...
bool	intersectSegment (U4DSegment &uSegment, U4DPoint3n &uIntersectionPoint)
	Method which computes if a 3D segment intersects a 3D plane. More...
bool	intersectPlane (U4DPlane &uPlane, U4DPoint3n &uIntersectionPoint, U4DVector3n &uIntersectionVector)
	Method which computes if two 3D planes intersect. More...
bool	intersectPlanes (U4DPlane &uPlane2, U4DPlane &uPlane3, U4DPoint3n &uIntersectionPoint)
	Method which computes if three 3D planes intersect. More...
float	angle (U4DPlane &uPlane)
	Compute the angle between planes. The plane normals must be normalized. More...

Public Attributes
U4DVector3n	n
	Plane Normal 3D vector. The point on a plane satisfy n.dox(x)=d.
float	d
	Distance of a 3D point to the plane. d=n.dot(p) for a given p on the plane.

Detailed Description

The U4DPlane class implements a mathematical representation of a 3D plane.

Member Function Documentation

angle()

float U4DEngine::U4DPlane::angle

(

U4DPlane &

uPlane

)

Compute the angle between planes. The plane normals must be normalized.

Parameters

uPlane

Plane to compute angle

Returns

Returns the angle in degrees

closestPointToPlane()

U4DPoint3n U4DEngine::U4DPlane::closestPointToPlane

(

U4DPoint3n &

uPoint

)

Method which computes the closest 3D point to a plane.

Parameters

uPoint

3D point to compute the closest point to a plane

Returns

Returns the closest 3D point to the plane

intersectPlane()

bool U4DEngine::U4DPlane::intersectPlane	(	U4DPlane &	uPlane,
		U4DPoint3n &	uIntersectionPoint,
		U4DVector3n &	uIntersectionVector
	)

Method which computes if two 3D planes intersect.

Parameters

uPlane	3D plane to test intersection
uIntersectionPoint	3D point where intersection occurs
uIntersectionVector	3D vector produced by the intersection between the two planes

Returns

Returns true if two 3D planes intersect

intersectPlanes()

bool U4DEngine::U4DPlane::intersectPlanes	(	U4DPlane &	uPlane2,
		U4DPlane &	uPlane3,
		U4DPoint3n &	uIntersectionPoint
	)

Method which computes if three 3D planes intersect.

Parameters

uPlane2	First 3D plane to test intersection
uPlane3	Second 3D plane to test intersection
uIntersectionPoint	3D point where intersection occurs

Returns

Returns true if three 3D planes intersect

intersectSegment()

bool U4DEngine::U4DPlane::intersectSegment	(	U4DSegment &	uSegment,
		U4DPoint3n &	uIntersectionPoint
	)

Method which computes if a 3D segment intersects a 3D plane.

Parameters

uSegment	3D segment to test intersection
uIntersectionPoint	3D point where intersection occurs.

Returns

Returns true if the 3D segment intersects the 3D plane

magnitudeOfPointToPlane()

float U4DEngine::U4DPlane::magnitudeOfPointToPlane

(

U4DPoint3n &

uPoint

)

Method which computes the magnitude(distance) of a 3D point to a plane.

Parameters

uPoint

3D point to compute the magnitude(distance) to a plane

Returns

Returns the magnitude(distance) of a 3D point to plane

magnitudeSquareOfPointToPlane()

float U4DEngine::U4DPlane::magnitudeSquareOfPointToPlane

(

U4DPoint3n &

uPoint

)

Method which computes the square magnitude(distance) of a 3D point to a plane. That is, it does not compute the square root of the magnitude.

Parameters

uPoint

3D point to compute the square magnitude(distance) to a plane

Returns

Returns the square magnitude(distance) of a 3D point to plane. That is, it does not compute the square root of the magnitude

operator=()

U4DPlane & U4DEngine::U4DPlane::operator=

(

const U4DPlane &

a

)

Copy constructor for a 3D plane object.

Parameters

a	3D plane to copy

Returns

Returns a copy of the 3D plane object