U4DEngine::U4DTriangle Class Reference

The U4DTriangle class implements a geometrical representation of a 3D triangle. More...

Public Member Functions
	U4DTriangle ()
	Constructor which creates a 3D triangle with vertices all set to zero components.
	U4DTriangle (U4DPoint3n &uPointA, U4DPoint3n &uPointB, U4DPoint3n &uPointC)
	Constructor which creates a 3D triangle with the given vertex points.
	~U4DTriangle ()
	Destructor for the class.
	U4DTriangle (const U4DTriangle &a)
	Copy constructor for the class.
U4DTriangle &	operator= (const U4DTriangle &a)
	Copy constructor for the class. More...
bool	operator== (const U4DTriangle &a)
	Method which determines if two 3D triangle are equal. That is, they have the same vertex 3D points. More...
bool	operator!= (const U4DTriangle &a)
	Method which determines if two 3D triangle are NOT equal. That is, they DO NOT have the same vertex 3D points. More...
U4DPoint3n	closestPointOnTriangleToPoint (U4DPoint3n &uPoint)
	Method which determins the closest 3D point on the 3D triangle from the given 3D point. More...
U4DPoint3n	getCentroid ()
	Method which determines the centroid point of the triangle. More...
bool	isPointOnTriangle (U4DPoint3n &uPoint)
	Method which determines if the 3D point lies on the 3D triangle. More...
void	getBarycentricCoordinatesOfPoint (U4DPoint3n &uPoint, float &baryCoordinateU, float &baryCoordinateV, float &baryCoordinateW)
	Method which computes the Barycentric coordinates of the 3D point in the triangle. More...
U4DVector3n	getTriangleNormal ()
	Method which returns a 3D normal vector to the triangle. The normal vector computation follows the right-hand rule. More...
std::vector< U4DSegment >	getSegments ()
	Method which returns all three vertices of the 3D triangle. More...
U4DTriangle	projectTriangleOntoPlane (U4DPlane &uPlane)
	Method which returns a projected 3D triangle to a 3D plane. More...
float	distanceToPlane (U4DPlane &uPlane)
	Method which computes the magnitude(distance) from the 3D triangle to a 3D plane. More...
float	distanceSquareToPlane (U4DPlane &uPlane)
	Method which computes the square magnitude fromt the 3D triangle to a 3D plane. More...
float	centroidDistanceToPlane (U4DPlane &uPlane)
	Method which computes the magnitude(distance) from the 3D triangle's centroid to a 3D plane. More...
float	centroidSquareDistanceToPlane (U4DPlane &uPlane)
	Method which computes the square magnitude(distance) from the 3D triangle's centroid to a 3D plane. More...
void	show ()
	Method which prints the vertices of the 3D triangle to the console log window.
bool	isValid ()
	Method which test if the 3D triangle is valid. That is, if the points are not colinear. More...

Public Attributes
U4DPoint3n	pointA
	3D vertex point of the triangle
U4DPoint3n	pointB
	3D vertex point of the triangle
U4DPoint3n	pointC
	3D vertex point of the triangle

Detailed Description

The U4DTriangle class implements a geometrical representation of a 3D triangle.

Member Function Documentation

centroidDistanceToPlane()

float U4DEngine::U4DTriangle::centroidDistanceToPlane

(

U4DPlane &

uPlane

)

Method which computes the magnitude(distance) from the 3D triangle's centroid to a 3D plane.

Parameters

uPlane

3D plane to compute centroid distance from

Returns

Returns the magnitude(distance) from the 3D triangle's centroid to a 3D plane

centroidSquareDistanceToPlane()

float U4DEngine::U4DTriangle::centroidSquareDistanceToPlane

(

U4DPlane &

uPlane

)

Method which computes the square magnitude(distance) from the 3D triangle's centroid to a 3D plane.

Parameters

uPlane

3D plane to compute centroid distance from

Returns

Returns the square magnitude(distance) from the 3D triangle's centroid to a 3D plane

closestPointOnTriangleToPoint()

U4DPoint3n U4DEngine::U4DTriangle::closestPointOnTriangleToPoint

(

U4DPoint3n &

uPoint

)

Method which determins the closest 3D point on the 3D triangle from the given 3D point.

Parameters

uPoint

3D point to determine closest point

Returns

Returns the closest 3D point to the triangle from the given 3D point

distanceSquareToPlane()

float U4DEngine::U4DTriangle::distanceSquareToPlane

(

U4DPlane &

uPlane

)

Method which computes the square magnitude fromt the 3D triangle to a 3D plane.

Parameters

uPlane

3D plane to compute distance

Returns

Returns the square magnitude from a 3D triangle to a 3D plane

distanceToPlane()

float U4DEngine::U4DTriangle::distanceToPlane

(

U4DPlane &

uPlane

)

Method which computes the magnitude(distance) from the 3D triangle to a 3D plane.

Parameters

uPlane

3D plane to compute distance

Returns

Returns the magnitude(distance) from a 3D triangle to a 3D plane

getBarycentricCoordinatesOfPoint()

void U4DEngine::U4DTriangle::getBarycentricCoordinatesOfPoint	(	U4DPoint3n &	uPoint,
		float &	baryCoordinateU,
		float &	baryCoordinateV,
		float &	baryCoordinateW
	)

Method which computes the Barycentric coordinates of the 3D point in the triangle.

Parameters

uPoint	3D point to compute barycentric coordinates from
baryCoordinateU	u-component of the barycentric coordinates of the 3D point
baryCoordinateV	v-component of the barycentric coordinates of the 3D point
baryCoordinateW	w-component of the barycentric coordinates of the 3D point

getCentroid()

U4DPoint3n U4DEngine::U4DTriangle::getCentroid

(

)

Method which determines the centroid point of the triangle.

Returns

Returns a 3D point representing the centroid

getSegments()

std::vector< U4DSegment > U4DEngine::U4DTriangle::getSegments

(

)

Method which returns all three vertices of the 3D triangle.

Returns

Returns the three vertices of the 3D triangle

getTriangleNormal()

U4DVector3n U4DEngine::U4DTriangle::getTriangleNormal

(

)

Method which returns a 3D normal vector to the triangle. The normal vector computation follows the right-hand rule.

Returns

Returns a 3D vector representing the normal vector to the 3D triangle

isPointOnTriangle()

bool U4DEngine::U4DTriangle::isPointOnTriangle

(

U4DPoint3n &

uPoint

)

Method which determines if the 3D point lies on the 3D triangle.

Parameters

uPoint

3D point to test

Returns

Returns true if the given 3D point lies on the 3D triangle

isValid()

bool U4DEngine::U4DTriangle::isValid

(

)

Method which test if the 3D triangle is valid. That is, if the points are not colinear.

Returns

Returns true if the 3D triangle construction is valid.

operator!=()

bool U4DEngine::U4DTriangle::operator!=

(

const U4DTriangle &

a

)

Method which determines if two 3D triangle are NOT equal. That is, they DO NOT have the same vertex 3D points.

Parameters

a	3D triangle to test

Returns

Returns true if both triangles DO NOT have the same vertex 3D points

operator=()

U4DTriangle & U4DEngine::U4DTriangle::operator=

(

const U4DTriangle &

a

)

Copy constructor for the class.

Parameters

a	3D triangle to copy to

Returns

Returns a copy of the 3D triangle

operator==()

bool U4DEngine::U4DTriangle::operator==

(

const U4DTriangle &

a

)

Method which determines if two 3D triangle are equal. That is, they have the same vertex 3D points.

Parameters

a	3D triangle to test

Returns

Returns true if both triangles have the same vertex 3D points

projectTriangleOntoPlane()

U4DTriangle U4DEngine::U4DTriangle::projectTriangleOntoPlane

(

U4DPlane &

uPlane

)

Method which returns a projected 3D triangle to a 3D plane.

Parameters

uPlane

3D plane to compute projected 3D triangle

Returns

Returns a 3D triangle projected to a 3D plane