Points and vectors using homogeneous coordinates. More...

#include <point4d.h>

Inheritance diagram for VART::Point4D:

Public Member Functions
	Point4D ()
	Creates the (0,0,0,1) point. More...

	Point4D (const Point4D &point)

	Point4D (double x, double y, double z, double w=1.0)

Point4D	operator- () const

bool	operator== (const Point4D &point) const

bool	operator!= (const Point4D &point) const

void	operator= (const Point4D &point)

bool	operator< (const Point4D &p) const
	Checks whether a point is "less then" other. More...

bool	LexicographicalLess (const Point4D &p) const
	Verifies whether a point is less than other by looking at coordinates in lexicographical (x, y, z then w) order. More...

bool	XThenZLess (const Point4D &p) const
	Verifies whether a point is less then other by looking at coordinates X, then Z only. More...

bool	YThenXLess (const Point4D &p) const

bool	YThenZLess (const Point4D &p) const

bool	ZThenXLess (const Point4D &p) const

bool	ZThenYLess (const Point4D &p) const

bool	WeightedLess (const Point4D &p) const

bool	WeightedGreater (const Point4D &p) const

Point4D	operator+ (const Point4D &vector) const
	Addition for point and vector (or vice versa). More...

void	operator+= (const Point4D &vector)

Point4D	operator- (const Point4D &point) const
	Subtraction of two points. More...

Point4D	operator* (double escalar) const

void	operator*= (double escalar)

Point4D	operator/ (double escalar) const

double	GetX () const

double	GetY () const

double	GetZ () const

double	GetW () const

const double *	VetXYZW () const
	Returns vertex coordinates as a pointer to 4 doubles. More...

double	DotProduct (const Point4D &p) const
	Computes the dot product between "this" and "p". More...

double	AngleTo (const Point4D &p) const
	Computes the angle up to p. More...

double	AngleTo (const Point4D &p, const Point4D &ref) const
	Computes the signed angle to p, using ref as a positive axis reference. More...

double	GenericAngleTo (const Point4D &p) const

Point4D	CrossProduct (const Point4D &p) const
	Computes the cross product between "this" and "p". More...

void	SetX (double x)

void	SetY (double y)

void	SetZ (double z)

void	SetW (double w)

void	SetXY (double x, double y)

void	SetXYZ (double x, double y, double z)

void	SetXYZW (double x, double y, double z, double w)

void	Normalize ()
	Normalizes the point/vector. More...

double	Length () const
	Returns the vector's length. More...

bool	AlmostEqual (const Point4D &v) const
	Check if vector is almost equal to some other vector. More...

Public Member Functions inherited from VART::Point
virtual	~Point ()

virtual float	GetX ()

virtual float	GetY ()

virtual float	GetZ ()

virtual float	GetW ()

virtual void	GetXY (float &x, float &y)

virtual void	GetXZ (float &x, float &z)

virtual void	GetYZ (float &y, float &z)

virtual void	GetXYZ (float &x, float &y, float &z)

virtual void	GetXYZW (float &x, float &y, float &z, float &w)

virtual void	SetX (float x)

virtual void	SetY (float y)

virtual void	SetZ (float z)

virtual void	SetW (float z)

virtual void	SetXY (float x, float y)

virtual void	SetXZ (float x, float z)

virtual void	SetYZ (float y, float z)

virtual void	SetXYZ (float x, float y, float z)

virtual void	SetXYZW (float x, float y, float z, float w)

Static Public Member Functions
static const Point4D &	DOWN ()
	The (0,-1,0,0) vector. More...

static const Point4D &	ORIGIN ()
	The (0,0,0,1) point. More...

static const Point4D &	X ()
	The X vector (1,0,0,0). More...

static const Point4D &	Y ()
	The Y vector (0,1,0,0). More...

static const Point4D &	Z ()
	The Z vector (0,0,1,0). More...

Static Public Attributes
static tCompareOper	operatorLess = &VART::Point4D::LexicographicalLess
	Points to the operator to use within operator<. More...

static float	xWeight = 1
	Weight of the X coordinate for Weighted comparisons. More...

static float	yWeight = 1
	Weight of the Y coordinate for Weighted comparisons. More...

static float	zWeight = 1
	Weight of the Z coordinate for Weighted comparisons. More...

static double	delta = 0.00001
	Maximum difference for equality. More...

Friends
std::ostream &	operator<< (std::ostream &output, const Point4D &p)
	Output operator. More...

Detailed Description

Points and vectors using homogeneous coordinates.

The Point4D class provides a unified way of representing point and vectors objects, easing operations between these "two" kinds of entities along with integration with the Transform class. A 4D is homogeneous point represented by a vector (x,y,z,w). W coordinate is 0 for vectors and 1 for normalized points. This class has been created long after the Point3D and Vector3D classes, wich are used by (at this point) all other classes. It is recommended that this class slowly substitutes the other two.

Definition at line 22 of file point4d.h.

Constructor & Destructor Documentation

VART::Point4D::Point4D ( )

Creates the (0,0,0,1) point.

Definition at line 17 of file point4d.cpp.

VART::Point4D::Point4D ( const Point4D & point )

Definition at line 23 of file point4d.cpp.

VART::Point4D::Point4D	(	double	x,
		double	y,
		double	z,
		double	w = `1.0`
	)

Definition at line 31 of file point4d.cpp.

Member Function Documentation

bool VART::Point4D::AlmostEqual ( const Point4D & v ) const

Check if vector is almost equal to some other vector.

Definition at line 327 of file point4d.cpp.

double VART::Point4D::AngleTo ( const Point4D & p ) const

Computes the angle up to p.

Requires both vectors to be normalized.

See Also: Point4D::GenericAngleTo(const Point4D& p)

Returns: the angle in radians of the smaller arc between "this" and "p".

Definition at line 126 of file point4d.cpp.

Referenced by VART::Transform::MakeRotation().

double VART::Point4D::AngleTo	(	const Point4D &	p,
		const Point4D &	ref
	)		const

Computes the signed angle to p, using ref as a positive axis reference.

Requires all three vectors to be normalized.

Returns: the angle in radians to p (for a rotation around ref).

Definition at line 141 of file point4d.cpp.

VART::Point4D VART::Point4D::CrossProduct ( const Point4D & p ) const

Computes the cross product between "this" and "p".

Definition at line 121 of file point4d.cpp.

References GetX(), GetY(), and GetZ().

Referenced by VART::MeshObject::AddFace(), VART::Camera::Camera(), VART::MeshObject::ComputeTriangleNormal(), VART::Camera::LeftVector(), VART::Camera::PitchAroundTarget(), and VART::Dof::Reconfigure().

double VART::Point4D::DotProduct ( const Point4D & p ) const

Computes the dot product between "this" and "p".

Definition at line 116 of file point4d.cpp.

Referenced by VART::Dof::Reconfigure().

const VART::Point4D & VART::Point4D::DOWN ( )

static

The (0,-1,0,0) vector.

Definition at line 55 of file point4d.cpp.

double VART::Point4D::GenericAngleTo ( const Point4D & p ) const

This method doesn't require both vectors to be normalized, but has poorer performance than Point4D::AngleTo(const Point4D& p) method.

Returns: the angle in radians of the smaller arc between "this" and "p".

Definition at line 152 of file point4d.cpp.

References Length().

Referenced by VART::Arrow::Arrow().

double VART::Point4D::GetW ( ) const

inline

Definition at line 81 of file point4d.h.

Referenced by VART::Transform::ApplyTo(), VART::Transform::operator*(), and VART::operator<<().

double VART::Point4D::GetX ( ) const

inline

Definition at line 78 of file point4d.h.

Referenced by VART::MeshObject::AddNormal(), VART::Transform::ApplyTo(), VART::BoundingBox::ApplyTransform(), VART::MeshObject::ApplyTransform(), VART::Arrow::Arrow(), VART::BoundingBox::ConditionalUpdate(), CrossProduct(), VART::Transform::MakeRotation(), VART::Transform::MakeTranslation(), VART::Transform::operator*(), VART::operator<<(), VART::MeshObject::SetVertex(), and VART::BoundingBox::testPoint().

double VART::Point4D::GetY ( ) const

inline

Definition at line 79 of file point4d.h.

Referenced by VART::MeshObject::AddNormal(), VART::Transform::ApplyTo(), VART::BoundingBox::ApplyTransform(), VART::MeshObject::ApplyTransform(), VART::Arrow::Arrow(), VART::BoundingBox::ConditionalUpdate(), CrossProduct(), VART::Modifier::GetMax(), VART::Modifier::GetMin(), VART::Transform::MakeRotation(), VART::Transform::MakeTranslation(), VART::Transform::operator*(), VART::operator<<(), VART::MeshObject::SetVertex(), and VART::BoundingBox::testPoint().

double VART::Point4D::GetZ ( ) const

inline

Definition at line 80 of file point4d.h.

Referenced by VART::MeshObject::AddNormal(), VART::Transform::ApplyTo(), VART::BoundingBox::ApplyTransform(), VART::MeshObject::ApplyTransform(), VART::Arrow::Arrow(), VART::BoundingBox::ConditionalUpdate(), CrossProduct(), VART::Transform::MakeRotation(), VART::Transform::MakeTranslation(), VART::Transform::operator*(), VART::operator<<(), VART::MeshObject::SetVertex(), and VART::BoundingBox::testPoint().

double VART::Point4D::Length ( ) const

Returns the vector's length.

Definition at line 111 of file point4d.cpp.

Referenced by VART::Arrow::Arrow(), and GenericAngleTo().

bool VART::Point4D::LexicographicalLess ( const Point4D & p ) const

Verifies whether a point is less than other by looking at coordinates in lexicographical (x, y, z then w) order.

Definition at line 254 of file point4d.cpp.

void VART::Point4D::Normalize ( )

Normalizes the point/vector.

Points are normalized by dividing coordinates by W. Vectors are normalized by having their length changed to 1. Warning: The homogeneous point (0,0,0,0) is neither a point nor a vector and will cause a division by zero!

Definition at line 88 of file point4d.cpp.

Referenced by VART::MeshObject::AddFace(), VART::Camera::Camera(), VART::MeshObject::ComputeTriangleNormal(), VART::Dof::Dof(), VART::Camera::FrontVector(), VART::Camera::LeftVector(), VART::XmlScene::loadDofs(), VART::Transform::MakeRotation(), VART::Camera::MoveForward(), VART::Camera::MoveSideways(), VART::Camera::MoveUp(), VART::Camera::PitchAroundTarget(), VART::Camera::Roll(), and VART::Dof::Set().

bool VART::Point4D::operator!= ( const Point4D & point ) const

Definition at line 230 of file point4d.cpp.

VART::Point4D VART::Point4D::operator* ( double escalar ) const

Definition at line 201 of file point4d.cpp.

void VART::Point4D::operator*= ( double escalar )

Definition at line 209 of file point4d.cpp.

VART::Point4D VART::Point4D::operator+ ( const Point4D & vector ) const

Addition for point and vector (or vice versa).

Both point and vector should be normalized.

Returns: a (translated) point.

Definition at line 181 of file point4d.cpp.

void VART::Point4D::operator+= ( const Point4D & vector )

Definition at line 193 of file point4d.cpp.

VART::Point4D VART::Point4D::operator- ( ) const

Definition at line 166 of file point4d.cpp.

VART::Point4D VART::Point4D::operator- ( const Point4D & point ) const

Subtraction of two points.

Both points should be normalized.

Returns: a vector (from "point" to "this").

Definition at line 173 of file point4d.cpp.

VART::Point4D VART::Point4D::operator/ ( double escalar ) const

Definition at line 246 of file point4d.cpp.

bool VART::Point4D::operator< ( const Point4D & p ) const

Checks whether a point is "less then" other.

The idea of ordering in 4D point comes from operatorLess public attribute.

Definition at line 225 of file point4d.cpp.

void VART::Point4D::operator= ( const Point4D & point )

Definition at line 238 of file point4d.cpp.

bool VART::Point4D::operator== ( const Point4D & point ) const

Definition at line 217 of file point4d.cpp.

const VART::Point4D & VART::Point4D::ORIGIN ( )

static

The (0,0,0,1) point.

Definition at line 61 of file point4d.cpp.

Referenced by VART::Bezier::Bezier(), and VART::Light::BRIGHT_AMBIENT().

void VART::Point4D::SetW ( double w )

inline

Definition at line 115 of file point4d.h.

Referenced by VART::Dof::ComputeLIM(), VART::Transform::GetTranslation(), VART::Transform::GetVectorX(), VART::Transform::GetVectorY(), VART::Transform::GetVectorZ(), and VART::Dof::MoveTo().

void VART::Point4D::SetX ( double x )

inline

Definition at line 112 of file point4d.h.

Referenced by VART::Transform::GetTranslation(), VART::Transform::GetVectorX(), VART::Transform::GetVectorY(), and VART::Transform::GetVectorZ().

void VART::Point4D::SetXY	(	double	x,
		double	y
	)

Definition at line 67 of file point4d.cpp.

void VART::Point4D::SetXYZ	(	double	x,
		double	y,
		double	z
	)

Definition at line 73 of file point4d.cpp.

Referenced by VART::MeshObject::SmallerVertex().

void VART::Point4D::SetXYZW	(	double	x,
		double	y,
		double	z,
		double	w
	)

Definition at line 80 of file point4d.cpp.

Referenced by VART::Transform::ApplyTo(), VART::MeshObject::ApplyTransform(), VART::MeshObject::ComputeBoundingBox(), VART::MeshObject::ComputeSubBBoxes(), VART::MeshObject::GetYProjection(), VART::XmlScene::loadDofs(), VART::Transform::MakeRotation(), and VART::MeshObject::SetVertices().

void VART::Point4D::SetY ( double y )

inline

Definition at line 113 of file point4d.h.

Referenced by VART::Arrow::Arrow(), VART::Transform::GetTranslation(), VART::Transform::GetVectorX(), VART::Transform::GetVectorY(), and VART::Transform::GetVectorZ().

void VART::Point4D::SetZ ( double z )

inline

Definition at line 114 of file point4d.h.

Referenced by VART::Transform::GetTranslation(), VART::Transform::GetVectorX(), VART::Transform::GetVectorY(), and VART::Transform::GetVectorZ().

const double* VART::Point4D::VetXYZW ( ) const

inline

Returns vertex coordinates as a pointer to 4 doubles.

This method is usefull to pass to glVertex4dv().

Definition at line 86 of file point4d.h.

bool VART::Point4D::WeightedGreater ( const Point4D & p ) const

Definition at line 317 of file point4d.cpp.

bool VART::Point4D::WeightedLess ( const Point4D & p ) const

Definition at line 312 of file point4d.cpp.

const VART::Point4D & VART::Point4D::X ( )

static

The X vector (1,0,0,0).

Definition at line 37 of file point4d.cpp.

Referenced by VART::Scene::MakeCameraViewAll().

bool VART::Point4D::XThenZLess ( const Point4D & p ) const

Verifies whether a point is less then other by looking at coordinates X, then Z only.

Definition at line 272 of file point4d.cpp.

const VART::Point4D & VART::Point4D::Y ( )

static

The Y vector (0,1,0,0).

Definition at line 43 of file point4d.cpp.

Referenced by VART::Scene::MakeCameraViewAll().

bool VART::Point4D::YThenXLess ( const Point4D & p ) const

Definition at line 280 of file point4d.cpp.

bool VART::Point4D::YThenZLess ( const Point4D & p ) const

Definition at line 288 of file point4d.cpp.

const VART::Point4D & VART::Point4D::Z ( )

static

The Z vector (0,0,1,0).

Definition at line 49 of file point4d.cpp.

bool VART::Point4D::ZThenXLess ( const Point4D & p ) const

Definition at line 296 of file point4d.cpp.

bool VART::Point4D::ZThenYLess ( const Point4D & p ) const

Definition at line 304 of file point4d.cpp.

Friends And Related Function Documentation

std::ostream& operator<<	(	std::ostream &	output,
		const Point4D &	p
	)

friend

Output operator.

Member Data Documentation

double VART::Point4D::delta = 0.00001

static

Maximum difference for equality.

Used to see if floating point numbers are almost equal.

Definition at line 163 of file point4d.h.

VART::Point4D::tCompareOper VART::Point4D::operatorLess = &VART::Point4D::LexicographicalLess

static

Points to the operator to use within operator<.

The application programmer should change this pointer to the desired comparison function. Default value is LexicographicalLess. To change its value, use something like: Point4D::operatorLess = &Point4D::LexicographicalLess . Currently, possible values are: LexicographicalLess and XThenZLess.

Definition at line 152 of file point4d.h.

float VART::Point4D::xWeight = 1

static

Weight of the X coordinate for Weighted comparisons.

Definition at line 155 of file point4d.h.

float VART::Point4D::yWeight = 1

static

Weight of the Y coordinate for Weighted comparisons.

Definition at line 157 of file point4d.h.

float VART::Point4D::zWeight = 1

static

Weight of the Z coordinate for Weighted comparisons.

Definition at line 159 of file point4d.h.

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

Public Member Functions

Static Public Member Functions

Static Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation