Vec Class Reference

The Vec class represents 3D positions and 3D vectors. More...

#include <QGLViewer/vec.h>

Public Attributes
qreal	x
qreal	y
qreal	z

Setting the value
	Vec ()
	Vec (qreal X, qreal Y, qreal Z)
template<class C >
	Vec (const C &c)
void	setValue (qreal X, qreal Y, qreal Z)

Accessing the value
qreal	operator[] (int i) const
qreal &	operator[] (int i)
	operator const qreal * () const
	operator qreal * ()
	operator const float * () const

Algebraic computations
Vec &	operator+= (const Vec &a)
Vec &	operator-= (const Vec &a)
Vec &	operator*= (qreal k)
Vec &	operator/= (qreal k)
Vec	orthogonalVec () const
Vec	operator+ (const Vec &a, const Vec &b)
Vec	operator- (const Vec &a, const Vec &b)
Vec	operator- (const Vec &a)
Vec	operator* (const Vec &a, qreal k)
Vec	operator* (qreal k, const Vec &a)
Vec	operator/ (const Vec &a, qreal k)
bool	operator!= (const Vec &a, const Vec &b)
bool	operator== (const Vec &a, const Vec &b)
qreal	operator* (const Vec &a, const Vec &b)
Vec	operator^ (const Vec &a, const Vec &b)
Vec	cross (const Vec &a, const Vec &b)

Norm of the vector
qreal	squaredNorm () const
qreal	norm () const
qreal	normalize ()
Vec	unit () const

Projection
void	projectOnAxis (const Vec &direction)
void	projectOnPlane (const Vec &normal)

XML representation
	Vec (const QDomElement &element)
QDomElement	domElement (const QString &name, QDomDocument &document) const
void	initFromDOMElement (const QDomElement &element)

Output stream
std::ostream &	operator<< (std::ostream &o, const qglviewer::Vec &)

Detailed Description

The Vec class represents 3D positions and 3D vectors.

Vec is used as a parameter and return type by many methods of the library. It provides classical algebraic computational methods and is compatible with OpenGL:

// Draws a point located at 3.0 OpenGL units in front of the camera
Vec pos = camera()->position() + 3.0 * camera()->viewDirection();
glBegin(GL_POINTS);
glVertex3fv(pos);
glEnd();

This makes of Vec a good candidate for representing positions and vectors in your programs. Since it is part of the qglviewer namespace, specify qglviewer::Vec or use the qglviewer namespace:

 using namespace
qglviewer; 

Interface with other vector classes

Vec implements a universal explicit converter, based on the [] operator. Everywhere a const Vec& argument is expected, you can use your own vector type instead, as long as it implements this operator (see the Vec(const C& c) documentation).

See also the Quaternion and the Frame documentations.

Constructor & Destructor Documentation

Vec() [1/4]

Vec

(

)

Default constructor. Value is set to (0,0,0).

Vec() [2/4]

Vec	(	qreal	X,
		qreal	Y,
		qreal	Z
	)

Standard constructor with the x, y and z values.

Vec() [3/4]

Vec ( const C &  c )

explicit

Universal explicit converter from any class to Vec. You can use your own vector class everywhere a const Vec& parameter is required, as long as it implements the operator[ ]:

class MyVec
{
  // ...
  qreal operator[](int i) const { returns x, y or z when i=0, 1 or 2; }
}
 
MyVec v(...);
camera()->setPosition(v);

Note that standard vector types (STL, qreal[3], ...) implement this operator and can hence be used in place of Vec. See also operator const qreal*() .

Vec() [4/4]

Vec ( const QDomElement &  element )

explicit

Constructs a Vec from a QDomElement representing an XML code of the form

< anyTagName x=".." y=".." z=".." />

If one of these attributes is missing or is not a number, a warning is displayed and the associated value is set to 0.0.

See also domElement() and initFromDOMElement().

Member Function Documentation

domElement()

QDomElement domElement	(	const QString &	name,
		QDomDocument &	document
	)		const

Returns an XML QDomElement that represents the Vec.

name is the name of the QDomElement tag. doc is the QDomDocument factory used to create QDomElement.

When output to a file, the resulting QDomElement will look like:

<name x=".." y=".." z=".." />

Use initFromDOMElement() to restore the Vec state from the resulting QDomElement. See also the Vec(const QDomElement&) constructor.

Here is complete example that creates a QDomDocument and saves it into a file:

Vec sunPos;
QDomDocument document("myDocument");
QDomElement sunElement = document.createElement("Sun");
document.appendChild(sunElement);
sunElement.setAttribute("brightness", sunBrightness());
sunElement.appendChild(sunPos.domElement("sunPosition", document));
// Other additions to the document hierarchy...
 
// Save doc document
QFile f("myFile.xml");
if (f.open(IO_WriteOnly))
{
  QTextStream out(&f);
  document.save(out, 2);
  f.close();
}

See also Quaternion::domElement(), Frame::domElement(), Camera::domElement()...

initFromDOMElement()

void initFromDOMElement

(

const QDomElement &

element

)

Restores the Vec state from a QDomElement created by domElement().

The QDomElement should contain x, y and z attributes. If one of these attributes is missing or is not a number, a warning is displayed and the associated value is set to 0.0.

To restore the Vec state from an xml file, use:

// Load DOM from file
QDomDocument doc;
QFile f("myFile.xml");
if (f.open(IO_ReadOnly))
{
  doc.setContent(&f);
  f.close();
}
// Parse the DOM tree and initialize
QDomElement main=doc.documentElement();
myVec.initFromDOMElement(main);

See also the Vec(const QDomElement&) constructor.

norm()

qreal norm

(

)

const

Returns the norm of the vector.

normalize()

qreal normalize

(

)

Normalizes the Vec and returns its original norm.

Normalizing a null vector will result in NaN values.

operator const float *()

operator const float *

(

)

const

Conversion operator returning the memory address of the vector.

Very convenient to pass a Vec pointer as a float parameter to OpenGL functions:

Vec pos, normal; glNormal3fv(normal); glVertex3fv(pos);

Note

The returned float array is a static shared by all Vec instances.

operator const qreal *()

operator const qreal *

(

)

const

Conversion operator returning the memory address of the vector.

Very convenient to pass a Vec pointer as a parameter to GLdouble OpenGL functions:

Vec pos, normal; glNormal3dv(normal); glVertex3dv(pos);

operator qreal *()

operator qreal *

(

)

Non const conversion operator returning the memory address of the vector.

Useful to pass a Vec to a method that requires and fills a qreal*, as provided by certain libraries.

operator*=()

Vec & operator*=

(

qreal

k

)

Multiply the vector by a scalar k.

operator+=()

Vec & operator+=

(

const Vec &

a

)

Adds a to the vector.

operator-=()

Vec & operator-=

(

const Vec &

a

)

Subtracts a to the vector.

operator/=()

Vec & operator/=

(

qreal

k

)

Divides the vector by a scalar k.

An absolute k value lower than 1E-10 will print a warning if the library was compiled with the "debug" Qt CONFIG flag. Otherwise, no test is performed for efficiency reasons.

operator<<()

std::ostream & operator<<	(	std::ostream &	o,
		const qglviewer::Vec &
	)

Output stream operator. Enables debugging code like:

Vec pos(...);
cout << "Position=" << pos << endl;

operator[]() [1/2]

qreal & operator[]

(

int

i

)

Bracket operator returning an l-value. i must range in [0..2].

operator[]() [2/2]

qreal operator[]

(

int

i

)

const

Bracket operator, with a constant return value. i must range in [0..2].

orthogonalVec()

Vec orthogonalVec

(

)

const

Returns a Vec orthogonal to the Vec. Its norm() depends on the Vec, but is zero only for a null Vec. Note that the function that associates an orthogonalVec() to a Vec is not continous.

projectOnAxis()

void projectOnAxis

(

const Vec &

direction

)

Projects the Vec on the axis of direction direction that passes through the origin.

direction does not need to be normalized (but must be non null).

projectOnPlane()

void projectOnPlane

(

const Vec &

normal

)

Projects the Vec on the plane whose normal is normal that passes through the origin.

normal does not need to be normalized (but must be non null).

setValue()

void setValue	(	qreal	X,
		qreal	Y,
		qreal	Z
	)

Equal operator. Vec &operator=(const Vec &v) { x = v.x; y = v.y; z = v.z; return *this; }

Set the current value. May be faster than using operator=() with a temporary Vec(x,y,z).

squaredNorm()

qreal squaredNorm

(

)

const

Returns the squared norm of the Vec.

unit()

Vec unit

(

)

const

Returns a unitary (normalized) representation of the vector. The original Vec is not modified.

Friends And Related Function Documentation

cross

Vec cross ( const Vec &  a, const Vec &  b  )

friend

Cross product of the two Vec. Mind the order !

operator!=

bool operator!= ( const Vec &  a, const Vec &  b  )

friend

Returns true only when the two vector are not equal (see operator==()).

operator* [1/3]

qreal operator* ( const Vec &  a, const Vec &  b  )

friend

Dot product of the two Vec.

operator* [2/3]

Vec operator* ( const Vec &  a, qreal  k  )

friend

Returns the product of the vector with a scalar.

operator* [3/3]

Vec operator* ( qreal  k, const Vec &  a  )

friend

Returns the product of a scalar with the vector.

operator+

Vec operator+ ( const Vec &  a, const Vec &  b  )

friend

Returns the sum of the two vectors.

operator- [1/2]

Vec operator- ( const Vec &  a )

friend

Unary minus operator.

operator- [2/2]

Vec operator- ( const Vec &  a, const Vec &  b  )

friend

Returns the difference of the two vectors.

operator/

Vec operator/ ( const Vec &  a, qreal  k  )

friend

Returns the division of the vector with a scalar.

Too small k values are not tested (unless the library was compiled with the "debug" Qt CONFIG flag) and may result in NaN values.

operator==

bool operator== ( const Vec &  a, const Vec &  b  )

friend

Returns true when the squaredNorm() of the difference vector is lower than 1E-10.

operator^

Vec operator^ ( const Vec &  a, const Vec &  b  )

friend

Cross product of the two vectors. Same as cross().

Member Data Documentation

x

qreal x

The internal data representation is public. One can use v.x, v.y, v.z. See also operator[]().

y

qreal y

z

qreal z