jm::Nurbs Class Reference

NURBS (nonuniform rational basis splines) are a generalized form of B-Splines. They allow for modeling many curves, including projected forms. DXF splines, for example, are based on NURBS. This class provides functions and methods to work with NURBS. More...

Inheritance diagram for jm::Nurbs:

Public Member Functions
	Nurbs ()
	Default constructor for the Nurbs class.
	Nurbs (uint32 degree, const Vertex3 *controlpoints, size_t controlCount, const double *knots, size_t knotCount, const double *weights, size_t weightCount)
	Constructor for the Nurbs class.
	~Nurbs () override
	Destructor.
Vertex3	point (double t)
	Returns a point on the curve at a given parameter value.
double	start () const
	This method returns the smallest value of t.
double	end () const
	This method returns the maximum value of t.
size_t	startIndex () const
	The start index for calculating min t.
size_t	endIndex () const
	The start index for calculating max t.
size_t	controlPointCount () const
	Returns the number of control points.
size_t	knotCount () const
	Returns the knot count.
double	knot (size_t index) const
	returns a knot
bool	isClamped () const
	Returns true, if the NURBS is clamped.
bool	isClosed () const
	Returns true, if NURBS is closed.
uint32	degree () const
	Returns the degree.
jm::Vertex3	controlPoint (size_t index) const
double	weight (size_t index) const
double	N (size_t i, uint32 k, double t)
	This method returns the value of N_i,k(t).
double	R (size_t i, uint32 k, double t)
	This method returns the weight of the control points R_i,k(t).
Public Member Functions inherited from jm::Object
	Object () noexcept
	Constructor.
virtual	~Object () noexcept
	Destructor.
void	release () noexcept
	Decreases the reference counter and releases the object immediately when the reference counter becomes 0.
Object *	retain () noexcept
	Increases the reference counter of this object by 1.
Object *	autorelease () noexcept
	Same function as release(), but releases the object with a delay if the reference counter is 0. AutoreleasePool::drain() must be called in the to release the object.
int32	referenceCount () const noexcept
	Returns the value of the reference counter.
virtual bool	equals (const Object *other) const
	Comparison of objects.
virtual String	displayName () const
	Returns the display name of the object intended to present to a user.
virtual void	printDiffInfo (DiffOperation operation, Object *other) const
	Output method for outputting the diff results for the diff algorithm.
void	setHighBit (bool status) noexcept
bool	highBit () const noexcept

Detailed Description

NURBS (nonuniform rational basis splines) are a generalized form of B-Splines. They allow for modeling many curves, including projected forms. DXF splines, for example, are based on NURBS. This class provides functions and methods to work with NURBS.

Advantages of NURBS (http://www-lehre.inf.uos.de/~cg/2006/PDF/kap-07.pdf):

• NURBS are a generalization of B-Splines. When hi = 1 for all i, the NURBS curve reduces to the corresponding B-Spline curve.
• NURBS are invariant under perspective projection. This means that not all curve points need to be projected, only the control points need to be projected and then connected to form a curve.
• NURBS are capable of describing circles (unlike non-rational B-Splines).

Constructor & Destructor Documentation

Nurbs() [1/2]

jm::Nurbs::Nurbs

(

)

Default constructor for the Nurbs class.

Nurbs() [2/2]

jm::Nurbs::Nurbs	(	uint32	degree,
		const Vertex3 *	controlpoints,
		size_t	controlCount,
		const double *	knots,
		size_t	knotCount,
		const double *	weights,
		size_t	weightCount
	)

Constructor for the Nurbs class.

Parameters

degree	The degree of the polynomial.
controlpoints	An array of control points.
controlCount	The length of the controlpoints array.
knots	An array of knots.
knotCount	The length of the knots array.
weights	An array of weights.
weightCount	The length of the weights array.

~Nurbs()

jm::Nurbs::~Nurbs ( )

override

Destructor.

Member Function Documentation

controlPoint()

jm::Vertex3 jm::Nurbs::controlPoint

(

size_t

index

)

const

controlPointCount()

size_t jm::Nurbs::controlPointCount

(

)

const

Returns the number of control points.

degree()

uint32 jm::Nurbs::degree

(

)

const

Returns the degree.

end()

double jm::Nurbs::end

(

)

const

This method returns the maximum value of t.

endIndex()

size_t jm::Nurbs::endIndex

(

)

const

The start index for calculating max t.

isClamped()

bool jm::Nurbs::isClamped

(

)

const

Returns true, if the NURBS is clamped.

isClosed()

bool jm::Nurbs::isClosed

(

)

const

Returns true, if NURBS is closed.

knot()

double jm::Nurbs::knot

(

size_t

index

)

const

returns a knot

knotCount()

size_t jm::Nurbs::knotCount

(

)

const

Returns the knot count.

N()

double jm::Nurbs::N	(	size_t	i,
		uint32	k,
		double	t
	)

This method returns the value of N_i,k(t).

Parameters

i	The index of the control point.
k	The degree of the polynomial for which N is returned. (Not necessarily the degree of the NURBS)
t	The parameter value along the curve.

Returns

The value of N_i,k(t) at the given parameter value.

point()

Vertex3 jm::Nurbs::point

(

double

t

)

Returns a point on the curve at a given parameter value.

Parameters

t	The parameter value on the curve. Should be in the range [0, t_max].

Returns

The point on the curve at the given parameter value.

R()

double jm::Nurbs::R	(	size_t	i,
		uint32	k,
		double	t
	)

This method returns the weight of the control points R_i,k(t).

Parameters

i	The index of the control point.
k	The degree of the polynomial for which R is returned.
t	The parameter value along the curve.

Returns

The weight of the control point at the given parameter value.

start()

double jm::Nurbs::start

(

)

const

This method returns the smallest value of t.

startIndex()

size_t jm::Nurbs::startIndex

(

)

const

The start index for calculating min t.

weight()

double jm::Nurbs::weight

(

size_t

index

)

const