BlendCubic Class Reference

Normalized blending functions (1-r²)³. More...

#include <blend.h>

Inheritance diagram for BlendCubic:

Public Member Functions
	BlendCubic (const double &, const double &=1.0)
	Creates a cubic polynomial potential function.
virtual double	Eval (const double &) const
	Computes the falloff function value.
virtual double	Gradient (const double &) const
	Computes the first derivative of the falloff function.
virtual double	K (const double &, const double &) const
	Returns the Lipschitz constant of the blend.
virtual BlendCubic *	Copy () const
	Deep copy.
double	Radius (const double &) const
	Computes the radius of the blend given a threshold value.
void	Analytic (const Quadric &, Polynomial &) const
	Compute the closed form expression of the field along the ray.
virtual double	K () const
	Returns the Lipschitz constant.
Public Member Functions inherited from BlendCompact
	BlendCompact ()
	Empty.
	BlendCompact (const double &, const double &)
	Stores the radius of influence and the strength (maximum intensity).
virtual	~BlendCompact ()
	Empty.
double	R () const
	Returns the radius of the blend.
double	I () const
	Returns the strength (maximum intensity) of the blend.
virtual void	Scale (const double &)
	Scales the radius if the blending function.
virtual void	Alpha (const double &)
	Scales the maximum intensity of the blending function.
virtual int	Memory () const
	Compute the size of a falloff node.

Protected Member Functions
Cubic	GetPoly () const
	Compute the cubic polynomial.

Additional Inherited Members
Protected Attributes inherited from BlendCompact
double	r = 1.0
	Radius.
double	strength = 1.0
	Strength, i.e., maximum intensity.
double	k = 1.0
	Lipschitz constant.

Detailed Description

Normalized blending functions (1-r²)³.

The Lipschitz constant is computed and stored.

The implementation of the cubic uses a specific optimized technique. The cubic polynomial function may be computed using Horner's scheme, which involves 3 adds and 3 multiplies.

Constructor & Destructor Documentation

BlendCubic()

BlendCubic::BlendCubic ( const double & r, const double & s = 1.0 )

explicit

Creates a cubic polynomial potential function.

Parameters

r	Radius.
s	Strength.

Member Function Documentation

Eval()

double BlendCubic::Eval ( const double & u ) const

virtual

Computes the falloff function value.

Parameters

u	Squared distance.

Implements BlendCompact.

Reimplemented in BlendWyvill.

Gradient()

double BlendCubic::Gradient ( const double & u ) const

virtual

Computes the first derivative of the falloff function.

Parameters

u	Squared distance.

Implements BlendCompact.

Reimplemented in BlendWyvill.

K()

double BlendCubic::K ( const double & a, const double & b ) const

virtual

Returns the Lipschitz constant of the blend.

Parameters

a,b

Interval.

Reimplemented from BlendCompact.

Radius()

double BlendCubic::Radius ( const double & T ) const

virtual

Computes the radius of the blend given a threshold value.

Parameters

T	Threshold value.

Reimplemented from BlendCompact.

Analytic()

void BlendCubic::Analytic	(	const Quadric &	r,
		Polynomial &	p ) const

Compute the closed form expression of the field along the ray.

Simply plug-in the quadric equation of the distance along the ray into the equation of the blending function.

Parameters

r	Equation of the squared distance to the skeleton.
p	Closed form expression of the field along the ray.