Wyvill's cubic falloff function. More...

#include <blend.h>

Inheritance diagram for BlendWyvill:

Public Member Functions
	BlendWyvill (const double &, const double &=1.0)
	Creates Wyvill's cubic falloff function.
virtual	~BlendWyvill ()
	Empty.
virtual BlendWyvill *	Copy () const
	Deep copy.
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.
Public Member Functions inherited from BlendCubic
	BlendCubic (const double &, const double &=1.0)
	Creates a cubic polynomial potential function.
virtual double	K (const double &, const double &) const
	Returns the Lipschitz constant of the blend.
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.
Protected Member Functions inherited from BlendCubic
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

Wyvill's cubic falloff function.

The cubic is defined as \(p(r)=-4/9 r^3+17/9 r^2-22/9 r+1\).

Constructor & Destructor Documentation

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

explicit

Creates Wyvill's cubic falloff function.

Parameters

r	Radius.
s	Strength.

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

virtual

Computes the falloff function value.

Parameters

u	Squared distance.

Reimplemented from BlendCubic.

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

virtual

Computes the first derivative of the falloff function.

Parameters

u	Squared distance.

Reimplemented from BlendCubic.