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

Protected Attributes
Cubic	blend
	Cubic polynomial blending function.
Protected Attributes inherited from BlendCompact
double	r [2] = { 1.0,1.0 }
	Radius and squared 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

Alpha()

void BlendCubic::Alpha ( const double &  t )

virtual

Scales the maximum intensity of the blending function.

This function scales the internal strength parameter of the blending function radius, as well as the Lipschitz constant.

Reimplemented from BlendAnalytic.

Analytic()

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

virtual

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.

Implements BlendAnalytic.

Eval()

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

virtual

Computes the falloff function value.

Parameters

u	Squared distance.

Implements BlendCompact.

Gradient()

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

virtual

Computes the first derivative of the falloff function.

Parameters

u	Input squared distance.

Implements BlendCompact.

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.

Scale()

void BlendCubic::Scale ( const double &  t )

virtual

Scales the radius if the blending function.

This function scales the internal radius, as well as the Lipschitz constant.

Parameters

t	Scaling factor.

Reimplemented from BlendAnalytic.