BlendQuartic Class Reference

Quartic polynomial potential function. More...

#include <blend.h>

Inheritance diagram for BlendQuartic:

Public Member Functions
	BlendQuartic (const double &, const double &=1.0)
	Creates a quartic polynomial potential function. More...
virtual	~BlendQuartic ()
	Empty.
virtual double	Eval (const double &) const
	Computes the blending function intensity given a squared distance value.
virtual double	Gradient (const double &) const
	Computes the first derivative of the blending function given a squared distance value.
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 BlendQuartic *	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...
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 double	K () const
	Returns the Lipschitz constant.
virtual double	K (const double &, const double &) const
	Returns the Lipschitz constant of the blend.
virtual int	Memory () const
	Compute the size of a falloff node.

Protected Attributes
Quartic	blend
	Quartic 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

Quartic polynomial potential function.

g(r)=(1-r²)⁴.

The Lipschitz constants are computed and stored internally.

Constructor & Destructor Documentation

BlendQuartic()

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

explicit

Creates a quartic polynomial potential function.

Parameters

r	Radius.
s	Strength.

Member Function Documentation

Alpha()

void BlendQuartic::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 BlendQuartic::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.

Radius()

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

virtual

Computes the radius of the blend given a threshold value.

This function uses the closed form expression of the quadric, cubic or quartic blending function to compute the root of the equation.

Parameters

T	Threshold value

Reimplemented from BlendCompact.

Scale()

void BlendQuartic::Scale ( const double &  t )

virtual

Scales the radius if the blending function.

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

Reimplemented from BlendAnalytic.