mitsuba::VonMisesFisherDistr Struct Reference

Von Mises-Fisher distribution on the 2-sphere. More...

#include <mitsuba/core/vmf.h>

Public Member Functions
	VonMisesFisherDistr (Float kappa=0)
	Create a new von Mises-Fisher distribution with the given concentration parameter. More...
void	setKappa (Float kappa)
	Return the concentration parameter kappa. More...
Float	getKappa () const
	Return the concentration parameter kappa. More...
Float	getMeanCosine () const
	Return the mean cosine of the distribution. More...
Float	eval (Float cosTheta) const
	Evaluate the distribution for a given value of cos(theta) More...
Vector	sample (const Point2 &sample) const
	Generate a sample from this distribution. More...
std::string	toString () const
	Return a string representation. More...

Static Public Member Functions
static Float	forPeakValue (Float x)
	Compute an appropriate concentration parameter so that the associated vMF distribution takes on the value x at its peak. More...
static Float	forMeanLength (Float length)
	Estimate the vMF concentration parameter based on the length of the mean vector that is produced by simply averaging a set of sampled directions. More...
static Float	forMeanCosine (Float g)
	Compute an appropriate concentration parameter so that the associated vMF distribution has the mean cosine g. More...
static Float	convolve (Float kappa1, Float kappa2)
	Compute an concentration parameter that approximately corresponds to the spherical convolution of two vMF distributions. More...

Detailed Description

Von Mises-Fisher distribution on the 2-sphere.

This is a basic implementation, which assumes that the distribution is centered around the Z-axis. All provided functions are implemented in such a way that they avoid issues with numerical overflow.

Author

Wenzel Jakob

Constructor & Destructor Documentation

mitsuba::VonMisesFisherDistr::VonMisesFisherDistr ( Float  kappa = 0 )

inlineexplicit

Create a new von Mises-Fisher distribution with the given concentration parameter.

Member Function Documentation

static Float mitsuba::VonMisesFisherDistr::convolve ( Float  kappa1, Float  kappa2  )

static

Compute an concentration parameter that approximately corresponds to the spherical convolution of two vMF distributions.

For details, see "Directional Statistics" by Mardia and Jupp, p.44

Float mitsuba::VonMisesFisherDistr::eval

(

Float

cosTheta

)

const

Evaluate the distribution for a given value of cos(theta)

static Float mitsuba::VonMisesFisherDistr::forMeanCosine ( Float  g )

static

Compute an appropriate concentration parameter so that the associated vMF distribution has the mean cosine g.

static Float mitsuba::VonMisesFisherDistr::forMeanLength ( Float  length )

static

Estimate the vMF concentration parameter based on the length of the mean vector that is produced by simply averaging a set of sampled directions.

This is an unbiased estimator [Banerjee et al. 05]

static Float mitsuba::VonMisesFisherDistr::forPeakValue ( Float  x )

static

Compute an appropriate concentration parameter so that the associated vMF distribution takes on the value x at its peak.

Float mitsuba::VonMisesFisherDistr::getKappa ( ) const

inline

Return the concentration parameter kappa.

Float mitsuba::VonMisesFisherDistr::getMeanCosine

(

)

const

Return the mean cosine of the distribution.

Vector mitsuba::VonMisesFisherDistr::sample

(

const Point2 &

sample

)

const

Generate a sample from this distribution.

Parameters

sample

A uniformly distributed point on [0,1]^2

void mitsuba::VonMisesFisherDistr::setKappa ( Float  kappa )

inline

Return the concentration parameter kappa.

std::string mitsuba::VonMisesFisherDistr::toString

(

)

const

Return a string representation.

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The documentation for this struct was generated from the following file:

• include/mitsuba/core/vmf.h