vcg::math::Legendre< ScalarType > Class Template Reference

#include <legendre.h>

Inheritance diagram for vcg::math::Legendre< ScalarType >:

[legend]

List of all members.

Static Public Member Functions
static double	AssociatedPolynomial (unsigned l, unsigned m, ScalarType cos_theta, ScalarType sin_theta)
static double	AssociatedPolynomial (unsigned l, unsigned m, ScalarType x)
static double	Polynomial (unsigned l, ScalarType x)
Static Protected Member Functions
static double	legendre_next (unsigned l, unsigned m, ScalarType P_lm1, ScalarType P_lm2, ScalarType x)
static ScalarType	legendre_next (unsigned l, ScalarType P_lm1, ScalarType P_lm2, ScalarType x)
static double	legendre_P_l (unsigned l, ScalarType x)
static double	legendre_P_l_m (unsigned l, unsigned m, ScalarType cos_theta, ScalarType sin_theta)
static double	legendre_P_m_m (unsigned m, ScalarType sin_theta)
static double	legendre_P_m_mplusone (unsigned m, ScalarType p_m_m, ScalarType x)

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Detailed Description

template<typename ScalarType>
class vcg::math::Legendre< ScalarType >

Definition at line 38 of file legendre.h.

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Member Function Documentation

template<typename ScalarType>

static double vcg::math::Legendre< ScalarType >::AssociatedPolynomial	(	unsigned	l,
		unsigned	m,
		ScalarType	cos_theta,
		ScalarType	sin_theta
	)			[inline, static]

Reimplemented in vcg::math::DynamicLegendre< ScalarType, MAX_L >, vcg::math::DynamicLegendre< double, MAX_BAND >, vcg::math::DynamicLegendre< ScalarType, MAX_BAND >, and vcg::math::DynamicLegendre< float, MAX_BAND >.

Definition at line 160 of file legendre.h.

template<typename ScalarType>

static double vcg::math::Legendre< ScalarType >::AssociatedPolynomial	(	unsigned	l,
		unsigned	m,
		ScalarType	x
	)			[inline, static]

Reimplemented in vcg::math::DynamicLegendre< ScalarType, MAX_L >, vcg::math::DynamicLegendre< double, MAX_BAND >, vcg::math::DynamicLegendre< ScalarType, MAX_BAND >, and vcg::math::DynamicLegendre< float, MAX_BAND >.

Definition at line 154 of file legendre.h.

template<typename ScalarType>

static double vcg::math::Legendre< ScalarType >::legendre_next	(	unsigned	l,
		unsigned	m,
		ScalarType	P_lm1,
		ScalarType	P_lm2,
		ScalarType	x
	)			[inline, static, protected]

Associated Legendre Polynomial three term Recurrence Relation. Raises the band index.

Definition at line 54 of file legendre.h.

template<typename ScalarType>

static ScalarType vcg::math::Legendre< ScalarType >::legendre_next	(	unsigned	l,
		ScalarType	P_lm1,
		ScalarType	P_lm2,
		ScalarType	x
	)			[inline, static, protected]

Legendre Polynomial three term Recurrence Relation

Definition at line 45 of file legendre.h.

template<typename ScalarType>

static double vcg::math::Legendre< ScalarType >::legendre_P_l	(	unsigned	l,
		ScalarType	x
	)			[inline, static, protected]

Definition at line 99 of file legendre.h.

template<typename ScalarType>

static double vcg::math::Legendre< ScalarType >::legendre_P_l_m	(	unsigned	l,
		unsigned	m,
		ScalarType	cos_theta,
		ScalarType	sin_theta
	)			[inline, static, protected]

Computes the Associated Legendre Polynomial for any given positive m and l, with m <= l and -1 <= x <= 1.

Definition at line 119 of file legendre.h.

template<typename ScalarType>

static double vcg::math::Legendre< ScalarType >::legendre_P_m_m	(	unsigned	m,
		ScalarType	sin_theta
	)			[inline, static, protected]

Starting relation to compute P_m_m according to the formula:

pow(-1, m) * double_factorial(2 * m - 1) * pow(1 - x*x, abs(m)/2)

which becomes, if x = cos(theta) :

pow(-1, m) * double_factorial(2 * m - 1) * pow(sin(theta), abs(m)/2)

Definition at line 76 of file legendre.h.

template<typename ScalarType>

static double vcg::math::Legendre< ScalarType >::legendre_P_m_mplusone	(	unsigned	m,
		ScalarType	p_m_m,
		ScalarType	x
	)			[inline, static, protected]

Recurrence relation to compute P_m_(m+1) given P_m_m at the same x

Definition at line 62 of file legendre.h.

template<typename ScalarType>

static double vcg::math::Legendre< ScalarType >::Polynomial	(	unsigned	l,
		ScalarType	x
	)			[inline, static]

Reimplemented in vcg::math::DynamicLegendre< ScalarType, MAX_L >, vcg::math::DynamicLegendre< double, MAX_BAND >, vcg::math::DynamicLegendre< ScalarType, MAX_BAND >, and vcg::math::DynamicLegendre< float, MAX_BAND >.

Definition at line 148 of file legendre.h.

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

• legendre.h