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Improved speed by using DynamicLegendre and precomputing Scaling Factors

This commit is contained in:
Paolo Cignoni 2009-10-14 16:10:42 +00:00
parent 8d8ed1efa8
commit 3705cb3cb9
1 changed files with 38 additions and 5 deletions
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43
vcg/math/spherical_harmonics.h
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@ -40,6 +40,33 @@ class DummyPolarFunctor{
inline ScalarType operator()(ScalarType theta, ScalarType phi) {return ScalarType(0);}
};
template <typename ScalarType, int MAX_BAND = 4>
class ScalingFactor
{
private :
ScalarType k_factor[MAX_BAND][MAX_BAND];
static ScalingFactor sf;
ScalingFactor()
{
for (unsigned l = 0; l < MAX_BAND; ++l)
for (unsigned m = 0; m <= l; ++m)
k_factor[l][m] = Sqrt( ( (2.0*l + 1.0) * Factorial<ScalarType>(l-m) ) / (4.0 * M_PI * Factorial<ScalarType>(l + m)) );
}
public :
static ScalarType K(unsigned l, unsigned m)
{
return sf.k_factor[l][m];
}
};
template <typename ScalarType, int MAX_BAND>
ScalingFactor<ScalarType, MAX_BAND> ScalingFactor<ScalarType, MAX_BAND>::sf;
/**
* Although the Real Spherical Harmonic Function is correctly defined over any
* positive l and any -l <= m <= l, the two internal functions computing the
@ -50,19 +77,22 @@ template <typename ScalarType, int MAX_BAND = 4>
class SphericalHarmonics{
private :
inline static ScalarType scaling_factor(unsigned l, unsigned m)
static DynamicLegendre<ScalarType, MAX_BAND> legendre;
static ScalarType scaling_factor(unsigned l, unsigned m)
{
return Sqrt( ( (2.0*l + 1.0) * Factorial<ScalarType>(l-m) ) / (4.0 * M_PI * Factorial<ScalarType>(l + m)) );;
return ScalingFactor<ScalarType, MAX_BAND>::K(l,m);
}
inline static ScalarType complex_spherical_harmonic_re(unsigned l, unsigned m, ScalarType theta, ScalarType phi)
{
return scaling_factor(l, m) * Legendre<ScalarType>::AssociatedPolynomial(l, m, Cos(theta), Sin(theta)) * Cos(m * phi);
return scaling_factor(l, m) * legendre.AssociatedPolynomial(l, m, Cos(theta), Sin(theta)) * Cos(m * phi);
}
inline static ScalarType complex_spherical_harmonic_im(unsigned l, unsigned m, ScalarType theta, ScalarType phi)
{
return scaling_factor(l, m) * Legendre<ScalarType>::AssociatedPolynomial(l, m, Cos(theta), Sin(theta)) * Sin(m * phi);
return scaling_factor(l, m) * legendre.AssociatedPolynomial(l, m, Cos(theta), Sin(theta)) * Sin(m * phi);
}
ScalarType coefficients[MAX_BAND * MAX_BAND];
@ -83,7 +113,7 @@ public :
if (m > 0) return SQRT_TWO * complex_spherical_harmonic_re(l, m, theta, phi);
else if (m == 0) return scaling_factor(l, 0) * Legendre<ScalarType>::Polynomial(l, Cos(theta));
else if (m == 0) return scaling_factor(l, 0) * legendre.Polynomial(l, Cos(theta));
else return SQRT_TWO * complex_spherical_harmonic_im(l, -m, theta, phi);
}
@ -154,6 +184,9 @@ public :
}
};
template <typename ScalarType, int MAX_BAND>
DynamicLegendre<ScalarType, MAX_BAND> SphericalHarmonics<ScalarType, MAX_BAND>::legendre;
}} //namespace vcg::math
#endif