/** Evaluates the LegendrePolynomial for L,M at X */
float LegendrePolynomial(int32 L,int32 M,float X)
{
switch(L)
{
case 0:
return 1;
case 1:
if(M == 0)
return X;
else if(M == 1)
return -SafeSqrt(1 - X * X);
break;
case 2:
if(M == 0)
return -0.5f + (3 * X * X) / 2;
else if(M == 1)
return -3 * X * SafeSqrt(1 - X * X);
else if(M == 2)
return -3 * (-1 + X * X);
break;
case 3:
if(M == 0)
return -(3 * X) / 2 + (5 * X * X * X) / 2;
else if(M == 1)
return -3 * SafeSqrt(1 - X * X) / 2 * (-1 + 5 * X * X);
else if(M == 2)
return -15 * (-X + X * X * X);
else if(M == 3)
return -15 * FMath::Pow(1 - X * X,1.5f);
break;
case 4:
if(M == 0)
return 0.125f * (3.0f - 30.0f * X * X + 35.0f * X * X * X * X);
else if(M == 1)
return -2.5f * X * SafeSqrt(1.0f - X * X) * (7.0f * X * X - 3.0f);
else if(M == 2)
return -7.5f * (1.0f - 8.0f * X * X + 7.0f * X * X * X * X);
else if(M == 3)
return -105.0f * X * FMath::Pow(1 - X * X,1.5f);
else if(M == 4)
return 105.0f * FMath::Square(X * X - 1.0f);
break;
case 5:
if(M == 0)
return 0.125f * X * (15.0f - 70.0f * X * X + 63.0f * X * X * X * X);
else if(M == 1)
return -1.875f * SafeSqrt(1.0f - X * X) * (1.0f - 14.0f * X * X + 21.0f * X * X * X * X);
else if(M == 2)
return -52.5f * (X - 4.0f * X * X * X + 3.0f * X * X * X * X * X);
else if(M == 3)
return -52.5f * FMath::Pow(1.0f - X * X,1.5f) * (9.0f * X * X - 1.0f);
else if(M == 4)
return 945.0f * X * FMath::Square(X * X - 1);
else if(M == 5)
return -945.0f * FMath::Pow(1.0f - X * X,2.5f);
break;
};
return 0.0f;
}
/** Evaluates the LegendrePolynomial for L,M at X */
FORCEINLINE FLOAT LegendrePolynomial(INT L,INT M,FLOAT X)
{
switch(L)
{
case 0:
return 1;
case 1:
if(M == 0)
return X;
else if(M == 1)
return -SafeSqrt(1 - X * X);
break;
case 2:
if(M == 0)
return -0.5f + (3 * X * X) / 2;
else if(M == 1)
return -3 * X * SafeSqrt(1 - X * X);
else if(M == 2)
return -3 * (-1 + X * X);
break;
case 3:
if(M == 0)
return -(3 * X) / 2 + (5 * X * X * X) / 2;
else if(M == 1)
return -3 * SafeSqrt(1 - X * X) / 2 * (-1 + 5 * X * X);
else if(M == 2)
return -15 * (-X + X * X * X);
else if(M == 3)
return -15 * appPow(1 - X * X,1.5f);
break;
case 4:
if(M == 0)
return 0.125f * (3.0f - 30.0f * X * X + 35.0f * X * X * X * X);
else if(M == 1)
return -2.5f * X * SafeSqrt(1.0f - X * X) * (7.0f * X * X - 3.0f);
else if(M == 2)
return -7.5f * (1.0f - 8.0f * X * X + 7.0f * X * X * X * X);
else if(M == 3)
return -105.0f * X * appPow(1 - X * X,1.5f);
else if(M == 4)
return 105.0f * Square(X * X - 1.0f);
break;
case 5:
if(M == 0)
return 0.125f * X * (15.0f - 70.0f * X * X + 63.0f * X * X * X * X);
else if(M == 1)
return -1.875f * SafeSqrt(1.0f - X * X) * (1.0f - 14.0f * X * X + 21.0f * X * X * X * X);
else if(M == 2)
return -52.5f * (X - 4.0f * X * X * X + 3.0f * X * X * X * X * X);
else if(M == 3)
return -52.5f * appPow(1.0f - X * X,1.5f) * (9.0f * X * X - 1.0f);
else if(M == 4)
return 945.0f * X * Square(X * X - 1);
else if(M == 5)
return -945.0f * appPow(1.0f - X * X,2.5f);
break;
};
return 0.0f;
}
