tfg.math.spherical_harmonics.evaluate_legendre_polynomial

Evaluates the Legendre polynomial of degree l and order m at x.

tfg.math.spherical_harmonics.evaluate_legendre_polynomial(
    degree_l,
    order_m,
    x
)

Defined in math/spherical_harmonics.py.

Note:

This function is implementing the algorithm described in p. 10 of Spherical Harmonic Lighting: The Gritty Details.

Note:

In the following, A1 to An are optional batch dimensions.

Args:

  • degree_l: An integer tensor of shape [A1, ..., An] corresponding to the degree of the associated Legendre polynomial. Note that degree_l must be non-negative.
  • order_m: An integer tensor of shape [A1, ..., An] corresponding to the order of the associated Legendre polynomial. Note that order_m must satisfy 0 <= order_m <= l.
  • x: A tensor of shape [A1, ..., An] with values in [-1,1].

Returns:

A tensor of shape [A1, ..., An] containing the evaluation of the legendre polynomial.