Abstract: The real spherical harmonics have been used extensively in computer graphics, but the conventional representation is in terms of spherical coordinates and involves expensive trigonometric functions. While the polynomial form is often listed for low orders, directly evaluating the basis functions independently is inefficient. This paper will describe in detail how recurrence relations can be used to generate pre-factored evaluation code that is smaller, more efficient, and presents a performance comparison of several alternative techniques to evaluate the spherical harmonics.