What is spherical harmonic coefficients?
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular functions (sines and cosines) via Fourier series.
How do you write spherical harmonics?
As stated, the spherical harmonics—almost always written as Ymℓ(θ, φ)—form an orthogonal and complete set. This means that they constitute an orthogonal basis of the Hilbert space of square integrable functions of the spherical polar angles θ and φ.
What kind of lighting is spherical harmonic lighting?
Spherical harmonic (SH) lighting is a family of real-time rendering techniques that can produce highly realistic shading and shadowing with comparatively little overhead. All SH lighting techniques involve replacing parts of standard lighting equations with spherical functions that have been projected…
How are spherical harmonics used to represent 2D functions?
Spherical Harmonics is a way to represent a 2D function on a surface of a sphere. Instead of spatial domain (like cubemap), SH is defined in frequency domain with some interesting properties and operations relevant to lighting that can be performed efficiently.
How are light probes related to spherical harmonics?
Now that you understand the basic operations and properties of SH, we can think how to apply them to GI. A light probe records how much light is coming from every direction to the point where the probe is located. This is a 2D function on a sphere and can be represented as SH (or 3 SH function for red, green and blue).
How are spherical harmonics similar to sine waves?
Spherical harmonics are just like Fourier transforms, but instead of sine waves, they use a spherical function, so instead of linear functions (such as images), they can represent functions defined on the sphere (such as environment maps).