[GAMES 202] Lecture Note 7

PRT Recap

PRT in Glossy Reflection

The light transpart in glossy case:

The BRDF term $\rho(i,o)$ is dependent to the exiting direction $o$ which may be any value, leading to another 2D function $L(o)$. More specifically: for each fixed $o$, we can SH project the light transport part, getting the coefficient $T_i(o)$.

Then for each $i=0...n$, we SH project $T_i(o)$ to get the final SH projection of $L(o)$, the coefficients of the reflected radiance.

This leads to a vector-matrix multiplication at runtime, resulting $O(n^2)$ computations at both precomputation and runtime.

Decomposing Lighting: Another Perspective

Take $B_i$ as a part of the environment lighting, and add them together.

SH: Limitations Low frequency Dynamic lighting but static scenes Huge precomputational costs

More Basis Functions

Wavelet* (All frequencies, pretain only the biggest coefficients for compression, but no fast rorations) Zonal Harmonics Sperical Gaussian Piecewise Constant

Realtime Global Illumination

[What is] one more indirect bounce? Any directly lit surface will act as a light source again (secondary light source w.r.t. primary light source)

[What is] needed for one bounce indirect illumination? Get every direct lit surface (the surface patches)(1) and their contributions (incident radiance) to each point(2). (1) Take each pixel as a surface patch, get through shadow map. (2) The outgoing radiance to eye is known, but we can assume secondary light sources are all lambertian surfaces.

Reflective Shadow Maps, RSM

Rendering equation: area-integration form

For a specific point $p$, not all pixels $p$ (surface patches) can contribute, due to their visibility $V(p\leftrightarrow q)$, distance $\Vert p-q\Vert$ and orientation $\max(0, \cos\theta_p)\cdot \max(0, \cos\theta_q)$. We omit the visibiilty term $V(p\leftrightarrow q)$ since it’s hard to compute.

Acceleration: All pixels in the shadow map can contribute to $p$. We can decease the number of contributing texels by consider only the nearby texels (nearby in shadow map: 2D neighborhood and similar depth) and sampling. (This is an approximation of 1-bounce indirect lighting!)

Pros: Easy implementation (similar to VSM)? Cons: Linear cost to nLights (Shadow Map) No visibility check Too many approximations (distance, diffuse secondary lights, etc.)

Extra notes: RSM is similar to Virtual Point Lights (VPL) in PBR. RSM is a screen space algorithm, but it has all necessary information in 3D space (i.e. the secondary light sources).