[GAMES202]Lecture Note 4

Deeper look into PCF

Convolutional Weighted Filtering in PCF:

Optimization Bottleneck: Averaging every texel inside the filter region (ave. blocker depth and visibility, step 1 and 3 in PCSS) Solution: sampling, cons: noisy (temporal effect: flickering)

Variance Soft Shadow Mapping, VSM

Faster, and more rough version of PCSS?

Motivation: the slow performance of PCSS at step 3 Idea: use CDF of Normal Distribution to approximate depth distribution Key: Fast computation of mean $\mu$ and variance $\sigma$

Solution:

Mean: Hardware MIPMAPing / Summed Area Tables, SAT Variance: (get $x^2$ through render-to-texture: multi-output, while generating $x$)

CDF of Gaussian PDF: Error Function, ERF (numerical, not analytical solution)

One more step: Chebyshev’s Inequality, instead of Gaussian CDF

The Remaining Issue: PCSS Step 1 Averaging the blocker depth $z_{occ}, \text{where } z_{occ}<t$ in filtering region Avaliable: $E(z)$ through MIPMAP, $P(\text{unocc}|z)=P(z>t)$ through Chebyshev Assumption: all $z_\text{unocc}=t$ (assumes surface parallel to light?) Anormalies caused by this assumption: light leaking

Mean Calculation for arbitrary rectangular: Range Query

MIPMAP Only for square, needs interpolation

SAT Preprocess: prefix sum (with Inclusion-Exclusion Principle in 2D) Parallelization: 2-pass, first row then column (multiple 1-D prefix-sum each row/column)

Moment Shadow Mapping

Motivation: more accurate distribution for VSSM using higher moments

Moments and orders: first $m$ orders of moments represents a function (CDF here!) with $m/2$ steps. $\text{order} = 4$ is fine, optimize time cost with packing&unpacking (SIMD?)