Distributed Ray Tracing Part 2

1. Distributed Ray Tracing Part 2 黃聰賢

2. Overview • Render Equation • BRDF • Importance Sampling • Implementation

3. Rendering Equation (1) ωo x • is the radiance from a point to given direction wo

4. Rendering Equation (2) ωo x • is the emitted radiance • is non-zero if x is emissive(a light source)

5. Rendering Equation (3) ωi ωo x • Sum of the contributionfrom all of the other direction in the scene

6. Rendering Equation (4) ωi ωo x • Radiance from all hemisphere direction

7. BRDF

8. Integration over hemisphere y0 ω0 y1 normal ω1 eye yi ωi x Spherical sample direction L(x,wo) = (2 PI / #samples) * ∑ [BRDF(x,wo,wi)*L(yi,-wi) * cos(n,ωi)]

9. Spherical Uniform Sampling Generate two uniform random variables in [0,1) : ξx, ξy x = sin(θ) cos(φ) y = sin(θ) sin(φ) z = cos(θ) φ

10. Importance Sampling

11. Why? Too Many Too Coarse Importance

12. Converge Speed

13. Implement of Importance Sampling • Generate enough samples (uniform samples) • Compute the importance of each sample • Build the CDF of importance • Generate uniform random variables over [0,1) • Use Inverse CDF to choose a sample • Divide the contribution of each sample by its probability

14. Direct Lighting • Use Phong Lighting Model. • Add the lighting effect if visibility is one. I * (Kd * dot(N, L) + Ks * pow(dot(E, R), Ns) ) N E L R

15. Indirect Lighting • Use importance sampling to choose direction • If the direction hits a point yi ,compute the yi direct lighting y0 ω0 y1 normal ω1 eye yi ωi x

16. L(x, ωo) = (2 PI / #samples) * ∑ [BRDF(x, ωo, ωi)*L(yi,-ωi) * cos(n,ωi)] L(x, ωo) = (1.0 / #samples) * ∑ { L(yi ,-ωi) * [Kd * dot(ωi, N) + Ks * pow(dot(E, reflect(ωi, N)), Ns) ] } N E yi ωi x