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Advanced Techniques in Distributed Ray Tracing: Importance Sampling and BRDF Integration

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This document covers advanced methodologies in distributed ray tracing, focusing on the Render Equation, Bidirectional Reflectance Distribution Function (BRDF), and importance sampling techniques. It elaborates on the integration of radiance contributions from various light sources and directions in a scene. The implementation sections guide how to generate sufficient samples, compute the importance of each sample, and utilize inverse cumulative distribution functions (CDF) for efficient sampling. The document also explores direct and indirect lighting models, enhancing realistic rendering through efficient computational techniques.

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Advanced Techniques in Distributed Ray Tracing: Importance Sampling and BRDF Integration

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  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

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