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Distributed Ray Tracing Part 2

Distributed Ray Tracing Part 2. 黃聰賢. Overview. Render Equation BRDF Importance Sampling Implementation. Rendering Equation (1). ω o. x. is the radiance from a point to given direction w o. Rendering Equation (2). ω o. x. is the emitted radiance.

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Distributed Ray Tracing Part 2

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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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