Monte Carlo Path Tracing and Caching Illumination Part

Monte Carlo Path Tracing and Caching Illumination Part II – Bidirectional Path Tracing and Photon Mapping

Path Notation • A path is written as a regular expression. • Examples: – Ray tracing: LD[S*]E – Radiosity: LD*E • Complete global illumination: L(D|S)*E

Path Tracing • See Pharr’s PBRT 2 nd Ed. 15. 3

Bi-direction Path Tracing • From Pharr’s PBRT 2 nd Ed. , Section 15. 3. 5. • Subpath from camera: p 1, p 2, …pi • Subpath from light: q 1, q 2, …qj • The whole path is p 1, …, pi, qj, …, q 1 • Check if pi can see qj • Some call this “vertex connection”

Bi-direction Path Tracing • Many open questions: – Where does pi or qj end? Does it end on specular or diffuse surfaces? – How to calculate the contribution of qj to pi?

Photon Mapping • See Pharr’s PBRT 2 nd Ed. , Section 15. 6 or SIGGRAPH 2008 Course, Advanced Global Illumination using Photon Mapping

Step 1: Photon Emmision From: SIGGRAPH 2008 Course, Advanced Global Illumination using Photon Mapping Figure 4. 1

Step 2: Photon Tracing From: SIGGRAPH 2008 Course, Advanced Global Illumination using Photon Mapping Figure 4. 3

Step 3: Photon Storing From: SIGGRAPH 2008 Course, Advanced Global Illumination using Photon Mapping Figure 4. 4

Caustic vs. Global Photon Maps From: SIGGRAPH 2008 Course, Advanced Global Illumination using Photon Mapping Figure 4. 6

Step 4: Radiance Estimate • Some call this “vertex merging” From: SIGGRAPH 2008 Course, Advanced Global Illumination using Photon Mapping Figure 4. 8

Typical Distributed Ray Path

Integrals • In rendering equation: – Reflection and transmission. – Visibility – Light source • In image formation (camera) – – Pixel Aperture Time Wavelength

Integral of BRDF and Light • Rendering Equation (revisted) • Ignoring emitted light and occlusion, we still have an expensive integral: • Let f(Xi)= (…) I (…) and evaluate its integral with Monte Carlo methods.

Integral of BRDF and Light • Let f(Xi)= (…) I (…) and evaluate its integral. • Case 1: a diffuse surface and a few area lights • Case 2: a specular surface and environment lighting • Uniform sampling isn’t efficient in both cases. Why? (…) I (…)

Can Importance Sampling Cure Them All? • Consider these two example: – How to handle diffuse reflection? – How to handle large area light source? • More in Veach’s thesis (especially Figure 9. 2) – Sampling BRDF vs. sampling light sources

Multiple Importance Sampling • See Pharr’s PBRT 2 nd Ed. 14. 4 (a) sampling the surface reflectance distribution (b) sampling the area light source

Source: Eric Veach, “Robust Monte Carlo Methods for Light Transport Simulation” Page 255, Figure 9. 2. Ph. D. Thesis, Stanford University

References • SIGGRAPH 2008 Course, Advanced Global Illumination using Photon Mapping • SIGGRAPH 2012 Courses, Advanced (quasi) Monte Carlo methods for image synthesis