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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.
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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 2nd Ed. 15.3
Bi-direction Path Tracing • From Pharr’s PBRT 2nd Ed., Section 15.3.5. • Subpath from camera: p1, p2, …pi • Subpath from light: q1, q2, …qj • The whole path is p1, …, pi, qj, …, q1 • 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 2nd 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
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. • Case1: a diffuse surface and a few area lights • Case2: 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 2nd 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