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Photon Tracing with Arbitrary Materials. Patrick Yau. Overview. Changes in Photon Map Changes in Photon Tracing Changes in Rendering. Caustic Photon Maps. Used only to store photons corresponding to caustics.

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overview
Overview
  • Changes in Photon Map
  • Changes in Photon Tracing
  • Changes in Rendering
caustic photon maps
Caustic Photon Maps
  • Used only to store photons corresponding to caustics.
  • Created by emitting photons towards the specular objects in the scene and storing these as they hit diffuse surfaces.
  • Photons are highly focused into a small area.
caustic photon maps cont d
Caustic Photon Maps (cont’d)
  • Separate into two photon maps because:
    • Render caustics is faster because it contains only photons related to caustics
    • Locating photons in global photon map is faster
      • Fewer photons
    • Improves accuracy of radiance estimate
      • Photons have energy levels that are more similar.
      • Caustics photons have high density and low energy
      • Normal photons have low density and high energy.
photon scattering
Photon Scattering
  • Specular reflection
    • Photons that hit specular surfaces are reflected in the mirror direction.
    • Calculated the same as specularly reflected rays in raytracing.
    • The power of the photon should be scaled by the reflectivity or the mirror. Unless using Russian Roulette.
photon scattering1
Photon Scattering

Diffuse reflection

  • Pick random direction in the hemisphere above the intersection point with a probability proportional to the cosine of the angle with the normal.
  • Photon map can be used as a heuristic for shadows.
photon scattering2
Photon Scattering
  • Arbitrary BRDF Reflection
    • New photon direction is computed by importance sampling the BRDF.
    • If importance-sampling function is not available then pick a random direction.
    • e.g. Ward’s anisotropic model, Lafortune’s reflection model (previous lecture)
photon scattering3
Photon Scattering
  • Russian Roulette:
    • Reflection or Absorption:
photon scattering4
Photon Scattering
  • Russian Roulette:
    • Specular or Diffuse Reflection:
photon mapping rendering1
Photon Mapping: Rendering
  • The Direct Illumination term:
    • Computed by sending shadow rays towards all light sources to check for visibility
    • Two ways: approximate or accurate evaluation
      • Accurate: Use the global photon map to identify the fully illuminated or shadow areas in the scene avoiding the trace of shadow rays.
      • Approximate: evaluate the radiance directly from the photon maps. No need for tracing other rays.
photon mapping rendering2
Photon Mapping: Rendering
  • Classification of photons in Photon Map
photon mapping rendering3
Photon Mapping: Rendering
  • The specular term
    • Is computed using standard Monte Carlo ray tracing by using importance sampling based on the BRDF.
photon mapping rendering4
Photon Mapping: Rendering
  • The caustics term:
    • The radiance is estimated based on the caustics photon map.
    • It is visualized directly and this is the reason why the number of photons in the caustics photon map must be high.
photon mapping rendering5
Photon Mapping: Rendering
  • The soft indirect illumination term
    • The approximate evaluation of this integral is the radiance estimate based on the global photon map.
    • In the accurate evaluation we use importance sampling to compute the indirect illumination (combined with the diffuse BRDF part)
photon mapping rendering6
Photon Mapping: Rendering
  • Estimating Radiance using the Photon Map (for caustics and soft indirect illumination)
    • The information in the photon map can be used to compute the radiance leaving a surface in a given direction. Since the incoming direction is stored with each photon we can integrate the information with any BRDF.
    • To compute the radiance, Lr, leaving an intersection point x at a surface BRDF fr we locate the N photons with the shortest distance to x.
    • Based on the assumption that each photon p represented by ∆ΦpX arriving at X from direction Ψi,p we get:
photon mapping rendering7
Photon Mapping: Rendering
  • *Code taken from Taylor’s lecture.
  • Estimating Radiance
    • 1. radiance_estimate(x,v,n) {
    • 2. locate k nearest photons
    • 3. r = distance to kth nearest photon
    • 4. flux = 0
    • 5. for each photon p {
    • 6. pd = direction of p
    • 7. phi = power of p
    • 8. flux += brdf(x, v, pd)*phi;
    • 9. }
    • 10. return flux/(2*pi*r^2)
    • 11. }
another example
Another example

=

+

Direct Illumination

Indirect Illumination

+

=

Specular Part

references
References
  • Henrik Wann Jensen: “Realistic Image Synthesis using Photon Maps”.
  • Henrik Wann Jensen: “Global Illumination using Photon Maps”.
  • Henrik Wann Jensen: “Rendering Caustics on Non Lambertian Surfaces”.
  • Michael Kaiser and Christian Finger: “Caustics Generation by using Photon Mapping” http://www.mpi-sb.mpg.de/units/nwg3/ws0304/lcn/projects/Michael/