1 Two Pass Method Components of Phong Illumination Remember the - - PDF document

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Photon Mapping

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– Introduction – Approach Taken – Implementation Details – Results – Appendix/Code

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Computer Graphics as Virtual Photography

camera (captures light) synthetic image camera model (focuses simulated lighting)

processing

photo processing tone reproduction real scene 3D models Photography: Computer Graphics: Photographic print

2 Two Pass Method

• Remember the Phong Illumination Model
• Most complete local illumination

approximation.

specular diffuse ambient

V) R ( N) S ( ) (

∑ ∑

• +
• +

=

i k i i s i i i d a a

e

L k L k L k V L

Components of Phong Illumination

• Specular

– Dependent upon incoming and outgoing direction – Mirror-like reflection

• Diffuse

– Assumes equal reflectance in all directions – BDRF is constant

Which Global Illumination Technique?

[Cohen85] [Heckbert84]

• 1. Why a Two-Pass Global

Illumination Method?

• Ray Tracing

– Good for specular reflections – Bad for diffuse reflections – View Dependent – Computationally intensive

• Radiosity

– Good for diffuse reflections – Bad for specular reflections – View independent – Even more computationally intensive

• A two-pass method gives us the best of both worlds

Two Pass Method

• Pass 1: View independent (radiosity)
• Pass 2: View dependent (ray tracing)

Two Pass Method

• Four mechanisms of light transport between two

surfaces

Diffuse to Diffuse Specular to Diffuse Diffuse to Specular Specular to Specular BRDF (std radiosity) (std ray tracing)

[Wallace87]

3 Two Pass Method - Preprocess

• Pass 1: Use hemi-cube radiosity method

– View independent pass – Will provide diffuse reflections for all objects – Already handles diffuse-to-diffuse reflections – Basic algorithm is modified to account for

• Diffuse reflections from specular sources
• Diffuse transmission
• Handles curved surfaces (Wallace)

(Sillion extended to all surface types)

Two Pass Method - Preprocess

• Recall:

– Form factors give fraction of light emitted at

• ne patch that arrive at another patch
• Modification:

– Increase form factor for patch to account for additional light arriving at the point via specular reflection. – And transmission

Two Pass Method - Preprocess

• Form Factor Modification

Like calculating reflection

[Wallace87]

Two Pass Method – Preprocessing Results For each surface, the diffuse intensity emitted by the surface has been calculated, whether light is received from diffuse or specular sources.

Two Pass Method - Pass Two

• Pass 2: Ray Tracing

– View dependent pass – Calculation per pixel limits work – Ray tracing already accounts for specular-to- specular – Must be modified to accurately account for diffuse-to-specular

Two Pass Method - Pass Two Diffuse-to-specular

• Ideally, would consider incoming light from all

directions that contribute to specular component.

• In reality, the light contributing MOST HEAVILY to

specular reflection comes from direction of incident ray.

• This allows limiting integration to solid angle over

which the weighted intensity is significant, rather than whole hemisphere.

4 Two Pass Method - Pass Two The Reflection Frustum

• Light is collected from a solid angle

surrounding the ray of incidence

• The smaller angle, the more mirror-like

(material properties)

• Solid angle is approximated by point samples
• Light to be considered for specular reflection

is determined by a weighted average of the sampled rays

The Reflection Frustum

• Sampling intensities arrive through reflection frustum
• Incoming specularity is obtained recursively,

reducing resolution each level

[Wallace87]

The Reflection Frustum

• Acts like integration with BDRF providing pre-

computed importance weights

• Used a 10 x 10 pixel array
• Used z-buffer
• Diffuse component - Gouraud shading
• Anti-aliasing performed by jittered rotation of

frustum

• Solution similar to that used in distributed ray tracing

Two Pass Method

• Reflection frustum - example

[Wallace87]

Two Pass Method - Example

Perfectly diffuse floors Floors after “polishing”

[Wallace87]

Two Pass Method - Summary

• Rendering in Two Passes
• Pass 1: Radiosity

– Considers diffuse-to-diffuse reflections – Considers specular-to-diffuse reflections

• Pass 2: Ray Tracing

– Considers diffuse-to-specular reflections – Considers specular-to-specular reflections

• The total light emitted at a point is

– Diffuse component, as calculated in Pass 1, plus – Specular component, as calculated in Pass 2

5 Results

[Wallace87]

Results

[Wallace87]

Two Pass Method - Example

Without diffuse Diffuse to diffuse added Full solution

[Wallace87]

Ray Tracing

• Integrated aspects of light and object

interaction that had formerly been handled by separate algorithms:

– Hidden surface removal – Reflection – Refraction – Shadows – Global specular interaction

Turner Whitted

Ray Tracing - Problems

• Object - ray intersection
• Ray traced images are point sampled

– “Too sharp” (super real) – “wrong image” – Sharp shadows – Sharp Reflection/Refraction

• Multiple reflections especially are too sharp

– Aliasing

• Doesn’t handle major light transport functions

– Diffuse interaction – Scattering of light – Caustics

• Computation time

Ray Tracing – Avoiding Ray Traced Look

• Avoiding that “ray traced look” , i.e., handle

diffuse interaction

– Ray tracing is point sampling

• 1 ray per pixel

– Assumes pixel is a single point – Assumes pin hole camera

• 1 ray for transmission & reflection

– Assumes all reflection is specular – Assumes that BRDF for all incoming directions is single

• ut going direction

6

Ray Tracing – Avoiding Ray Traced Look

• Problem

– Only considering single path of light to eye for each pixel. – Only considering rays in perfectly reflective and transmissive directions.

• Some approaches

– Trace objects other than rays – Stochastic sampling

The Rendering Equation

• Local vs Global Illumination Models

Local illumination - only considers direct component Global illumination - also considers other scattered component

… + + + + =

scattering 3rd 3 scattering 2nd 2 scattering 1st direct

) ( ) ( ) ( Rg g Rg g Rg g g I ε ε ε ε

Indirect lighting

• The ambient kludge

– Used to approximate light in those latter term of the rendering equation expansion

Indirect Lighting

Classic ray tracing Using photon mapping

Photon Mapping

• Combines “backward”/ “reverse” ray tracing with

stochastic ray tracing

• Used to simulate the interaction of light with a

variety transparent substances (caustics)

– Glass – Water – Diffuse Inter-reflections between illuminated objects – Effects of particulate matter

• Smoke
• Water vapor

Photon Mapping - Motivation

Without With

7 Photon Mapping

• Henrik Wann Jensen 95/96
• Simulates the transport of individual photons

emitted from light sources

• Photons bounce off specular surfaces
• Photons deposited on diffuse surfaces
• Photons collected by ray tracing from eye
• http://www.ypoart.com/

Photon Mapping

• Pass 1 – Shoot and Store Photons

– photons are shot from the light into the scene. – Photons are allowed to interact with objects in the environment – Where photons fall are stored in a special data structure called a “photon map” – 1000s of photons not billions

• Statistical approximation based on density

Photon Mapping

• Shooting photons

point directional square general [Jensen 2002]

Photon Mapping

• Photon Scattering

[Jensen 2002]

Photon Map

• The photon
• Placed in k-d tree for efficient access

Photon Mapping

• Pass 2 – Gather illumination

– Use ray tracing – Direct illumination determined by ray tracing – Indirect illumination determined by stochastically sampling photon map

8 Monte Carlo methods

• Driven by chance / randomness
• Rendering and Monte Carlo

– Multiple rays per pixel

• See how many reach a light

– Multiple rays from light

• See how many reach the eye

– Photon Mapping

• Goes from both sides

Photon Mapping - Caustics

• Pattern of light focused on a surface after having
• riginal light path bent by intermediate surface.

[Jensen]

Caustics

Reflective caustics Refractive caustics Yves Poissant

Photon Mapping

• Three separate photon maps

– Global – photon emitted toward all objects – Caustics – specular to diffuse interactions – Volume – for volumetric effects

Photon Mapping

caustic global

The Light of Mies van der Rohe

2000ET

9 Photon Mapping in real time

• video

Want to learn more? Summary

• Fixing ray tracing

– Spawning complex structures (cones, cylinders, etc.) – Stochastic sampling (distributed ray tracing, monte carlo) – “backwards” ray tracing (Photon Mapping)

• Break.