Global Illumination:Radiosity, Photon Mapping & Path Tracing

Rama Hoetzlein, 2009Lecture NotesCornell University

Rendering Equation

Outgoing light

Emitted light

Bidirectional ReflectanceDistribution Function(BRDF)

Incoming light

Incidentattenuation

X Surface pointw Outgoing directionλ Wavelengtht Current time

Integral over all incoming light directions

James Kajiya, 1982. The rendering equation. SIGGRAPH.

incoming

outgoing

x

w

w’

N

Perfect Reflection: Light entering at one angle, leaves at same angle only.

incoming

outgoing

x

w

w’

N

Phong Reflectance: Light entering at some angle, leaves in a uniform diffuse direction, and in a cone of around reflected angle.

incoming

outgoing

x

w

w’

N

Diffuse Reflectance: Light entering at any angle, canleave at any angle, as a different color, or a different time.

incoming

outgoing

x

w

w’

N

Diffuse Reflectance: Light entering at any angle, canleave at any angle, as a different color, or a different time.

Mapping from incoming angle and color to outgoing angle and color,is called the:

Bidirectional Reflectance Distribution Function (BRDF)

Phong is a simple example of a BRDF:

incoming

outgoing

wavelength

time

position

= cos ( θ )n

Bidirectional Reflectance Distribution Function

BRDF can be measured directly from materials.

BRDF

How does a material respond at

every incoming light angle?

Rendering Equation

Outgoing light

Emitted light

Bidirectional ReflectanceDistribution Function(BRDF)

Incoming light

Incidentattenuation

X Surface pointw Outgoing directionλ Wavelengtht Current time

Integral over all incoming light directions

James Kajiya, 1982. The rendering equation. SIGGRAPH.

Global Illumination

Consider all energy moving in a space,

not just the light that reaches the eye.

First used in the study of Heat Transfer (1950s),

how does energy move around a room or object.

First radiosity experiment. 1984

Real box (color-sensitive photography)

Spherical Harmonic Radiosity. 1991

First used in Computer Graphics, 1984

Radiosity

Modeling the interaction of light between diffuse surfaces,C. Goral, K. E. Torrance, D. P. Greenberg and B. Battaile. 1984Computer Graphics, Vol. 18, No. 3.

Fij

ij

Radiosity Solution

One eqn. for each patch

Radiosity - Overview

- Each patch contributes energy to other patches

- Each patch i has a Radiosity equation:

- Solve all equations simultaneously to get the energy at each patch

- What is the hardest part of this eqn?

Ei = Energy emitted Ri = Energy reflectedFij = Energy on patch I from j

Radiosity - Form Factors

What things might contribute to the Form Factor?

Remember: Form Factor is amount of energy hitting patch i from patch j

Radiosity - Form Factors

What things might contribute to the Form Factor?

Remember: Form Factor is amount of energy hitting patch i from patch j

1. Size of the patch Bigger = more energy

2. Angle between patches Direct = more energy

3. Dist. between patches Father = less energy

4. Objects between patches Occlusion = less energy

How much does patch j block patch i ?

Raytracing

Raytracing /w Caustics

Radiosity

Radiosity

• Benefits 1. Very realistic (actually computes energy) 2. View independent.. Compute once, then view 3. Effects: Caustics, Color bleeding

• Drawbacks 1. Even more expensive than raytracing 2. Cannot simulate mirror reflections !

(energy travels diffusely, not coherently)

Combine Raytracing and Radiosity:

- Radiosity to give energy transfer: Color bleeding Light diffusion Caustics Soft shadows

-Raytracing to give view-dependent terms: Reflections Refractions Specular highlights

Hybrid Rendering

Lady and Gentleman at the Virginals Johannes Vermeer (Dutch), 1662-65

Two Pass RenderingWallace, Cohen, Greenberg, 1987

Photon Mapping

Instead of computing all patches simultaneously,

cast “photon rays” from light source.Uses points instead of patches.

Photon Mapping - photons propogate Radiosity – patches don’t move

Photon Mapping

- Much faster.. No form factors

- Need lots of photons but easier to compute.

- Realistic. Photons move the way light does.

Two pass approach:

1. Shoot photons around scene

2. Collect photons to create image (nearby photons are smoothed)

Photon Mapping Made Easy, Yu, Lowther, Shene, SIGCSE 2005

Photon Mapping Made Easy, Yu, Lowther, Shene, SIGCSE 2005

Future Trends

Recent Developments (past 5 yrs):

- Ambient Occlusion – Approximation to Photon Mapping

- Real-Time Raytracing using GPUs

- Hybrid Rasterization and Raytracing

- Volumetric Raytracing & Radiosity