Precomputed Global Illumination of Isosurfaces

Master’s Defense

Kevin BeasonDavid C. Banks, Advisor

Computer Graphics

• Sphere { position 1 0 0}

Visualization

Data

Image

Scalar Field

Level Sets

Example Level Sets

Rendering

Photon Mapping

Thesis Statement

• Level sets can be displayed in real time with high quality graphics

Is this new?

Local Illumination Global Illumination

Fast (hw)

Slow(sw)

X

X X

NEW

Local vs. Global Illumination

Local Global

Rendering Equation

Global

Local

Perceptual Cues

Boat wake

Boat wake

Image Credits

• Neuron - Blanco, Ouimet, Banks, Beason

• Vislab - Yagi, Banks, Beason

• Boatwake - Sussman, Banks, Beason

• Atrium - Dabrovic, Beason

Global Illumination of Isosurfaces

• Global Illumination is good

• How do I apply it to isosurfaces quickly?

• Precompute GI for all level sets Lc

• Save solutions

How?

• Naïve approach:

• Extract a level set

• Illuminate it (wait…)

• Save illumination

• Repeat for every isovalue c

• Retrieve at runtimeamira

Example heightfield

Scalar Field

Level sets

• Lc = (x,y) : h(x,y) = c

Raised Level Sets

= (x, y, h(x,y)) : h(x,y) = c

Flat Light in D

Flat Light in DxR

Flat Light on Graph

Physical Example

2D Analytic Heightfield Function

plaster

Flattened Light

Raising water level

Sum of Level Sets Illumination

Mathematical Model

• Flattened Light Transport

• 2D case

Duality

• Two isosurfaces

• Same light

Ordinary Light

Flattened Light

Flat 3D Rend. Eqn.

• Requires modification of Emission and Reflection

Flat 4D Rend Eqn.

• Behaves just like ordinary 3D light

• Operates it in raised leaf of R4

Ordinary vs. Flattened

Sample Illumination on Graph

Samples are taken uniformly in Domain (R3)

Interpolate into 3D Texture

• Use Shepard Interpolation

• Or Tent Filter

Apply Texture

• Use Marching Squares to extract Level Set

• Use texture-mapping to apply 3D texture

=

Results

• Movies

• Amira

Thank You

• Brad Futch, Josh Grant, Wilfredo Blanco (amira network), Hui Song

• Dr. Ouimet, Dr. Hussaini, Dr. Piekarewicz, Dr. Smith (Datasets)

• Dr. Liu, Dr. Sussman (Committee)

• Dr. Banks (Advisor)