Wavelet Applications for Rendering

Speaker: Yung Chum Lu

Outline

• Introduction of Rendering• Application I• Application II• Review Haar• Something Interesting

Rendering

Story Board

Create a 2D picture of a 3D world

Ray Tracing

Direct Illumination

Direct Illumination

Direct Illumination

Direct Illumination

Direct Illumination

point light

Path Tracing

point lightpoint light

point light

Direct Illumination

Path Tracing

Pixar

Why Ray Tracing

Tron

Review of 1-D Haar

Mother Basis

General Basis

Scaled Basis

0 1

1

-1

1/2

2

0 1

1/2

2

0 1

1/2

2

1/2

2

Property 1

, ', ' 1, 2 1, 2*n k n k n n k kdt

0 1

1

-1

1/2

2

0 1

1/2

2

Property 2

, 0n kdt 0 1

1

-1

Property 3

1/2

2

0 1

1/2

2

, ', '* 0n k n k dt , ', 'n k n kand are not overlap

0 1

1/2

2

1/2

2

Application I

Triple Product Wavelet Integrals for All-Frequency Relighting

Ren NgStanford University

Ravi RamamoorthiColumbia University

Pat HanrahanStanford University

Triple Core Problem

Double Product Integral

Triple Product Integral

2-D Haar

1/2

2

0 1

1/2

2

0 1

1

Triple Product Integral in 2-D Haar

Preliminaries

All three basis are wavelet

Some are scaling function

Application II

Wavelet Importance Sampling:

Efficiently Evaluating Products of Complex Functions

Petrik ClarbergLund University / UC San

Diego

Wojciech JaroszUC San Diego

Tomas Akenine-M¨ollerLund University

Henrik Wann JensenUC San Diego

The Core Problem

The Core Problem

Warping

Generalized Wavelet Product

Light Field Camera

Ren Ng