Functional Image Synthesis

Pan

• An image synthesis “language”

• Images are functions

• Continuous and infinite

• Embedded in a functional host language

• Reusable optimizing compiler

Examples

What’s an image?

• Assignment of color to points:

R2 Color

• Infinite, but color may be transparent

• Useful generalization:

R2

Expressing functions

• Use -calculus (Church, Curry, etc):

• Or, non-anonymously:

• Currying isomorphism:

( )

Good for partial application

Spatial transforms

Images

Higher-order functions

Apply filter “about” a point:

Examples

Programming example

Another

Some details

Another

Implementation

• An “embedded language”, but compiled.

• Programs manipulate expression trees.

• Almost transparent, via overloading.

• Automatic full inlining.

• Simplification via smart constructors.

• First-order CSE and loop hoisting.

• Easy to reuse for new “language”.

More examples

Conclusions

• Modular & efficient image synthesis• DSL design & implementation technique:

– Simple, computable semantics– Embed in functional host language– Reusable optimizer & code generator

• To try: sound, 3D, …• Freely available – try it out:

http://research.microsoft.com/~conal/pan