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: R 2  Color Infinite, but color may be transparent Useful generalization: R 2  

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: