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Tuesday, May 12 • 2:30pm - 4:00pm
Functional Geometry: Producing Pure Spaces

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Continuing our investigation of generic compile-time synthesis of geometric spaces from last year's conference, we formalize our approach to designing a spatial computation engine using category theory and functional programming paradigms. We examine cartesian product spaces and develop a theory of computable movements, categorizing our geometric structs as we go, providing a case-study lesson in category theory, geometric algebra, differential geometry, C++ template metaprogramming, and generic lambdas. Specifically, we use C++14 to combine two formalisms: the first is Geometric Algebra, a mathematical system for multidimensional synthesis and analysis. It serves as a unifying substrate for modeling physical relationships in any dimension, and within any ambient metric. The second, Functional Programming, organizes the system of constructions, coincidences, and causes that generate our geometric world. With this union of form and process we demonstrate how morphing structures - kinematic chains, curved-crease origami, knotted weaves and braids, organic forms - can be deductively modeled by structured morphisms - algebras, monadic continuations, declarative constraint networks, and metaprogramming techniques. Developing these programmable abstractions into a C++ template library, we achieve a dimensional fluency - an ability to solve complex geometric problems visually and intuitively. The result is a compact, expressive and extendable system for articulating spatial configurations, and a potential contribution to the Boost library.


avatar for Pablo Colapinto

Pablo Colapinto

UCSB, AlloSphere Research Group
Pablo Colapinto is a video artist and computer scientist specializing in geometric algebra.  He is pursuing a PhD from the Media Art and Technology Program at UC Santa Barbara, having received a bachelor's degree in Visual and Environmental Studies from Harvard University in 2000.  With prior support from an Olivia Long Fellowship in Biology, he has used hypercomplex algebras to explore the dynamics of biological morphogenesis, and is currently... Read More →

Tuesday May 12, 2015 2:30pm - 4:00pm

Attendees (21)