Abstract

This visually stimulating presentation investigates the Euclidean, Spherical, and Hyperbolic transformational capacities of Conformal Geometric Algebra [CGA].  I introduce VERSOR, a CGA-based open source cross-platform computer graphics synthesis library for manipulating immersive 3D environments and activating dynamic animations.  VERSOR aims to advance spatial systems thinking by introducing Geometric Algebra to artists and engineers within an integrated multimedia platform.  A highly expressive and remarkably consistent mathematical grammar for describing closed form solutions within various metric spaces, Geometric Algebra is finding increased application in computer vision and graphics, neural nets, DSP, robotics, astronomy, gauge theory, particle physics, and recently in metamaterials research, among other sciences. Geometric Algebra is a combinatoric system of spatial logic derived from William Clifford’s hypercomplex algebras developed in the 1860s.. Introduced into the Geometric Algebra community by physicists Hongbo Li, Alan Rockwood, and David Hestenes in 2001, the particular model implemented here represents a 5-dimensional graded algebra based on Riemannian projection of 3D Euclidean space onto a hypersphere – a higher dimensional mapping which opens the door to a rich set of functions for describing Mobius Transformations typically restricted to the 2D plane.  Integrated with various dynamic solvers, a graphics user interface library and audio synthesis library, VERSOR introduces some novel compositional methods into the CGA research landscape enabling exciting new techniques for the analysis and synthesis of dynamic structures and spaces, such as fluid-like warp fields and spontaneous surface generation.  It provides a path for researchers eager to engage in advanced concepts from fields as diverse as quantum mechanics, bio-surface design, hyperbolic tessellation, form-generation, and worldmaking.  A short introduction to the geometric algebraic system and its provenance is accompanied by explorations into its features and demonstrations of various organic animations. versor.mat.ucsb.edu   wolftype.com/a/grid_x.html

• Pablo Colapinto, Media Arts and Technology,University of California, Santa Barbara, USA

Full text (PDF) p. 474-479