# Tag Archives: geometric algebra

## Transversion and the Torus

As a first test of the efficacy of the new Transversion Automaton design, I set it up to carve out a simple torus.  Since a torus only has two loops whose product generates the surface, it’s easy to model simply … Continue reading

## A Transversion Machine Redux

Thoughts on the Original Design The motivation for constructing a transversion-based spatial automaton was to construct a surface in 3D Euclidean space from as little local geometric information as possible.  It was the automaton’s role to expand the information into … Continue reading

## Hyperbolic Translations

One of the crucial issues in the construction of the implementation of the transversion automaton is how it interpolate its geometric relationships (transversions and rigid body motions) through space to generate a surface in 3D.  The input data is pentagonal … Continue reading

## Geometric Algebra: The Meet Operation

Background The Meet operation in Geometric Algebra (GA) calculates the intersection of two subspaces. In set theoretical terms, the intersection is given by the relationship where M is the intersection (or Meet). Frequently in GA papers and books, you’ll find … Continue reading

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## A Transversion-Based Machine for Curvature

Fundamental Forms One of the key properties of a manifold is its curvature.  For simple shapes such a sphere or a plane, curvature is constant, but for the most part it is a function dependent on position in the manifold. … Continue reading

## From Rigid Body Motions to Surfaces: Experiment 1

As mentioned in pervious posts, I’ve been exploring how Geometric Algebra (GA) can be used to generate a surface from a topology.  More specifically, I’m interested in how a pentagonal (5, 4) tiling of the hyperbolic plane can be procedurally … Continue reading