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Gajit: Symbolic Optimisation and JIT Compilation of Geometric Algebra in Python with GAALOP and Numba
TLDR
Gajit is a system that aims to get the best of both worlds, it allows us to prototype and debug algorithms with the Python library clifford and then to optimise the authors' code both symbolically with GAALOP and via the LLVM pipeline with Numba resulting in highly performant code for very little additional effort. Expand
Calculating the Rotor Between Conformal Objects
In this paper we will address the problem of recovering covariant transformations between objects—specifically; lines, planes, circles, spheres and point pairs. Using the covariant language ofExpand
Direct Linear Interpolation of Geometric Objects in Conformal Geometric Algebra
Typically we do not add objects in conformal geometric algebra (CGA), rather we apply operations that preserve grade, usually via rotors, such as rotation, translation, dilation, or via reflectionExpand
Direct Linear Interpolation of Geometric Objects in Conformal Geometric Algebra
Typically we do not add objects in conformal geometric algebra (CGA), rather we apply operations that preserve grade, usually via rotors, such as rotation, translation, dilation, or via reflectionExpand
REFORM: Rotor Estimation From Object Resampling and Matching
In this paper we tackle the problem of correspondence and rotor estimation between models composed of geometric primitives of different types. We frame this problem as searching for the rotor thatExpand
Evaluating the Epley Canalolith Repositioning Procedure With and Without a Visual Assistive Device.
TLDR
A simple visual guidance device can increase the execution accuracy of canalith repositioning procedures, and further research is required to show how such improvements influence treatment efficacy. Expand
Constrained Dynamics in Conformal and Projective Geometric Algebra
TLDR
This paper constructs a screw-theory based formulation of dynamics in CGA and notes the equivalence between this and the PGA dynamics presented by Gunn in [1], and applies the standard mechanical engineering technique of virtual power to the constraint problem in the Geometric Algebra framework. Expand
Exploring Novel Surface Representations via an Experimental Ray-Tracer in CGA
Conformal Geometric Algebra (CGA) provides a unified representation of both geometric primitives and conformal transformations, and as such holds significant promise in the field of computerExpand
Ray-Tracing Objects and Novel Surface Representations in CGA
TLDR
A simple ray tracer is implemented with a Blinn-Phong lighting model and used to examine ray intersections with surfaces generated from interpolating between objects, and an analytical method for finding the normal line to these interpolated surfaces is described. Expand
The Forward and Inverse Kinematics of a Delta Robot
TLDR
This paper analyses the forward and inverse kinematics of the Delta robot from a geometric perspective using Conformal Geometric Algebra and calculates explicit formulae for all joints in both the forwards and inverse problems to allow for velocity and force control. Expand