E.M.S. Hitzer, G. Utama

**The GeometricAlgebra Java Package - Novel Structure Implementation of 5D
Geometric Algebra R(4,1) for Object Oriented Euclidean Geometry,
Space-Time Physics and Object Oriented Computer Algebra
**

*Mem. Fac. Eng. Univ. Fukui* **53**(1) (2005).

**Abstract:**
This paper first briefly reviews the algebraic background of the conformal (homogeneous)
model of Euclidean space in Clifford geometric algebra R_(4,1)= Cl(4,1), concentrating on
the subalgebra structure. The subalgebras include space-time algebra (STA), Dirac and
Pauli algebras, as well as real and complex quaternion algebras, etc. The concept of
the Horosphere is introduced along with the definition of subspaces that intuitively
correspond to three dimensional Euclidean geometric objects. Algebraic expressions
for the motions of these objects and their set theoretic operations are given.
It is shown how 3D Euclidean information on positions, orientations and radii
can be extracted.

The second main part of the paper concentrates on the GeometricAlgebra Java package
implementation of the Clifford geometric algebra R_(4,1) = Cl(4,1) and the homogeneous
model of 3D Euclidean space. Details are exemplified by looking at the structure and
code of the basic MultiVector class and of the 3D Euclidean object model class Sphere.
Finally code optimization issues and the ongoing open source project implementation
are discussed.

GeometricAlgebra Java Package at SourceForge (project & download bundled with KamiWaAi application).

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