KamiWaAI – interactive 3D sketching with Java based on Cl(4, 1) conformal model of Euclidean space

Abstract.

This paper introduces the new interactive Java sketching software KamiWaAi, recently developed at the University of Fukui. Its graphical user interface enables the user without any knowledge of both mathematics or computer science, to do full three dimensional “drawings” on the screen. The resulting constructions can be reshaped interactively by dragging its points over the screen. The programming approach is new. KamiWaAi implements geometric objects like points, lines, circles, spheres, etc. directly as software objects (Java classes) of the same name. These software objects are geometric entities mathematically defined and manipulated in a conformal geometric algebra, combining the five dimensions of origin, three space and infinity. Simple geometric products in this algebra represent geometric unions, intersections, arbitrary rotations and translations, projections, distance, etc. To ease the coordinate free and matrix free implementation of this fundamental geometric product, a new algebraic three level approach is presented. Finally details about the Java classes of the new GeometricAlgebra software package and their associated methods are given. KamiWaAi is available for free internet download.