The conformal model of Euclidean geometry in Geometric Algebra pro vides a compact way to characterize Euclidean objects such as spheres, planes, circles, lines, etc. as blades. The algebraic structure of the model provides a ‘grammar’ for these objects and their relationships. In this rather informal paper we explore this grammar, developing a new geOmetric intuition to use it effectively. This results in the identification of two important construction products, the known meet and the new plunge. These provide compact specification techniques to parametrize operators and objects directly in terms of other objects.
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