Splossoms: Spherical Blossoms

This paper provides an overview of spherical blossoms, called splossoms, and some of its implications. The blossom of a polynomial is a multi-affine function of euclidean space with the same number of variables as the degree of the polynomial. It provides many insights to the polynomial and simplifies methods not otherwise apparent. One example is the de Casteljau algorithm for computing and subdividing a Bezier curve. This report describes a blossom for a parametric de Casteljau-like curve on the sphere, leading to similar insights and simplification of algorithms on the sphere. Two earlier such methods are the well-known SLERP and SQUAD interpolations of points on the sphere. These methods are re-formulated with our new concept, the splossom, which plays the role of a blossom in spherical space. Some of its implications are briefly sketched to illustrate its potential. The splossom itself is neatly described in terms of spinors in Geometric Algebra. This development follows the Geometric Algebra approach and points to considerable further research within its broad vista.