Algorithms for generating motion trajectories described by prepositions

A list of representative directional prepositions of the English language is investigated to develop computation models that output some general motion trajectory or goal direction, given instructions involving prepositional phrases. Computation models are implemented through geometric definitions and procedures such as: centroid, quasi-centroid, convex-hull, closest, nearest-neighbour, and next-to. All algorithms are defined by or derived from standard computational geometry concepts.