Successful solutions of problems in robotics, computer vision, image processing, and computer graphics are frequently intertwined with efficient representations of spatial data. Hierarchical representations of spatial data focus the work on the area in which the information has the greatest density. It is proposed to find solutions to spatial problems that make use of hierarchical data structures; hierarchical solutions to path planning and polygon expansion will be attempted. The concept of neighbor-finding will be generalized, and the use of the active- border paradigm in octree construction will be explored. The surface spatial data type will be investigated. We will examine the question of whether spatial queries can be processed inteligently by the construction of an expert system interface that uses the representation of the spatial elements to which the query refers. Theoretical investigation of Delaunay triangulations will be continued. We will explore the relationship between hierarchical solutions to geometric problems, and those used in computational geometry based on the plane-sweep method. The feasibility of parallel solutions will be considered when possible.
