Application of 3D Voronoi Diagram to Direction Relation Calculation

A new method,3D direction relation calculation based on 3D Voronoi diagram is proposed.The 27 direction relations are proposed to represent the qualitative direction relation based on the 2D four direction relations.Shape,distance and other factors play very import role in direction relation calculation.3D Voronoi diagram being an approximation of spatial object plays well in the situation of complex shape and various distances.The principles and methods of 3D Voronoi diagram for the calculation of the 3D direction relations are elaborated.The weighted normal of surfaces in 3D Voronoi diagram is used to calculate the direction relation of the non-intersecting spatial objects.The direction relation in intersection case of the spatial objects is also discussed.