Modeling contact of two complex objects, with an application to characterizing dental articulations

The interference of the motion paths of objects has been an important theme of research. Previous works concentrate on detecting collisions and finding colliding points, and little has been done on characterizing the contact of two objects considering the structures of the space between the objects. This paper proposes a novel method to characterize the interference of objects. Our method is based on the analysis of the structures of the complementary space of three-dimensional objects. The topological structures are analyzed using the coding method based on the Morse theory and the Reeb graph. The method is applied to actual dental articulations to validate the model.