Layered Cylindrical Algebraic Decomposition

Abstract

Abstract. In this paper the idea of a Layered CAD is introduced, a truncation of a CAD to only high dimensional cells. Limiting to full-dimensional cells has already been investigated in the literature, but including another level can be beneficial for applications. A related topological property is defined and related to robotics motion planning. The distribution of cell dimensions in a CAD is investigated and layered CAD ideas are combined with other research.