Validation of Medial Axis Transform Objects

Medial Axis Transform (MAT) satisfies most of the demands of present day solid modeling and product development methods as it captures the geometric proximity of the boundary elements in a simple form. However, Euler type topology-verification equations are not available for MAT. Different features of 3D MAT like seam-end points, junction points, seams, etc. are described. Available algorithms are used to generate the 3D MATs. MATs available in the literature are also used. From the generated and available MATs, basic relations between number of seam-end points (NSEP), number of junction points (NJP) and number of seams (NS) are developed experimentally. These equations are generalized in such a way that they are valid for both 2D and 3D MATs. The applications of these equations include MAT validation and validation of MAT generation methods. Limitations of the work is presented. The relationships developed are experimental only and mathematical proof is not yet developed.