Characterization of 3D Digital Straight Segments and Planes towards Polygonization and Decomposition of 3D Objects

Abstract

This research work deals with the characterization of geometric primitives such as 3D straight line segments and 3D plane segments in the digital domain. An attempt has been made to explore the characteristics of a 3D digital straight segment. Furthermore, in course of these explorations, it was newlineobserved that a 3D digital plane is a consecutive arrangement of a shifted 3D digital straight segment. This observation motivated the next work, which is the construction of 3D digital planes using the Greatest Common Divisor (GCD) of the components of its normal vector. An algorithm has been developed to construct the 3D digital plane corresponding to any integer normal vector. newline newline Next, an algorithm has been proposed to polygonize the surface of 3D digital objects, originally having triangulated surface. If the cosine of the dihedral angle between two face triangles is above a predefined threshold, then the faces are considered to be similar with respect to their normal vectors. In this work, such similar face triangles are called as quasi-coplanar face triangles. Starting with a base face, such faces are identified in a breadth first manner, merged together, and replaced with a polygon, which yields a significant amount of compression with respect to storage. Finally, another algorithm has been presented to decompose the surface of 3D digital objects into approximate convex regions. The proposed method is based on the volumetric analysis of the tetrahedrons generated by each two edge-adjacent face triangles of the input object. The volumes of the tetrahedrons are calculated using the scalar triple product of the vectors corresponding to the newlineedge-adjacent faces. Starting from a base face, each convex surface is grown by considering the edge-adjacent face triangles in a breadth first manner. newline newline The proposed methods of polygonization and approximate convex decomposition reveal interesting features regarding the shape of the input 3D digital object of concern.