On the Characterization of Absentee-Voxels in a Spherical Surface and Volume of Revolution in  $${\mathbb Z}^3$$ Z 3

Abstract

We show that the construction of a digital sphere by circularly sweeping a digital semi-circle (generatrix) around its diameter results in the appearance of some holes (absentee-voxels) in its spherical surface of revolution. This incompleteness calls for a proper characterization of the absentee-voxels whose restoration in the surface of revolution can ensure the required completeness. In this paper, we present a characterization of the absentee-voxels using certain techniques of digital geometry and show that their count varies quadratically with the radius of the semi-circular generatrix. Next, we design an algorithm to fill up the absentee-voxels so as to generate a spherical surface of revolution, which is complete and realistic from the viewpoint of visual perception. We also show how the proposed technique for absentee-filling can be used to generate a variety of digital surfaces of revolution by choosing an arbitrary curve as the generatrix. We further show that covering a solid sphere by a set of complete spheres also results to an asymptotically larger count of absentees, which is cubic in the radius of the sphere. A complete characterization of the absenteevoxels that aids the subsequent generation of a solid digital A preliminary version of this work appeared in ICAA'14 [5].

A digital geometric approach for discrete Voronoi diagram construction using GPU

“…In Reference 14 the authors also mentioned a technique close concept of construction of 3D Voronoi diagram with a prime factor of considering the real sphere(3D sphere). Bera et al has proposed a decent work 26 on the characterization of absentee‐voxels in a spherical surface and volume of revolution in $$$ {Z}^3 $$$ gives a insightful investigation into a complex computational domain. The methodology employed in the paper reflects a thoughtful and systematic approach to the problem.…”