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Published in:
2014 | OriginalPaper | Chapter
A Digital-Geometric Algorithm for Generating a Complete Spherical Surface in ℤ3
Authors : Sahadev Bera, Partha Bhowmick, Bhargab B. Bhattacharya
Published in: Applied Algorithms
Publisher: Springer International Publishing
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We show that the construction of a digital sphere by circularly sweeping a digital semicircle (generatrix) around its diameter results in 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 semicircular 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. Test results have also been furnished to substantiate our theoretical findings. The proposed technique will find many potential applications in computer graphics and 3D imaging.