Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space

  • Shivam Dwivedi
  • Aniket Gupta
  • Siddhant Roy
  • Ranita BiswasEmail author
  • Partha Bhowmick
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10502)


Space filling circles and spheres have various applications in mathematical imaging and physical modeling. In this paper, we first show how the thinnest (i.e., 2-minimal) model of digital sphere can be augmented to a space filling model by fixing certain “simple voxels” and “filler voxels” associated with it. Based on elementary number-theoretic properties of such voxels, we design an efficient incremental algorithm for generation of these space filling spheres with successively increasing radius. The novelty of the proposed technique is established further through circular space filling on 3D digital plane. As evident from a preliminary set of experimental result, this can particularly be useful for parallel computing of 3D Voronoi diagrams in the digital space.


Digital circle Digital sphere Space filling curve Space filling surface Spherical propagation Voronoi diagram 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Shivam Dwivedi
    • 1
  • Aniket Gupta
    • 1
  • Siddhant Roy
    • 1
  • Ranita Biswas
    • 1
    Email author
  • Partha Bhowmick
    • 2
  1. 1.Department of Computer Science and EngineeringIndian Institute of TechnologyRoorkeeIndia
  2. 2.Department of Computer Science and EngineeringIndian Institute of TechnologyKharagpurIndia

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