The Visual Computer

, Volume 31, Issue 6–8, pp 787–797 | Cite as

Layer the sphere

For accurate and additive voxelation by integer operation
  • Ranita Biswas
  • Partha BhowmickEmail author
Original Article


Voxelation today is not only limited to discretization and representation of 3D objects, but has also been gaining tremendous importance in rapid prototyping through 3D printing. In this paper, we introduce a novel technique for discretization of a sphere in the integer space, which gives rise to a set of mathematically accurate, 3D-printable physical voxels up to the desired level of precision. The proposed technique is based on an interesting correspondence between the voxel set forming a discrete sphere and certain easy-to-compute integer intervals defined by voxel position and sphere dimension. It gives us several algorithmic leverages, such as computational sufficiency with simple integer operations and amenability to layer-by-layer additive fabrication. Theoretical analysis, prototype characteristics, and experimental results demonstrate its efficiency, versatility, and further prospects.


3D printing Discrete sphere Integer algorithm  Rapid prototyping Sphere voxelation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Computer Science and Engineering DepartmentIndian Institute of TechnologyKharagpurIndia

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