Layer the Sphere

for Accurate and Additive Voxelation by Integer Operation


Ranita Biswas and Partha Bhowmick,
Layer the Sphere, CGI'15: Computer Graphics International, 32nd Annual Conference, June 2014, Strasbourg, France.
Published in The Visual Computer, Springer, Vol. 31, pages 787-797, 2015.


Voxelation today is not only limited to discretization and representation of 3D objects but also gaining tremendous importance in rapid prototyping through 3D printing. Out of different 3D geometric primitives, the one which is most difficult to manufacture is a sphere or a spherical surface, be it by conventional machining or be it by additive processing. 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.

Voxel compression

from r = 5 to r = 15.

Voxel strength

(decreasing: violet, blue, green, yellow, red, deep red, blackish red) with r2 = 10 and wall thickness w = 1, 2, 3 from left to right.
Notice that low-strength voxels (red) are very few for w > 1.

r2 = 30, w ≥ 2.