Data parallel volume rendering as line drawing
VVS '92 Proceedings of the 1992 workshop on Volume visualization
Segmented ray casting for data parallel volume rendering
PRS '93 Proceedings of the 1993 symposium on Parallel rendering
Computer graphics (2nd ed. in C): principles and practice
Computer graphics (2nd ed. in C): principles and practice
Using 3D-Bresenham for Resampling Structured Grids
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Spatial and temporal competition as a two dimensional kinetic Voronoi diagram
Computer-Aided Design
Flying Fast and Low Among Obstacles: Methodology and Experiments
International Journal of Robotics Research
Particle-based viscoplastic fluid/solid simulation
Computer-Aided Design
Algorithm for computer control of a digital plotter
IBM Systems Journal
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Bresenham's Algorithm for plotting a two-dimensional line segment is elegant and efficient in its deployment of mid-point comparison and integer arithmetic. It is natural to investigate its three-dimensional extensions. In so doing, this paper uncovers the reason for little prior work. The concept of the mid-point in a unit interval generalizes to that of nearest neighbours involving a Voronoi diagram. Algorithmically, there are challenges. While a unit interval in two-dimension becomes a unit square in three-dimension, ''squaring'' the number of choices in Bresenham's Algorithm is shown to have difficulties. In this paper, the three-dimensional extension is based on the main idea of Bresenham's Algorithm of minimum distance between the line and the grid points. The structure of the Voronoi diagram is presented for grid points to which the line may be approximated. The deployment of integer arithmetic and symmetry for the three-dimensional extension of the algorithm to raise the computation efficiency are also investigated.