Best approximate circles on integer grids
ACM Transactions on Graphics (TOG)
Algorithms for drawing anti-aliased circles and ellipses
Computer Vision, Graphics, and Image Processing - Lectures notes in computer science, Vol. 201 (G. Goos and J. Hartmanis, Eds.)
Solved and unsolved problems in number theory
Solved and unsolved problems in number theory
Double-step incremental generation of lines and circles
Computer Vision, Graphics, and Image Processing
A high speed algorithm for circular object location
Pattern Recognition Letters
A hybrid sequential-parallel approach to accurate circle centre location
Pattern Recognition Letters
A simple approach for the estimation of circular arc center and its radius
Computer Vision, Graphics, and Image Processing
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
On the number of factors of Sturmian words
Theoretical Computer Science
Cramer-Rao lower bounds for estimation of a circular arc center and its radius
Graphical Models and Image Processing
Data structures using C and C++ (2nd ed.)
Data structures using C and C++ (2nd ed.)
Recognition of partial circular shapes from segmented contours
Computer Vision and Image Understanding
A novel method for parameter estimation of digital arc
Pattern Recognition Letters
Curve-drawing algorithms for Raster displays
ACM Transactions on Graphics (TOG)
A linear algorithm for incremental digital display of circular arcs
Communications of the ACM
A two-step circle detection algorithm from the intersecting chords
Pattern Recognition Letters
An efficient randomized algorithm for detecting circles
Computer Vision and Image Understanding
Hybrid Scan-Conversion of Circles
IEEE Transactions on Visualization and Computer Graphics
Rendering: Parallelization of Bresenham's Line and Circle Algorithms
IEEE Computer Graphics and Applications
Digitized Circular Arcs: Characterization and Parameter Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
An elementary algorithm for digital arc segmentation
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Digital straightness: a review
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Characterization of digital circles in triangular grid
Pattern Recognition Letters
An effective voting method for circle detection
Pattern Recognition Letters
A High-Speed Algorithm for the Generation of Straight Lines and Circular Arcs
IEEE Transactions on Computers
How Many Ways Can You Draw a Circle?
IEEE Computer Graphics and Applications
Approximation of digital circles by regular polygons
ICAPR'05 Proceedings of the Third international conference on Advances in Pattern Recognition - Volume Part I
Digital Circularity and Its Applications
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Determining Digital Circularity Using Integer Intervals
Journal of Mathematical Imaging and Vision
On covering a digital disc with concentric circles in Z2
Theoretical Computer Science
Fast Circular Arc Segmentation Based on Approximate Circularity and Cuboid Graph
Journal of Mathematical Imaging and Vision
Hi-index | 0.05 |
This paper presents a new interpretation of a digital circle in terms of the distribution of square numbers in discrete intervals. The number-theoretic analysis that leads to many important properties of a digital circle succinctly captures the original perspectives of digital calculus and digital geometry for its visualization and characterization. To demonstrate the capability and efficacy of the proposed method, two simple algorithms for the construction of digital circles, based on simple number-theoretic concepts, have been reported. Both the algorithms require only a few primitive operations and are completely devoid of any floating-point computation. To speed up the computation, especially for circular arcs of high radii, a hybridized version of these two algorithms has been given. Experimental results have been furnished to elucidate the analytical power and algorithmic efficiency of the proposed approach. It has been also shown, how and why, for sufficiently high radius, the number-theoretic technique can expedite a circle construction algorithm.