Voronoi diagrams and arrangements
Discrete & Computational Geometry
Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Digital circles with non-lattice point centers
The Visual Computer: International Journal of Computer Graphics
On the recognition of digital circles in linear time
Computational Geometry: Theory and Applications
The linear time recognition of digital arcs
Pattern Recognition Letters
Constructive fitting and extraction of geometric primitives
Graphical Models and Image Processing
The Discrete Analytical Hyperspheres
IEEE Transactions on Visualization and Computer Graphics
Digital disks and a digital compactness measure
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
An elementary algorithm for digital arc segmentation
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Measure of circularity for parts of digital boundaries and its fast computation
Pattern Recognition
On three constrained versions of the digital circular arc recognition problem
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Ellipse detection with elemental subsets
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Analytical description of digital circles
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Distance between separating circles and points
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
IEEE Transactions on Pattern Analysis and Machine Intelligence
Separating Point Sets by Circles, and the Recognition of Digital Disks
IEEE Transactions on Pattern Analysis and Machine Intelligence
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The family of separating circles of two finite sets in the plane consists of all the circles that enclose the first set but exclude the second set. We prove some theoretical results on distances between families of circles, and properties about enclosure and intersection. Most of these results state that a property that involves one or more infinite families of circles can be verified by examining a finite subcollection of circles. As a result enclosure and intersection can be decided, and distances can be computed with simple geometric algorithms. Furthermore, the circles of the finite subcollections correspond to the vertices of a polytope in the parameter space of separating circles. A polytope of separating circle parameters is well-known computational geometry, but we prove some new properties and we introduce the concept of an elementary circular separation as a concise way to define such a polytope.