Computational-geometric methods for polygonal approximations of a curve
Computer Vision, Graphics, and Image Processing
Curve fitting algorithm for rough cutting
Computer-Aided Design
Computational geometry: curve and surface modeling
Computational geometry: curve and surface modeling
On approximating polygonal curves in two and three dimensions
CVGIP: Graphical Models and Image Processing
Approximating smooth planar curves by arc splines
Journal of Computational and Applied Mathematics
Approximating monotone polygonal curves using the uniform metric
Proceedings of the twelfth annual symposium on Computational geometry
Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere
Computational Geometry: Theory and Applications
ACM SIGGRAPH Asia 2010 papers
Deconstructing approximate offsets
Proceedings of the twenty-seventh annual symposium on Computational geometry
Approximation of a closed polygon with a minimum number of circular arcs and line segments
Computational Geometry: Theory and Applications
Approximating minimum bending energy path in a simple corridor
Computational Geometry: Theory and Applications
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We present an algorithm for approximating a given open polygonal curve with a minimum number of circular arcs. In computer-aided manufacturing environments, the paths of cutting tools are usually described with circular arcs and straight line segments. Greedy algorithms for approximating a polygonal curve with curves of higher order can be found in the literature. Without theoretical bounds it is difficult to say anything about the quality of these algorithms. We present an algorithm which finds a series of circular arcs that approximate the polygonal curve while remaining within a given tolerance region. This series contains the minimum number of arcs of any such series. Our algorithm takes O(n^2logn) time for an original polygonal chain with n vertices. Using a similar approach, we design an algorithm with a runtime of O(n^2logn), for computing a tangent-continuous approximation with the minimum number of biarcs, for a sequence of points with given tangent directions.