| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 441434 | Computer Aided Geometric Design | 2014 | 16 Pages |
•A method for approximating point sequences by arc splines is presented.•The breakpoints of the arc spline are not restricted to any pre-defined set of points.•For any user-defined accuracy, the minimal number of segments is guaranteed.•The resulting compact curve representation enables an efficient further processing.•Among others, it is hence suited for the generation of highly accurate digital maps.
We present a method for approximating a point sequence of input points by a G1G1-continuous (smooth) arc spline with the minimum number of segments while not exceeding a user-specified tolerance. Arc splines are curves composed of circular arcs and line segments (shortly: segments). For controlling the tolerance we follow a geometric approach: We consider a simple closed polygon P and two disjoint edges designated as the start s and the destination d. Then we compute a SMAP (smooth minimum arc path), i.e. a smooth arc spline running from s to d in P with the minimally possible number of segments. In this paper we focus on the mathematical characterization of possible solutions that enables a constructive approach leading to an efficient algorithm.In contrast to the existing approaches, we do not restrict the breakpoints of the arc spline to a predefined set of points but choose them automatically. This has a considerably positive effect on the resulting number of segments.
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