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Hybrid curve fitting

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Abstract

We consider a parameterized family of closed planar curves and introduce an evolution process for identifying a member of the family that approximates a given unorganized point cloud {p i } i =1,..., N . The evolution is driven by the normal velocities at the closest (or foot) points (f i ) to the data points, which are found by approximating the corresponding difference vectors p i -f i in the least-squares sense. In the particular case of parametrically defined curves, this process is shown to be equivalent to normal (or tangent) distance minimization, see [3], [19]. Moreover, it can be generalized to very general representations of curves. These include hybrid curves, which are a collection of parametrically and implicitly defined curve segments, pieced together with certain degrees of geometric continuity.

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Authors and Affiliations

  1. Institute of Applied Geometry, Johannes Kepler University, 4040, Linz, Austria

    M. Aigner & B. Jüttler

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  1. M. Aigner
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  2. B. Jüttler
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Correspondence to B. Jüttler.

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Aigner, M., Jüttler, B. Hybrid curve fitting. Computing 79, 237–247 (2007). https://doi.org/10.1007/s00607-006-0201-3

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  • DOI: https://doi.org/10.1007/s00607-006-0201-3

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