Hybrid curve fitting

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 {pi}i=1,...,N . The evolution is driven by the normal velocities at the closest (or foot) points (fi) to the data points, which are found by approximating the corresponding difference vectors pi − fi 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.

• Type: Journal
• Year: 2007
• Where: COMPUTING
• Authors: Martin Aigner, Bert Jüttler
• Keywords: COMPUTING 2007, Corresponding Difference Vectors, Planar Curves, Unorganized Point Cloud