Evolution-based least-squares fitting using Pythagorean hodograph spline curves
Computer Aided Geometric Design
Dual evolution of planar parametric spline curves and T-spline level sets
Computer-Aided Design
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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.