Constrained Interpolation with Implicit Plane Cubic A-Splines
In this work we focus on the following problem: given an ordered set of points in the plane lying on one side of a given boundary polygon, construct a smooth curve interpolating these points, such that the curve lies on the same side of the polygon as the data.
We have developed a G 2-continuous cubic A-spline scheme smoothing the polygon defined by the line segments joining consecutive data points, such that the spline curve lies completely on the same side of the boundary polygon as the data. The proposed A-spline scheme provides an efficient method for generating a smooth robot’s path that avoids corners or polygonal objects for a given planned path, for designing a smooth curve on a polygonal piece of material, etc.
KeywordsConstrained interpolation G2-continuous cubic A-spline Shape preserving spline
Mathematics Subject Classification65D07 (splines) 65D05 (interpolation) 65D17 (Computer Aided Design)
- 3.Goodman, T.N.T.: Shape preserving interpolation by parametric rational cubic splines. In: International Series of Numerical Mathematics, vol. 86, pp. 149–158. Birkhäuser Verlag, Basel (1988)Google Scholar
- 5.Paluszny, M., Patterson, R.: G 2-continuous cubic algebraic splines and their efficient display. In: Laurent, P.J., Le Méhauté, A., Schumacker, L.L. (eds.) Curves and Surfaces II, pp. 353–359 (1994)Google Scholar