Abstract

ESPINOSA BEDOYA, ALBEIRO; SANCHEZ TORRES, GERMÁN  and  BRANCH BEDOYA, JOHN WILLIAN. AN INTERPOLATING CURVE SUBDIVISION SCHEME BASED ON DISCRETE FIRST DERIVATIVE. Dyna rev.fac.nac.minas [online]. 2013, vol.80, n.180, pp.16-24. ISSN 0012-7353.

This paper develops a new scheme of four points for interpolating curve subdivision based on the discrete first derivative (DFDS), which reduces the apparition of undesirable oscillations that can be formed on the limit curve when the control points do not follow a uniform parameterization. We used a set of 3000 curves whose control points were randomly generated. Smooth curves were obtained after seven steps of subdivision using five schemes DFDS, Four-Point (4P), New four-point (N4P), Tight four-point (T4P) and the geometrically controlled scheme (GC4P). The tortuosity property was evaluated on every smooth curve. An analysis for the frequency distributions of this property using the Kruskal-Wallis test reveals that DFDS scheme has the lowest values in a close range.

Keywords : Curve subdivision; curve interpolation; four-point subdivision scheme.

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