ON INTERPOLATING SUBDIVISION SCHEMES. REPRODUCING CIRCLE ARCS. Dayron Garc´ıa Pérez*. Wilfredo Morales Lezca**. Sof´ıa Behar Jequ´ın**.
ON INTERPOLATING SUBDIVISION SCHEMES REPRODUCING CIRCLE ARCS. Dayron Garc´ıa P´ erez* Wilfredo Morales Lezca** Sof´ıa Behar Jequ´ın** Jorge Estrada Sarlabous* *ICIMAF, Cuba **Universidad de la Habana, Cuba
Abstract It is well known that among all simply-connected closed plane curves, the circles are the ones that minimize the average bending energy functional. But it does not hold true for plane curves interpolating points with arbitrary tangent directions. We propose a functional, which is a linear combination of the bending energy and arc-length functionals, and show that for a special selection of the coefficients of the linear combination, the functional has the following property: if two points and tangent directions are sampled from a circle C, then C is the B´ezier conic plane curve minimizing that functional. This fact gives rise to the definition of 3 interpolating subdivision schemes, whose properties such as Gk -continuity, interpolation of previously prescribed tangent directions, reproduction of line segments and circle arcs, affine invariance, etc. are discussed in the present work. Key words: Conic spline, bending energy, subdivision scheme, Hermite interpolation. AMS Subject Classification: 65D17, 68U05, 53A04
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