Abstract
A solution to the problem of formation of a smooth closed curve given an array of points is proposed. For the curve, a spline consisting of fractional rational Bezier curves of second order is taken. It is shown that upon appropriate reparametrization, the standard form of representation of this Bezier curve can be reduced to a more simple form. This form is convenient in construction of a closed spline from said segments, which are connected in the process of formation according to the second order of smoothness. Depending on the calculated value of control parameter in the proposed form of representation of fractional rational Bezier curve, it is possible to construct a closed spline of segments of certain curves of second order.
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