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COMPUTER REALIZATIONS OF THE CUBIC PARAMETRIC SPLINE CURVE OF BÈZIER TYPE

Oleg Stelia, Leonid Potapenko, Ihor Sirenko

Abstract


This paper presents a new method for constructing a third degree parametric spline curve of C1 continuity. Like the Bèzier curve, the proposed curve is constructed and operated by control points. The peculiarity of the proposed algorithm is the assignment of some unknown values of the spline in the control points abscissas, which are based on the conditions of the first derivative continuity of the curve at these points. The position of the touch points, as well as the control points, can be set interactively. Changing of these points positions leads to a change in the curve shape. This allows the user to flexibly adjust the shape of the curve. Systems of algebraic equations with tridiagonal matrix for calculating the coefficients of a spline curve are constructed. Conditions for the existence and uniqueness of such a curve are presented. Examples of the use of the proposed curve, in particular, for monotone data sets, approximation the ellipse and constructing the letter "S" are given.

Keywords


Bèzier-type curve; parametric spline curve; third-degree curve; monotonicity.

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