# NEW METHODS OF GENERATING PARABOLIC CURVES OF OVERHAUSER

There are two new methods of the analytical formation of mixed parabolic curves that differ from currently used methods for forming such graphic elements. The proposed methods do not impose any restrictions on the loca-tion of the sequence of reference points in space relative to each other. Methods allow effectively generate and edit curves when you change the coordinates of any points specified in the sequence. The effect is reached at the expense of the appropriate choice of local coordinate systems for the mathematical description of each parabola which in total define a composite interpolation curve. Detailed mathematical descriptions for both methods of parabolic interpolation of curves – with use of vectorial expressions and on the basis of application of matrix computation are provided in operation. The examples of creation of parabolical curves calculated with use old (Overkhauzer and Brevera-Anderson) and the offered methods are provided. The table of volumes of a program code, required for implementation of the considered methods of parabolic interpolation in the C# language is provided. The possibility of simple formation of parabolic surfaces on the basis of a matrix of points of its set-ting rectangle is shown.

**Authors:** Yu. T. Lyachek, A. A. Vasil’ev, V. Yu. Martinov

**Direction:** Informatics and Computer Technologies

**Keywords:** Computer graphics, parabolic curves, local coordinate system, new methods of forming, vector and matrix cal-culation

View full article