Open AccessCOMPUTER REALIZATIONS OF THE CUBIC PARAMETRIC SPLINE CURVE OF BÈZIER TYPE
Author(s) -
Олег Стеля,
Leonid Potapenko,
I. Sirenko
Publication year - 2019
Publication title -
computing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.184
H-Index - 11
eISSN - 2312-5381
pISSN - 1727-6209
DOI - 10.47839/ijc.18.4.1612
Subject(s) - mathematics , parametric equation , curve fitting , stable curve , asymptote , ellipse , tripling oriented doche–icart–kohel curve , uniqueness , smoothing spline , bézier curve , hessian form of an elliptic curve , spline (mechanical) , jacobian curve , parametric statistics , monotone polygon , data point , osculating circle , mathematical analysis , algorithm , geometry , algebraic number , elliptic curve , spline interpolation , real algebraic geometry , schoof's algorithm , statistics , structural engineering , bilinear interpolation , engineering , quarter period
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.