Abstract
A Bezier curve is significant with its control points. When control points are given, the Bezier curve can be written using De Casteljau's algorithm. An important property of Bezier curve is that every coordinate function is a polynomial. Suppose that a curve is a curve which coordinate functions are polynomial. Can we find points that make the curve as Bezier curve? This article presents a method for finding points which present as a Bezier curve.
Highlights
The curve theory is used in differential geometry, kinematics, robotics and engineering
Bezier curves have been used in computer-aided geometric design (CAGD) and in many areas [1,2,3,4,5]
It is possible to establish the linear relationship of the control points of a Bezier curve and surface [8, 9]
Summary
The curve theory is used in differential geometry, kinematics, robotics and engineering. When the control points are given, using the Bernstein polynomial and De Castaljeu algorithm we can write the Bezier curve. The coordinates of a Bezier curve are polynomial functions including the coefficients of Bernstein polynomial and the component of the control points. Α1(t), α2(t), α3(t) are polynomial with degree m1, m2 and m3, respectively In this case, we can find max{m1, m2, m3} + 1 points which are control points of the curve α(t) as a Bezier curve. We need only the coefficients of polynomial coordinate functions These coefficients give us the coordinates of control points using the inverse of creator matrix. The control points are given for finding the Bezier curve in the existing methods but the control points are found in our method. We introduce a method to find the control points of a given curve in Section 3, which is the original part of this article
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