Applied for Higher Order Bezier Curve using MATLAB

Abstract

A Bézier curve is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula. The piecewise nature of a Bezier curve means that its representative equation is a linear combination of Bezier of particular degrees. The aim of this study is to infer Bézier curve graphs from higher orders using MATLAB. Where the applied analytical method was used I have reached .Will be clarified, and the following results have been reached is used in the linear curve association to express the distance ( on the line between the points and , In a second-order Bezier curve, we can create intermediate points such as and . These points have a value located in the interval , To obtain a Bezier curve for higher degrees, note that the idea in arriving at drawing the curve is to divide each line by placing a point on it and then connect the new points to each other (note that we get rid of a point at each stage), and we repeat the process until we have only one line left. So, we put ( on it and then we draw the curve. By comparing the manual solution and the solution using MATLAB, we find that the solution using MATLAB is faster and more accurate, especially at higher levels. And the study recommends the following : It is noted that the curve lies completely within the convex closure of the points, so these points are used with ease to form the required curve, it is also possible to apply geometric transformations (such as rotation and sliding) to the curve by applying this transformation to the control points of this curve.