Plotting Bézier curves directly and with De Casteljau's algorithm

Posted on in Learning • Tagged with Font, Captcha, Programming, Mathematics, Learning, Bézier

Last major Update: 21.10.2013

Github repo that contains the presented code in this post.

Introduction

In this article I will present you a very simple and in no sense optimized algorithm written in Python 3 that plots quadratic and cubic Bézier curves. I'll implement several variants of Bézier rasterization algorithms. Let's call the first version the direct approach, since it computes the corresponding x and y coordinates directly by evaluation of the equation that describes such Bézier curvatures.

The other possibility is De Casteljau's algorithm, a recursive implementation. The general principle is illustrated here. But the summarize the idea very briefly: In order to compute the points of the Bézier curve, you subdivide the lines of the outer hull that are given from the n+1 control points [Where n denotes the dimension of the Bézier curve) at a ratio t (t goes from 0 to 1 in a loop). If you connect the interpolation points, you'll obtain n-1 connected lines. Then you apply the exactly same principle to these newly obtained lines as before (recursive step), until you finally get one line remaining. Consider again the point at the ratio t on this single line left and …


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