Mercyhurst UniversityDept of Math and ITDr Williams Home

Bezier Curves

Cubic         Quadratic

About Bezier Curves

Bezier curves are smooth curves that are frequently linked together to create paths in computer graphics. It is possible to create degree \(n\) curves, but quadratic and cubic are the most common. A Bezier curve between points \(A\) and \(B\) with degree \(n\) will have \(n-1\) control points \(C_0, C_1, C_2, \ldots \) between \(A\) and \(B\). A quadratic Bezier curve from \(A\) to \(B\) is traced by the function \[ P(t) = (1-t^2)A+2(1-t)tC_0+t^2B \] as \(t\) ranges from 0 to 1. Similarly, a cubic Bezier curve from \(A\) to \(B\) is traced by the function \[ P(t) = (1-t)^3A+3(1-t)^2tC_0++3(1-t)^2tC_1 + t^3B \]

Using the Applet

Drag the handles to adjust the end points of the path and the control point(s). Choose to display the quadratic or cubic curve using the radio buttons at the top. The SVG path will be displayed above the canvas.

About this Applet

This applet was created using JavaScript and the Raphael library. If you are unable to see the applet, make sure you have JavaScript enabled in your browser. This applet may not be supported by older browsers.