Fascinating Bezier curves...

I am fascinated with Bézier curve and playing with it a lot these days. No graphic design software is complete without Bezier curves. The mathematical definitions here seem complicated, but the animations(Constructing Bézier curves in wikipedia) make for such easy understanding.

When working with Inkscape, this tutorial gives you the basic idea of editing bezier curves. Illustrating complex objects needs some mastery of bezier curves.


Here's an understanding my mind has about bezier curves.



Each bezier curve has two end points (p1 and p2) and two control points (c1 and c2).
Control line is line joining control point and corresponding end point(p1,c1 or p2,c2).
The shape of bezier curve depends on the position of control point, that is
a) distance between control point and the corresponding end point (control length).
b) angle made by control line with line joining end points (control angle).

The control line from an end point is tangent to the bezier curve starting from that end point.
A straight line is a bezier curve where control angles are zero.
A complex object can be drawn using multiple bezier curves.

Though control length may seem less important(in deciding the curvature) but when the end points are near, it makes a lot of difference.