What is the best way to draw a bezier curve, in iOS application, that passes through a set of given points
You can easily google some example of how to create bezier curve on the web. I found this short tut as an example.
You can create a close bezier curve for e.g. with the following code snippet:
UIBezierPath* path = [UIBezierPath bezierPath];
[path moveToPoint:pt1];
[path addLineToPoint:pt2];
[path addLineToPoint:pt3];
[path closePath];
I hope it will help as a starting point.