A function that can smooth out line joining three points

Question

I want to know if there is a function with which we can smooth out line joining two( or more )points . I've read we can do it with Quad and cubic splines or something but I am not clear with them. i want a simple function which can be computed efficiently with a mobile device , so can someone explain Quad spline .Help appreciated

This picture shows my requirement.

Answer 1

The computationally simplest solution would probably be so-called Catmull-Rom splines. You can look them up on the web. There's a simple formula that gives you the tangent vector at each point. So, then, for each two consecutive points, you know their locations and tangent vectors, and this is enough information to construct a Bezier cubic curve between them. A lot of PC drawing programs use these curves. They are not very smooth, but they're easy to implement.