UIBezierPath allows us to create curved line segments between points, but things get complicated when trying to draw smooth curves between changing sets of points.
Here’s a nice guide submitted by Atomic Object that explains how to create smooth cubic bezier curves neatly through a set of points.
The guide provides to simple methods for interpolating cubic bezier curves using cubic Hermite splines, and Catmull-Rom curves with some easy to follow code examples and no complex math.
You can find the tutorial over on the Atomic Object blog.
An example demonstrating the principles used to create the curves in the tutorial can be found on Github here.
A nice guide on bezier curves.
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