Most excellent article here on conceptualizing how to put together those Bézier path thingamabobbies in code, with by leaps and bounds the best explanation we’ve ever seen of how curves work:
… Once you’ve learnt to break down one path you can apply the same tools and divide it into lines, arc and curves. One by one, in any combination. The more you do the better you’ll get at it. But we missed curves and curves are awesome. Curves are the center of you favorite vector drawing program. They draw a curved line to another point, bending towards two “control points” on its way there. I said bending towards because the curve doesn’t go all the way to neither of the two control points.
There is a little bit of math involved in how the path is drawn between the four points (the start point, 2 control points and the end point) but unless you are interested you will never have to use it. I am interested so I will gladly explain the math. Feel free to skip ahead if you are afraid that you might learn something…
Master that fear and read the whole thing!
h/t: iOS Dev Weekly!