Bezier curves, tangent angles, and arc length

[ZippyDee]

I am trying to do some calculations that involve cubic Bezier curves. I've been looking all over the place for information about Bezier curves, but I can't find anything that has what I'm looking for.

I need to be able to figure out the length of any curve with known control points (approximations are fine). And then I need to be able to get the tangent angle at any point on the curve.

I really have no idea how to figure this out, and most of the equations on lots of math websites and in the wikipedia entry have lots of complex equations that are only explained using terms that someone who already knew what they were looking at would understand...

Thanks in advance!
-Zippy Dee
Ted Newman

 

[fresh_42]

If a Bezier curve is parameterized then calculation of tangent or curve lengths should be easy. So the question is how to parameterize it. This leads to the question how the Bezier curve is given.

 

[WWGD]

The length would then be given by the standard arc length formula, which would require I think, some $C^k$ condition on the component functions.