Hi,

Aaron Keesing has left the following comment at Add a primitive surface area function ... for right hyperbolic cylinders (RHC) http://www.google-melange.com/gci/task/view/google/gci2012/7982218:


Arc Length


I believe that to work out the surface area you need to know the arc length of the cros-sectional hyperbola, but trying to work this out exactly involves incomplete elliptical integrals and other complicated calculus, and it might not even be possible to work out exactly.

The only solution I can think of is to try and approximate the arc length somehow, so that is is within a certain accuracy (so many dp for example). Simpson's Rule may be one method of doing this. But I'm not sure what would be the best way to implement this in code (whether to write a separate function to do the aproximation of the integral, or do it in the main function). Apart from the arc length I think that the surface area will be relatively easy to compute.

Aaron K


Greetings,
The Google Open Source Programs Team


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