Difficulty computing the surface area of a quartic triangle Bezier patch.

[Davis Vigneault]

All--

I'm a new user of sympy, and have been really impressed by how easy it is to get started.  :-)  However, I recently came across a problem that's been causing sympy to hang, and am not sure whether (a) it is an intractable problem that sympy simply can't solve, (b) there is some hint I could give sympy which would let it proceed, or (c) I just need to let it run for a week.  Specifically, I'm trying to compute the surface area of a quartic triangle Bezier patch.  The way this works is that you have fifteen control points (X, a 15 x 3 matrix) and a corresponding fifteen basis functions (b, a vector length fifteen, in terms of parameters s and t).  The position for a given s and t is given by X^T b.  I'm trying to solve for a general patch, X is a matrix of yet unknown constants.  The surface area can be found by evaluating a pretty intense double integral [1], which is what's giving sympy trouble.

I've attached the script I'm using--I'd be infinitely grateful if someone with more experience could offer any advice!

Best, and thanks to everyone who has contributed to this invaluable software!

--Davis

P.S. I've added a guard to the beginning of the script because when I ran this with 0.7.4 (default for Ubuntu 14.04 when installing with apt-get) it resulted in unbounded memory use and crashed my machine--happily, updating to the development branch fixed this.

[1] https://en.wikipedia.org/wiki/Parametric_surface#Surface_area

[Aaron Meurer]

There seem to be some serious performance issues in the polys here. I
was unable to even compute the degree of the polynomial under the
square root.

Do you know if this integral has a closed form? If so, my only
suggestion would be to try some change of variable to make it easier
to compute.

Aaron Meurer

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