While this is a simple question, I'm totally lost. Is there any general formula for generation of n-point gaussian quadrature over a triangle?

I'll use this formula to generate a variable-point (7, 10, 13, ...) gaussian quadrature tables for triangle and use it to take integrals of many triangles. In my case, simulation results are not precise enough when integrals taken with 7 point tables.

If any direct answer is unlikely, any nudge in the right direction is also very welcome.

Thanks in advance.

  • $\begingroup$ This paper contains tables for up to $13$ points. It says that "the equations [...] are highly non-linear and their solution is not straightforward", so unless progress has been made on that since 1972, it seems you won't get a general formula. $\endgroup$
    – joriki
    Feb 20, 2012 at 10:00

1 Answer 1


There are many rules for quadrature over the triangle, the only "open-end" end one that I know of is Silvester's construction from open/closed Newton-Cotes formulas. They are not optimal though in terms of points vs. degree of precision.

Check out quadpy (a small software project of mine) for more schemes (and their implementation).


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