I am looking for a reference for the calculation of integrals of bivariate normal distributions over (convex) polygons.
$$P\{X\in\mathcal{A}\} = \int_{\Omega} \frac{1}{\sqrt{(2\pi)^2|\Sigma|}}e^{-\frac{1}{2}(x-\mu)^T\Sigma^{-1}(x-\mu)}dx$$
$$\Omega:=\{x\in\mathbb{R}^2\,|\,\,Ax\leq b\}$$
For the case of triangular domains, formulae exist and are used for example in the polyCub R package. The approach can be extended to arbitrary polygons, based on a triangulation of the domain.
I came across a paper [1] from 1978 that seemingly provides a more efficient solution, without the need for a triangulation. Here the integral over the complement of the region is calculated, based on a partitioning to external angular regions. For these semi-analytical solutions using special functions $(\operatorname{erf}, \operatorname{erfc})$ are given.
I was wondering if a more recent work using such an approach exists? The original document is sometimes barely readable due to the scan quality.
[1] A. R. DiDonato, M. P. Jarnagin Jr, and R. K. Hageman, “Computation of the bivariate normal distribution over convex polygons,” DTIC Document, 1978.