Efficient random variable generation: ratio of uniforms and polar rejection sampling

Efficient sampling from truncated bivariate Gaussians via Box-Muller transformation

“…In this case all points in D are completely expressed by the inequalities r ≥ 0 and tan −1 {−b/a} ≤ u ≤ tan −1 {−b/a} + p, and A is again a rectangle. Additional examples of simple A regions where exact sampling can be performed include triangles and sectors of circles [5,7].…”