Let A B C D be a square of side length 1, and let P_{1}, P_{2} and P_{3} be points on the perimeter such that \angle P_{1} P_{2} P_{3}= 90^{\circ} and P_{1}, P_{2}, P_{3} lie on different sides of the square. As these points vary, the locus of the circumcenter of \triangle P_{1} P_{2} P_{3} is a region \mathcal{R}; what is the area of \mathcal{R}?