In this paper, we present an electro-optical architecture called the Optical Reconfigurable Mesh (ORM). The ORM has two layers: the deflection layer and the processing layer. The processing layer is an N_N reconfigurable mesh. The deflection layer, situated directly above the processing layer, provides unittime free space optical interconnections for the processors. The architecture supports three types of unit-time communication mechanisms. The first is for arbitrary planar connections among sets of locally connected processors using the electrical reconfigurable mesh. The second is for arbitrary connections among N of the processors using the electrical buses on the processing layer and N 2 fixed passive optical deflecting units on the deflection layer. The third is for arbitrary free space optical connections among any of the N 2 processors using the N 2 mechanically reconfigurable deflectors in the deflection layer. The reconfiguration time of the first two communication mechanisms is on the order of nanoseconds, while for the third mechanism it is on the order of milliseconds. Therefore, algorithms are designed to utilize all three types of mechanisms but minimize or avoide the use of the third type during the execution of algorithms. We present a set of basic data movement algorithms for ORM and, as an applicate example, outline an O(log N) time algorithm for finding the convex hulls of all figures in an N_N digitized image.