In a multiprocessor system, a limited number of resources need to be uniformly distributed so that all processor nodes can have equal access to these resources. This is referred to as the resource placement problem. In a perfect t--placement each nonresource node is at a distance of t or less from exactly one resource node. Here, we first find all perfect t-placements in the infinite square and triangular grids. That information is then used to show that translates of earlier sets are the only perfect t-placements in Gaussian and EJ interconnection networks.