Methods and apparatus are disclosed that arrange mask patterns in response to the contribution of a second pattern to image intensity. In some methods of arranging mask patterns, a distribution of functions h(ξ−x) is obtained which represents the contribution of a second pattern to image intensity on a first pattern. Neighboring regions of the first pattern are discretized into finite regions, and the distribution of the functions h(ξ−x) is replaced with representative values h(x,ξ) of the discretized regions. A position of the second pattern is determined using polygonal regions having the same h(x,ξ). As described, the term x is the position of the first pattern and the term ξ is the position of the assist.