Abstract
In this paper, the problem for choosing design points in the two dimensional case is condidered. In the one dimensional case, given the design density function, we can choose design points using the quantile function. However, in the two dimensional case, there is no clear definition of the percentile. Therefore, the idea of choosing design points in the univariate case can not be applied directly to the two dimensional case. We convert this problem into an optimization problem using the Voronoi diagram.