It is generally accepted that Poisson disk sampling provides great properties in various applications in computer graphics. We present KD-tree based randomized tiling (KDRT), an e cient method to generate maximal Poisson-disk samples by replicating and conquering tiles clipped from a pa ern of very small size. Our method is a twostep process: rst, randomly clipping tiles from an MPS(Maximal Poisson-disk Sample) pa ern, and second, conquering these tiles together to form the whole sample plane. e results showed that this method can e ciently generate maximal Poisson-disk samples with very small trade-o in bias error. ere are two main contributions of this paper: First, a fast and robust Poisson-disk sample generation method is presented; Second, this method can be used to combine several groups of independently generated sample pa erns to form a larger one, thus can be applied as a general parallelization scheme of any MPS methods.