Delaunay Triangulation(DT) is one of the important geometric problems that is used in various branches of knowledge such as computer vision, terrain modeling, spatial clustering and networking. Kinetic data structures have become very important in computational geometry for dealing with moving objects. However, when dealing with moving points, maintaining a dynamically changing Delaunay triangulation can be challenging. So, In this case, we have to update triangulation repeatedly. If points move so far, it is better to rebuild the triangulation. One approach to handle moving points is to use an incremental algorithm. For the case that points move slowly, we can give a faster algorithm than rebuilding it. Furthermore, sequential algorithms can be computationally expensive for large datasets. So, one way to compute as fast as possible is parallelism. In this paper, we propose a parallel algorithm for moving points. we propose an algorithm that divides datasets into equal partitions and give every partition to one block. Each block satisfay the Delaunay constraints after each time step and uses delete and insert algorithms to do this. We show this algorithm works faster than serial algorithms.

翻译：Delaunay三角剖分是计算机视觉、地形建模、空间聚类和网络等诸多知识领域中应用的重要几何问题之一。在处理运动对象时，动力学数据结构在计算几何中变得至关重要。然而，面对运动点，维护动态变化的Delaunay三角剖分可能具有挑战性。因此，在这种情况下，我们必须反复更新三角剖分。若点运动范围较大，则重新构建三角剖分更为合适。处理运动点的一种方法是使用增量式算法。对于点缓慢运动的情形，我们可以给出比重新构建更快的算法。此外，对于大规模数据集，串行算法计算成本可能较高。因此，实现尽可能快速计算的一种途径是并行化。本文提出了一种面向运动点的并行算法。我们提出了一种将数据集划分为相等分区，并将每个分区分配给一个计算块的算法。每个块在每个时间步后满足Delaunay约束条件，并采用删除与插入算法来实现此目标。我们证明该算法比串行算法运行速度更快。