Power diagrams, as a powerful extension of Voronoi diagrams, have been utilized in a wide range of applications in various fields. By imposing the capacity constraint and the centroid constraint to the ordinary power diagram, capacity-constrained power diagram and centroidal capacity-constrained power diagram can be obtained respectively, in which, all the capacity constraints are fixed values. However, some practical applications require a special kind of power diagrams, called hybrid capacity-constrained centroidal power diagrams, where not all capacity constraints are fixed values, and instead there are some capacities of sites constrained to intervals. To this end, we propose an iterative computation method for the power diagrams with hybrid capacity constraints. On the one hand, a weight evaluated method is introduced to update the weights of interval capacity-constrained sites, and Newton’s method is applied to optimize the weights of fixed-value capacity-constrained sites. On the other hand, Lloyd’s method is employed to move the sites to their respective mass centers. Experimental results prove that the proposed method can effectively compute the centroidal power diagram with hybrid capacity constraints.

功率图作为Voronoi图的强大扩展，已在各个领域的许多应用中得到利用。通过对普通功率图施加容量约束和质心约束，可以分别得到容量约束功率图和质心容量约束功率图，其中所有容量约束均为固定值。但是，某些实际应用需要一种特殊的功率图，称为混合容量受限的质心功率图，其中并非所有容量约束都是固定值，而是某些站点的容量受限于间隔。为此，我们提出了一种具有混合容量约束的功率图迭代计算方法。一方面，引入了权重评估法来更新区间容量受限站点的权重，牛顿法则用于优化固定值容量受限站点的权重。另一方面，采用劳埃德（Lloyd）方法将站点移动到其各自的质心。实验结果表明，该方法能够有效地计算出混合容量约束下的质心功率图。