Discretizing the input curves into points or lines is a way of constructing an approximate Voronoi diagram. Sampling the input curves into points requires a fine sample density to obtain a reasonable topological and geometrical accuracy of the Voronoi diagram. In this work, it is shown that an accurate computation of the Voronoi diagram for a set of circles employing a very coarse sample set is possible. The approach proposes the selection of varying number of sample points on each circle dynamically, using the Delaunay graph of center points of circles. We then show that this approach can be used to identify neighborhood information of the circles. The touching disc method is then used to construct the Voronoi diagram with an algorithmic complexity of $O(nlogn)$. The work also demonstrates the robustness and theoretical correctness of the proposed algorithm by considering inputs in non-general position and for a large number of circles of the order of ${\mathbf{10}}^{\mathbf{5}}$.

将输入曲线离散为点或线是构建近似 Voronoi 图的一种方法。将输入曲线采样成点需要精细的样本密度，以获得 Voronoi 图的合理拓扑和几何精度。在这项工作中，表明可以使用非常粗略的样本集准确计算一组圆的 Voronoi 图。该方法建议使用圆的中心点的 Delaunay 图动态地选择每个圆上不同数量的样本点。然后我们展示了这种方法可用于识别圆圈的邻域信息。然后使用触摸盘方法构建 Voronoi 图，算法复杂度为$哦(n升○Gn)$. 该工作还通过考虑非一般位置的输入和大量的圈数，证明了所提出算法的鲁棒性和理论正确性。${\mathbf{10}}^{\mathbf{5}}$.