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中文摘要：
提出一种基于线性四叉树结构并顾及矢量与栅格计算性质的Voronoi图生成方法，其核心思想是利用线性四又树结构以减小空间剖分所产生的空间复杂度，改变膨胀模拟操作的计算方向以减小时间复杂度。讨论了基于数学形态学的反向膨胀计算模型及推理出基于该计算模型的几个优化计算性质。实验验证，这种方法能够有效地平衡时空复杂度，并且易于求取邻元，其时间复杂度小于均匀格网结构与常规四叉树结构。一般情况下，空间复杂度小于均匀格网结构。
英文摘要：
An integrated raster-vector method based on linear quadtree structure for generating the Voronoi Diagram is proposed. The key idea of this method is to reduce the spatial complexity in the space partition by linear quadtree structure and reduce the time complexity by changing the calculating direction of dilatation. The computing model of backward inflation based on mathematical morphology and several optimized computing characteristics of the model are proposed. The test proves the time complexity of the method is lower than that of uniform grid structure and that of common quadtree structure and the space complexity is lower than that of uniform grid structure.
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