中文摘要：

以生长速度为视角,普通Voronoi图及权重Voronoi图是理想欧氏平面上的生长元匀速生长结果。然而,以Voronoi图为基础的实际分析与建模情况不尽如此,通常表现为非理想平面的非匀速生长过程。本文以权重距离函数描述各向异性的非理想平面,以其时间消耗导数一致性形式化生长速度,定义一种新的Voronoi图——梯度Voronoi图。通过以高程变化诱发的梯度生长为例,借助栅格空间中形态学膨胀操作,给出梯度Voronoi图的典型构建算法。算例与分析表明,在等距离边界、势力范围与邻近关系表达方面,梯度Voronoi图更具优势。

英文摘要：

Taking the growing processing results as angles,an ordinary Voronoi diagram and weighted Voronoi diagram are produced at uniform speed on an ideal Euclidean plane.However,based on analysis,modeling is not always sound in that a Voronoi diagram progresses at varying velocities on a non-ideal plane.The anisotropic non-ideal plane is depicted by weight distance and the growth velocity is formalized in a form conforming to the time derivative of weight distance.Therefore,a new Voronoi diagram,namely Gradient Voronoi Diagram（GVD）was defined in this paper.Taking the gradient caused by changes in elevation as an example,a typical construction model for GVD was propounded with the help of the dilation operator for mathematical morphology in raster space.An analysis shows that GVD has better guided significance and practical application value in the expression of influence regions and the Voronoi adjacency relationship.