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Power图的离散生成

Direct Construction of 2D Power Diagram by Growing Circles

  • 摘要: Power图是一种特殊的加权Voronoi图,该图中每个生成元点pi都带有权值wi .给出了一种直接构造Power图的算法.以每个生成元点pi为圆心,Power距离wi为半径画圆;然后将这些圆以不同颜色填充,并以相同速率向外扩展这些圆的边界,直到屏幕上所有像素点都涂上颜色为止,环绕pi的新边界构成Power图.该算法改进了在Voronoi图基础上构造Power图的传统方法,具有较高的效率.

     

    Abstract: Power diagram generalized the Voronoi diagram by assigning weight w i to each given point pi. A straight forward way of constructing Power diagram is presented. Using the Power distance w i as radius, construct circles with each pi as center. Filling all these circles with different colored pixels and propagating the boundary of all circles at the same speed until no blank space is left. The new boundaries surrounding pi present the required Power diagram. Such an approach is more efficient than the traditional way of first generating Voronoi diagram and then converting it to Power diagram.

     

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