Direct Construction of 2D Power Diagram by Growing Circles

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.