A Study on Voronoi Diagrams with Obstacles in the Architectural and Urban Space

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This research consists of two parts, the first part is the methodology of the Voronoi diagrams with obstacles, and the second one is the application of the method to the actual architectural and urban space, which shows the efficiency and benefit by this method.In the first part, we propose a method for constructing Voronoi diagrams with two-dimensional obstacles by a simple and practical computer algorithm, using the shortest-path distance of a Delaunay network of many random vertices, which we termed as rDn. By measuring the shortest-path distance of the rDn for the detour distance, this method provides an approximate solution for the Voronoi diagrams with obstacles. We verify the isotropy and stability of the ratio of the shortest-path distance of the rDn and the Euclid distance by a computer experiment. We then show the reliability of the approximate solution by comparing with the exact solution in a simple case, and the effectiveness of this method by solving a sample problem with free shaped obstacles.The second part describes the construction and application of Voronoi diagrams with obstacles. By applying the model, we analyzed the domain of Automated External Defibrillators (AED) around Ueno Park in Tokyo, Japan, and indicated a more efficient AED location by including the necessary time for the rescuer and his or her helper both of whom happened to be near the victim of Sudden Cardiac Arrest (SCA), to get an AED avoiding various obstacles: pond, building, planting, fence, in the park. After indicating the current location of AEDs, we proposed a new location plan with additional AEDs placed in public facilities in the park with no AED that will improve the average shortest-path distance from 343m to 119m, which is equivalent to almost 18% improvement in survival rate.