Architectural Form by Voronoi Diagram with Ambiguous Boundaries

Abstract

The diagram of the territory of points distributed in space is a Voronoi diagram. The ordinary Voronoi diagram is clearly determined by the perpendicular bisector, an equal distance from two points. On the other hand, ambiguity is taken in about the equal distance for two points. That is, the ambiguous boundary means the equal distance generally. The ordinary Voronoi diagram is made of in straight lines, but the Voronoi diagram that has ambiguous boundaries is formed by circles or hyperbolas. In this research, the Voronoi diagram with ambiguous boundaries is applied to architectural forms, such as a hemisphere, a cuboid and a free form. It is shown by this method that a new form can be formed.