SmartVolumes - Adaptive Voronoi Power Diagramming for Real-Time Volumetric Design Exploration
Voronoi Diagrams and Delaunay Triangulations are two concepts fundamental to computational geometry, which have been applied in the most varied disciplines. In recent years, they are increasingly used in architectural design. In this paper, a novel method
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Abstract. Voronoi Diagrams and Delaunay Triangulations are two concepts fundamental to computational geometry, which have been applied in the most varied disciplines. In recent years, they are increasingly used in architectural design. In this paper, a novel method for volumetric design exploration based on three-dimensional (additively weighted) Voronoi power diagrams is described. The method combines fast calculation of three-dimensional weighted Voronoi Power Diagrams with a volume-dependent feedback loop, resulting in a real-time interactive modeling tool. This tool, named SmartVolumes, has been integrated into the modeling environment BehaviourLinks, where the interaction between parametric volumes and other entities can be further elaborated through behavioral linkages. Applications of SmartVolumes in urban design and architectural design are described, implications of the use of Voronoi diagrams for architectural modeling and environments are discussed and directions of consecutive developments are indicated. Keywords: Design Exploration, Interactive Architecture, Design Environments, Computational Design, Voronoi diagram, Delaunay triangulation
1 Introduction The Voronoi diagram resembles many different kinds of natural structures and thus may be a concept of considerable antiquity. One of the first known appearances resembling a Voronoi diagram is an illustration showing the disposition of matter in the solar system published by Descartes in 1644. Though the first comprehensive representations date back to the mid-nineteenth and early twentieth century, given by respectively Dirichlet and Voronoï, Voronoi diagrams were repeatedly rediscovered in various disciplines, even up to the 1980’s [1]. During the first decade of the third millennium, Voronoi diagrams are increasingly applied in urban and architectural design. Two-dimensional Voronoi diagrams have been used in interactive environments for the dynamic assignment of regions of augmented space [2], in urban design stakeholder games for dividing an urban area into parcels, iteratively optimizing plots [3], and structural surface tessellations [4]. Three-dimensional Voronoi diagrams have been used for space-filling structural design [5], and functional optimization of various environmental aspects in architectural design [6]. T.G. Wyeld, S. Kenderdine, and M. Docherty (Eds.): VSMM 2007, LNCS 4820, pp. 132–142, 2008. © Springer-Verlag Berlin Heidelberg 2008
SmartVolumes - Adaptive Voronoi Power Diagramming
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In all architectural applications Voronoi diagrams were arguably also used for their inherent aesthetics. In this paper, a novel method for volumetric design exploration based on threedimensional (additively weighted) Voronoi power diagrams is described. The method combines fast calculation of three-dimensional weighted Voronoi Power Diagrams with a volume-dependent feedback loop, resulting in a real-time interactive modeling tool. This tool, named SmartVolumes, has been integrated into the modeling environment BehaviourLinks, where the interact
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