Figure 1: (Left) 1024 points with constant density in a toroidal square and its spectral analysis to the right; (Center) 2048 points with the density function ρ = e (−20x 2 −20y 2 ) + 0.2 sin 2 (πx) sin 2 (πy); (Right) 4096 points with a density function extracted from a grayscale image. AbstractWe present a new general-purpose method for optimizing existing point sets. The resulting distributions possess high-quality blue noise characteristics and adapt precisely to given density functions. Our method is similar to the commonly used Lloyd's method while avoiding its drawbacks. We achieve our results by utilizing the concept of capacity, which for each point is determined by the area of its Voronoi region weighted with an underlying density function. We demand that each point has the same capacity. In combination with a dedicated optimization algorithm, this capacity constraint enforces that each point obtains equal importance in the distribution. Our method can be used as a drop-in replacement for Lloyd's method, and combines enhancement of blue noise characteristics and density function adaptation in one operation.

In this paper we present a hierarchy-based visualization approach for software metrics using Treemaps. Contrary to existing rectangle-based Treemap layout algorithms, we introduce layouts based on arbitrary polygons that are advantageous with respect to the aspect ratio between width and height of the objects and the identification of boundaries between and within the hierarchy levels in the Treemap. The layouts are computed by the iterative relaxation of Voronoi tessellations. Additionally, we describe techniques that allow the user to investigate software metric data of complex systems by utilizing transparencies in combination with interactive zooming.

Figure 1: (Left) 1024 points with constant density in a toroidal square and its spectral analysis to the right; (Center) 2048 points with the density function ρ = e (−20x 2 −20y 2 ) + 0.2 sin 2 (πx) sin 2 (πy); (Right) 4096 points with a density function extracted from a grayscale image. AbstractWe present a new general-purpose method for optimizing existing point sets. The resulting distributions possess high-quality blue noise characteristics and adapt precisely to given density functions. Our method is similar to the commonly used Lloyd's method while avoiding its drawbacks. We achieve our results by utilizing the concept of capacity, which for each point is determined by the area of its Voronoi region weighted with an underlying density function. We demand that each point has the same capacity. In combination with a dedicated optimization algorithm, this capacity constraint enforces that each point obtains equal importance in the distribution. Our method can be used as a drop-in replacement for Lloyd's method, and combines enhancement of blue noise characteristics and density function adaptation in one operation.

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The level-of-detail techniques presented in this paper enable a comprehensible interactive visualization of large and complex clustered graph layouts either in 2D or 3D. Implicit surfaces are used for the visually simplified representation of vertex clusters, and so-called edge bundles are formed for the simplification of edges. Additionally, dedicated transition techniques are provided for continuously adaptive and adjustable views of graphs that range from very abstract to very detailed representations.