Michael Balzer

Voronoi treemaps for the visualization of software metrics

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.

Capacity-constrained point distributions: a variant of Lloyd's method

We 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 Lloyds 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 Lloyds method, and combines enhancement of blue noise characteristics and density function adaptation in one operation.

Voronoi treemaps

Treemaps are a well known method for the visualization of attributed hierarchical data. Previously proposed treemap layout algorithms are limited to rectangular shapes, which cause problems with the aspect ratio of the rectangles as well as with identifying the visualized hierarchical structure. The approach of Voronoi treemaps presented in this paper eliminates these problems through enabling subdivisions of and in polygons. Additionally, this allows for creating treemap visualizations within areas of arbitrary shape, such as triangles and circles, thereby enabling a more flexible adaptation of treemaps for a wider range of applications.

Level-of-detail visualization of clustered graph layouts

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.

Software landscapes: visualizing the structure of large software systems

Modern object-oriented programs are hierarchical systems with many thousands of interrelated subsystems. Visualization helps developers to better comprehend these large and complex systems. This paper presents a three-dimensional visualization technique that represents the static structure of object-oriented programs using landscape-like distributions of three-dimensional objects on a two-dimensional plane. The familiar landscape methaphor facilitates intuitive navigation and comprehension. The visual complexity is reduced by adjusting the transparency of object surfaces to the distance of the viewpoint. An approach called Hierarchical Net is proposed for a clear representation of the relationsships between the subsystems.

Hierarchy Based 3D Visualization of Large Software Structures

Modern object-oriented programs are hierarchical systems with many thousands of interrelated subsystems. Visualization helps developers to better comprehend these large and complex systems. This work presents a three-dimensional visualization technique that represents the static structure of object-oriented software using distributions of three-dimensional objects on a two-dimensional plane. The visual complexity is reduced by adjusting the transparency of object surfaces to the distance of the viewpoint. An approach called Hierarchical Net is proposed for a clear representation of the relationships between the subsystems.

Exploring Relations within Software Systems Using Treemap Enhanced Hierarchical Graphs

The clear and meaningful visualization of relations between software entities is an invaluable tool for the comprehension, evaluation, and reengineering of the structure of existing software systems. This paper presents an interaction and representation scheme for the visualization and exploration of complex hierarchical graphs to analyze relations within software systems. Thereby aggregated parts of the software system are represented as treemaps that visualize the structure of the contained software entities. An adaptation of existing rectangle-based treemap algorithms for layouts within convex polygonal bounding geometries is introduced to allow for a differentiation of various entity types in the graph visualization. Furthermore, a visual clustering method based on implicit surfaces is presented to create meaningful visualizations of distorted hierarchical graphs of software systems

Capacity-Constrained Voronoi Diagrams in Continuous Spaces

A Voronoi diagram of a set of sites partitions a bounded space into regions of different areas. A capacity-constrained Voronoi diagram is a partition in which the area for each Voronoi region is predefined. In this paper, we present two approaches for computing such capacity-constrained Voronoi diagrams in continuous spaces. Our firstapproach is based on ordinary (non-weighted) distance functions and achieves the capacity constraint by a general optimization of the site locations. Our second approach is based on weighted distance functions and optimizes the weights of the sites. Both approaches are iterative methods that start with an initial set of sites and then optimize the area of one Voronoi region at a time. As a consequence, the dimensionality of the individual optimization problem is minimal, which enables a reliable and fast convergence even for large sets of sites.

Expressive illumination of foliage based on implicit surfaces

This paper presents an approach for vivid representations of foliage based on implicit surfaces. It approximates the complex lighting interaction within the foliage and enables a clear illustration of its general shape and local density, thus supporting the three-dimensional depth cue of the viewer. Due to its straightforward implementation as a preprocessing step that only adjusts the normal vectors of the geometry, this method has no additional memory requirements during the rendering process, and is especially applicable to real-time visualizations.

Detail‐In‐Context Visualization for Satellite Imagery

We use the complex logarithm as a transformation for the visualization and navigation of highly complex satellite and aerial imagery. The resulting depictions show details and context with greatly different scales in one seamless image while avoiding local distortions. We motivate our approach by showing its relations to the ordinary perspective views and classical map projections. We discuss how to organize and process the huge amount of imagery in realtime using modern graphics hardware with an extended clipmapping technique. Finally, we provide details and experiences concerning the interpretation of and interaction with the resulting representations.