In this paper we introduce methods for the visualization of ontologies using different geometrical representations. An ontology is a formal way to define domain knowledge by means of axioms about domain concepts, properties and individuals. Currently, ontologies are modeled with the OWL language; this language is very expressive and provides challenges for ontology visualization. Expressive ontologies can be difficult to understand and to that end ontology visualization can be extremely helpful for ontology inspection during the process of development as well as for inspection of existing ontologies. Our improved approach for ontology visualization includes two different tree-visualization techniques: i.e., the node-link technique and the containment technique. The node-link technique visualizes the ontology as a graph. The graph can be build for each concept with different levels of depth. The core visualization component is based on the spanning tree skeleton of the graph and it includes five different geometrical views, i.e., two Euclidean, two hyperbolic and one spherical. All the views are augmented with corresponding geometrical transformations so that user interaction like pan, zoom and rotate can be invoked. Another approach encompasses a 3-dimensional spherical alternative of the treemap method, in which nodes are placed on the surface of a sphere. Each parental node contains its children, which are places on the surface of the parent. We augmented this method with semantic zoom technique. With this technique the level of details depends on the distance from the viewer. Our approach provides the means to visualize ontology from different perspectives and different levels of detail. The interaction that is provided greatly enhances the user perception of otherwise complex information.
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