Abstract:
Dokument1.pdf contains this text of the thesis, Dokument2.html is an index to accompanying electronic videos.
In this thesis, new and improved methods for the visualization of four-dimensional spacetimes are presented. The first part of this thesis deals with the flat spacetime of special relativity. Issues of illumination, color vision, transformation of properties of light, and the kinematics of accelerating bodies are discussed. It is shown how relativistic effects on illumination can be included in well-known rendering techniques. Relativistic radiosity, texture-based relativistic rendering, and image-based relativistic rendering are proposed as new rendering methods. Interactive virtual environments for the exploration of special relativity are introduced, including the relativistic-vehicle-control metaphor for navigating at high velocities.
The second part of the thesis deals with curved four-dimensional spacetimes of general relativity. Direct visualization of what an observer would see in a general relativistic setting is achieved by means of non-linear ray tracing. Extensions to single-chart general relativistic ray tracing are proposed to incorporate the differential-geometric concept of an atlas. Furthermore, it is shown how the visualization of gravitational lensing can be included in a ray tracing system. The caustic finder is proposed as a numerical method to identify two-dimensional caustic structures induced by a gravitational lens. The inner geometry of two-dimensional spatial hypersurfaces can be visualized by isometric embedding in three-dimensional Euclidean space. A method is described which can embed surfaces of spherical topology. Finally, an algorithm for the adaptive triangulation of height fields is presented as a specific application in classical visualization.