Thesis (Ph.D.) - Indiana University, Computer Science, 1996Curves and surfaces are two of the most fundamental types of objects in computer graphics. Most existing systems use only the 3D positions of the curves and surfaces, and the 3D normal directions of the surfaces, in the visualization process. In this dissertation, we attach moving coordinate frames to curves and surfaces, and explore several applications of these frames in computer graphics and scientific visualization. Curves in space are difficult to perceive and analyze, especially when they are densely clustered, as is typical in computational fluid dynamics and volume deformation applications. Coordinate frames are useful for exposing the similarities and differences between curves. They are also useful for constructing ribbons, tubes and smooth camera orientations along curves. In many 3D systems, users interactively move the camera around the objects with a mouse or other device. But all the camera control is done independently of the properties of the objects being viewed, as if the user is flying freely in space. This type of domain-independent navigation is frequently inappropriate in visualization applications and is sometimes quite difficult for the user to control. Another productive approach is to look at domain-specific constraints and thus to create a new class of navigation strategies. Based on attached frames on surfaces, we can constrain the camera gaze direction to be always parallel (or at a fixed angle) to the surface normal. Then users will get a feeling of driving on the object instead of flying through the space. The user's mental model of the environment being visualized can be greatly enhanced by the use of these constraints in the interactive interface. Many of our research ideas have been implemented in Mesh View, an interactive system for viewing and manipulating geometric objects. It contains a general purpose C++ library for nD geometry and supports a winged-edge based data structure. Dozens of examples of scientifically interesting surfaces have been constructed and included with the system.