Curve and surface framing for scientific visualization and domain dependent navigation

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

Comments on event driven animation

Event driven animation provides a general method of describing controlling values for various computer animation techniques. A definition and comments are provided on genralizing motion description with events. Additional comments are also provided about the implementation of twixt

Time-like definition of quaternions in exterior algebra

A formal description of quaternions by means of exterior calculus is provided. Considering a three-dimensional space-time characterized by having three time coordinates, we have been able to consistently recover a suitable formulation of quaternions by means of the properties arising from exterior algebra and calculus. As an application, it is also illustrated how rotations may be written in terms of quaternions according to the exterior-algebraic notation.Comment: 7 page

Фундаментальні основи ефективного подання та обробки данихна базі гіперкомплексних числових систем

Розглянуто різні способи отримання гіперкомплексних числових систем (ГЧС), у тому числі методом переходу від нескінченновимірних гіперкомплексних систем шляхом факторизації до скінченновимірних ГЧС. Розглянуто засоби подання та обробки інформації за допомогою ГЧС.Рассмотрены различные способы получения гиперкомплексных числовых систем (ГЧС), в том числе методом перехода от бесконечномерных гиперкомплексных систем путем факторизации до конечномерных ГЧС. Рассмотрены способы представления и обработки данных с помощью ГЧС.The various ways of obtaining hypercomplex numerical systems (HNS), including the method of transition from infinite hypercomplex systems by factorization to the finite HNS are considered. The methods of data presentation and processing using HNS are given