Mathematical techniques for shape modelling in computer graphics: A distance-based approach.

This research is concerned with shape modelling in computer graphics. The dissertation provides a review of the main research topics and developments in shape modelling and discusses current visualisation techniques required for the display of the models produced. In computer graphics surfaces are normally defined using analytic functions. Geometry however, supplies many shapes without providing their analytic descriptions. These are defined implicitly through fundamental relationships between primitive geometrical objects. Transferring this approach in computer graphics, opens new directions in shape modelling by enabling the definition of new objects or supplying a rigorous alternative to analytical definitions of objects with complex analytical descriptions. We review, in this dissertation, relevant works in the area of implicit modelling. Based on our observations on the shortcomings of these works, we develop an implicit modelling approach which draws on a seminal technique in this area: the distance based object definition. We investigate the principles, potential and applications of this technique both in conceptual terms (modelling aspects) and on technical merit (visualisation issues). This is the context of this PhD research. The conceptual and technological frameworks developed are presented in terms of a comprehensive investigation of an object's constituent primitives and modelling constraints on the one hand, and software visualisation platforms on the other. Finally, we adopt a critical perspective of our work to discuss possible directions for further improvements and exploitation for the modelling approach we have developed

Overview of database projects

The use of entity and object oriented data modeling techniques for managing Computer Aided Design (CAD) is explored

3D reconstruction of cerebral blood flow and vessel morphology from x-ray rotational angiography

Three-dimensional (3D) information on blood flow and vessel morphology is important when assessing cerebrovascular disease and when monitoring interventions. Rotational angiography is nowadays routinely used to determine the geometry of the cerebral vasculature. To this end, contrast agent is injected into one of the supplying arteries and the x-ray system rotates around the head of the patient while it acquires a sequence of x-ray images. Besides information on the 3D geometry, this sequence also contains information on blood flow, as it is possible to observe how the contrast agent is transported by the blood. The main goal of this thesis is to exploit this information for the quantitative analysis of blood flow. I propose a model-based method, called flow map fitting, which determines the blood flow waveform and the mean volumetric flow rate in the large cerebral arteries. The method uses a model of contrast agent transport to determine the flow parameters from the spatio-temporal progression of the contrast agent concentration, represented by a flow map. Furthermore, it overcomes artefacts due to the rotation (overlapping vessels and foreshortened vessels at some projection angles) of the c-arm using a reliability map. For the flow quantification, small changes to the clinical protocol of rotational angiography are desirable. These, however, hamper the standard 3D reconstruction. Therefore, a new method for the 3D reconstruction of the vessel morphology which is tailored to this application is also presented. To the best of my knowledge, I have presented the first quantitative results for blood flow quantification from rotational angiography. Additionally, the model-based approach overcomes several problems which are known from flow quantification methods for planar angiography. The method was mainly validated on images from different phantom experiments. In most cases, the relative error was between 5% and 10% for the volumetric mean flow rate and between 10% and 15% for the blood flow waveform. Additionally, the applicability of the flow model was shown on clinical images from planar angiographic acquisitions. From this, I conclude that the method has the potential to give quantitative estimates of blood flow parameters during cerebrovascular interventions

ARCAID: The ARChitects computer graphics AID

technical reportARCAID?The ARChitect's Computer Graphics AID?is one part of a two-part research program at the University of Utah under the direction of David C. Evans. ARCAID is a specification for the organization of computer processes including data and procedures for the use of architects, engineers, and others in design. As the second part of this research C. Stephen Carr is developing the complex data structure which supports ARCAID. This data structure includes a graphics FORTRAN, a compiler-compiler, an associative memory, and a tree structure for organizing the data for a building scheme. ARCAID is an interactive computer graphics system relying on the Cathode Ray Tube (CRT) for feedback and a typing keyboard, stylus and tablet, trackball, and zoom pedal for input. The picture at the CRT is refreshed by a small computer, and manipulations of alphanumerics and graphic elements are handled by a large computer. ARCAID envisions the design of a building from first briefing and schematics through construction without the use of paper. ARCAID incorporates a computer graphics language called SPACEFORM. I t provides for graphic elements and procedures by which elements are manipulated. The basic graphic elements, "spaceforms," are built up from such primitives as points, lines, and surfaces. Basic spaceforms may be shaped and assembled for more complex (shaped) spaceforms and objects. Proposed manipulations include housekeeping, shaping, assembling, viewing, orienting, and miscellaneous manipulations. Spaceforms are topologically described with respect to geometry and at tributes. By geometric topology the corners, edges, and faces of objects are constrained to retain fixed relationships permitting rotations and other viewing manipulations thereby. By attribute topology the descriptions of objects are also linked to such at tributes as texture, color, weight, and the like