This thesis describes the improvements in the mathematical aspects of the high-level programming language for interactive graphics (LIG). Improvement possibilities were investigated in three areas: dependence on the order of transformations, arithmetic expressions appearing in LIG statements, and the implementation to allow the programming of graphical functions. The method of implementation of the proposed improvements is also discussed. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Researchers developing high-level graphics languages have, according to the literature, focused their attention towards line-drawing graphics. Little effort has been devoted to systematic investigations of languages that handle graphical data representing line-drawings as well as solid areas. The latter type of graphical data is usually represented hy outlines, and solid area properties are visualized by hatching or filling techniques. A study of the literature on programming languages leads to the conclusion that graphical data should be treated as a data type. Based on the concept of treating graphical data as a data type in its own right, the mathematical and conceptual aspects of this type of data are investigated and established. Much scattered information, such as the representation of regions, has been unified using formal descriptions. Hatching, one of the many ways of achieving external representation of regions, is also investigated. A hatching algorithm is proposed and implemented that envelops the good features of others, and establishes a framework for hatching algorithms. Its implementation achieves the expected tasks. A proposal for a graphics language demonstrates the usefulness and feasibility of this type of graphics. Some of its features have been implemented. Finally, a fairly complete bibliography serves as a gateway for further research in this area. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Unknown

This thesis is concerned with the design and implementation of a surface fitting package in an interactive graphics environment. Surface fitting techniques are used to generate a smooth looking, easy to evaluate, bivariate function given a set of data points on some domain in the plane, and are thus useful for a variety of applications. We consider the implementation of a surface fitting technique using weighted least squares with tensor products of B-splines on regular data grids (i.e. the position of the data points can be represented as the cross product of two vectors). While somewhat more restrictive than other surface fitting methods, this technique, when applicable, is extremely efficient. Knot placement and weight placement are discussed as methods of adapting the spline surface to rapidly varying regions on the domain. A disadvantage of the original method used to solve for the coefficients of the spline surface is that the domain of the function to be approximated must be rectangular. An algorithm to extend the surface fitting method to non-rectangular domains, thus removing this restriction, is presented. An interactive surface fitting package is provided, which allows a user to fit a spline surface to a set of data points on a regular grid. This provides a powerful tool which may be used to effectively modify the spline surface and indicate the accuracy of the approximation. / Science, Faculty of / Computer Science, Department of / Graduate

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<p dir="ltr">The fidelity and efficiency of physics simulations in computer graphics, particularly those involving deformable bodies, hinge significantly on the computational methods employed. This thesis investigates the optimization of Extended Position-Based Dynamics (XPBD), a variant of Position-Based Dynamics known for its stability and real-time performance, through the integration of voxel constraints in a parallel computing framework. The primary focus is on three aspects: efficient computation of XPBD models from large meshes, optimization of constraint partitioning to enhance simulation performance, and the automatic generation of long-range constraints to increase stiffness.</p><p dir="ltr">Our approach leverages voxelization to transform complex 3D models into a manageable, discrete representation, facilitating the use of Levels of Detail (LoD) to handle varying mesh resolutions effectively. This technique allows for the straightforward application of XPBD simulations by reducing the computational complexity associated with traditional tetrahedral meshes. Additionally, the thesis explores the use of compute shaders to manage parallel read/write operations efficiently, thereby addressing the challenges commonly associated with real-time physics simulations.</p><p dir="ltr">The research demonstrates that voxel-based constraints, particularly when combined with LoD strategies, not only improve the performance but also enhance the stiffness and stability of XPBD simulation. This allows for more detailed and complex simulations. </p>

Title from title page of PDF (University of Missouri--St. Louis, viewed February 23, 2010). Includes bibliographical references (p. 33-35).