| We address the problem of direct graphical processing of B-spline based models in a graphics system. We focus on graphics systems intended for interactive design and engineering applications, primarily architectural and mechanical CAD. It is desirable that these systems: (1) retain the graphical data in order to support the concept of graphical data editing, and (2) preform basic rendering techniques on continually changing (dynamic) data in order to achieve maximum interactivity.;We present a solution that emphasizes formality by ensuring the generation of accurate images, and completeness by ensuring the proper processing of general graphical data. There are cases of mathematically well-defined data that were not addressed in the past because they were judged as impractical. We suggest that there are important, practical applications for these cases and we demonstrate how they are handled within the framework of our solution. This drive for formality and completeness is an important step towards ensuring the robustness and credibility of graphics systems.;The emphasis on formality and completeness has a potentially negative impact on efficiency. We successfully counter this concern by developing the general concept of graphical data compilation. This concept facilitates and speeds traversal by identifying components of the graphical data that can be computed at creation time and that remain usable after data edit operations. We systematically apply this concept to reduce the mathematical form of the graphical data into a simpler but still complete form.;Furthermore, we develop and provide algorithms for the factorization and classification of homogeneous transformations that lead to enhanced forms of the conceptual pipeline. We compare and contrast adaptive and uniform tessellation techniques, whereby we conclude that uniform techniques are more favorable for solving the problem at hand. Uniform techniques meet the approximation criteria based on a priori differential analysis of the primitives. We absorb the majority of the complexity of trimmed surfaces at compilation time, and we incorporate support for the simplified form of trimming with the tessellation process. We give the results of extensive experimentation with different approximation schemes on geometric reflectance parameters, and we treat such approximations more formally than they have been treated in the past. |
