Storti, DuaneUchytil, Christopher2024-02-122024-02-122024-02-122023Uchytil_washington_0250E_26366.pdfhttp://hdl.handle.net/1773/51209Thesis (Ph.D.)--University of Washington, 2023This work addresses the challenges of representing, designing, and interacting with high resolution volumetric models for computer-aided design (CAD) applications by presenting a novel function-based representation (F-rep) geometric modeling kernel aimed at providing the capabilities to efficiently design, visualize, and interrogate large scale volumetric models. F-Reps provide a model basis which allows for unambiguous and highly parallelizable point membership classification (PMC) [8, 63, 42] while still supporting modeling techniques common to traditional boundary representation (B-Rep) geometry kernels. Our geometric modeling kernel framework consists of two components: a novel interpreter used to evaluate user-defined models and a sparse volume data structure which stores output produced by the interpreter for visualization and manipulation. Together these two components, in conjunction with the graphics processing unit (GPU), provide the means to support large-scale volumetric modeling applications at scales and speeds not currently achievable by existing software tools. Chapter 2 discusses the geometry kernel interpreter and sparse volume database implementations. Performance metrics are included which demonstrate significant improvements over existing methods in both evaluation and rendering performance as well as supported model size. In the interest of supporting an efficient design process, it is desirable to incorporate into the modeler analysis tools to interrogate properties of the model as it is created. As an initial step toward incorporating analysis tools, Chapter 3 covers a novel integration technique that can be applied to volumetric models created through the F-Rep geometry kernel to measure integral properties, like center of mass, useful for model validation. The integration technique utilizes Federer’s coarea formulation providing a means to integrate functions sampled over a grid when the integrand is not known analytically.application/pdfen-USCC BYAdditive ManufacturingComputer Aided DesignHigh Performance ComputingMechanical engineeringMechanical engineeringThesis