This research focuses on the generation of representational structure from unstructured inputs for model reconstruction to facilitate subsequent geometry processing. In particular, the results include spline-based curve reconstruction of sharp features in point-sampled geometry, and quadrilateral-only mesh processing and generation from polygonal models. The challenges of model reconstruction, as well as the relationship between continuous and discrete geometry, are important thematic elements of this research.;Virtual surface models are ubiquitous in computer graphics, representing fundamental entities in visualization and modeling toolkits. Applications of surface geometry are as diverse as the representational formats constructed to achieve these ends, each designed with different characteristics and advantages. Translation between the assorted forms is often necessitated by the allowable inputs of system implementations and desired algorithms, and requires techniques to reconstruct the model with new geometry. Consequently, model reconstruction algorithms are prevalent in most modeling pipelines, used to augment the availability of applicable algorithms and to improve the robustness and efficiency of subsequent geometry processing. In this work, my simplification and reconstruction results are demonstrated on a variety of organic and mechanical models whose original representations range from point clouds to unstructured and structured triangle, quadrilateral, and hybrid meshes.
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