High-quality Spline and Subdivision Surfaces

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Superior shape and surface quality have a visible impact on new product design and industrial competitiveness. Decreasing the need for human, heuristic intervention when modeling surfaces is a precondition for accurate engineering simulation and high-quality geometry processing and it reduces effort, time, cost and variability. Characterizing and creating surfaces that withstand scrutiny in the detail is a fundamental unresolved challenge to applied differential geometry and geometric design.This research will characterize high-quality surfaces and develop tools for their creation. The effort centers on surfacing schemes that are computationally efficient, finite and affine invariant, and generate fair, curvature-continuous, parametric surfaces that are representable in a standard rational or polynomial form. The starting hypothesis is that a blend between multiple primary surfaces is good if it does not create curvature features that were not present in the defining data.The research will analyze why the existing techniques fail to generate satisfactory curvature distributions, develop a practical notion of surface quality, repair existing techniques or declare why they are fundamentally flawed and develop new approaches to be tested against a carefully chosen obstacle course of joins of multiple primary surfaces.