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High-order and regularly sampled surface representations are more efficient and compact than general meshes and considerably simplify many geometric modeling and processing algorithms. A number of recent algorithms for conversion of arbitrary meshes to regularly sampled form (typically quadrangulation) aim to align the resulting mesh with feature lines of… (More)
We present an extension of recently developed Loop and Schaefer's approximation of Catmull-Clark surfaces (ACC) for surfaces with creases and corners which are essential for most applications. We discuss the integration of ACC into Valve's Source game engine and analyze performance of our implementation.
Quadrangulation methods aim to approximate surfaces by semi-regular meshes with as few extraordinary vertices as possible. A number of techniques use the harmonic parameterization to keep quads close to squares, or fit parametrization gradients to align quads to features. Both types of techniques create near-isotropic quads; feature-aligned quadrangulation… (More)
Behavioral experiments were performed on 342 subjects to determine whether behavior, which could affect the level of personal exposure, is exhibited in response to odors and labels which are commonly used for household chemicals. Potential for exposure was assessed by having subjects perform cleaning tasks presented as a product preference test, and noting… (More)
Meshes with T-joints (T-meshes) and related high-order surfaces have many advantages in situations where flexible local refinement is needed. At the same time, designing subdivision rules and bases for T-meshes is much more difficult, and fewer options are available. For common geometric modeling tasks it is desirable to retain the simplicity and… (More)
We present an extension of Loop and Schaefer's approximation of Catmull-Clark surfaces (ACC) for surfaces with creases and corners. We discuss the integration of ACC into Valve's Source game engine and analyze performance of our implementation.
Nonlinear Galerkin methods utilize approximate inertial manifolds to reduce the spatial error of the standard Galerkin method. For certain scenarios, where a rough forcing term is used, a simple postprocessing step yields the same improvements that can be observed with nonlinear Galerkin. We show that this improvement is mainly due to the information about… (More)
Acknowledgments First of all, I must thank my advisor Denis Zorin under whose guidance I have learned how to conduct rigorous computer science research. Denis's knowledge is vast, and his opinions are measured. His curriculum extended beyond computer science and mathematics into life, public policy, and common sense. During my time at NYU, I have been lucky… (More)
Dedication To my beautiful daughter Lilu, who reminded me of the incredible wonders possible in this universe and gave me the motivation I needed to get reinstated into the graduate program at NYU and complete my dissertation. iii Acknowledgments I would like to thank New York University, the Graduate School of Arts and Sciences, the Courant Institute and… (More)
We use notation introduced in the Appendix of the paper. To compute the value of P 1 j we need to define a stencil of control points P 0 i that influence its value. We exhaustively enumerate the 1-ring neighborhood configurations (with a suitable extension at T-vertices and T-edges) of a vertex in all possible T-mesh configurations. Here we show that such a… (More)