منابع مشابه
Curvature Smoothness of Subdivision Surfaces
We examine the smoothness properties of the principal curvatures of subdivision surfaces near extraordinary points. In particular we give an estimate of their Lp class based on the eigen structure of the subdivision matrix. As a result we can show that the popular Loop and Catmull-Clark schemes (among many others) have square integrable principal curvatures justifying their use as shape functio...
متن کاملInvariant smoothness measures for surfaces
Two novel smoothness measures for surfaces are presented in this paper. The second and third order smoothness are defined as the squared normal curvature and the squared variation in normal curvature integrated over all directions in the tangent plane. Both quantities are truly geometric in the sense that they are invariant with respect to the actual parametrization of the surface. All the same...
متن کاملWeak systems of determinacy and arithmetical quasi-inductive definitions
We locate winning strategies for various Σ3-games in the L-hierarchy in order to prove the following: THEOREM 1. KP +Σ2-Comprehension ` ∃αLα |=“Σ2-KP +Σ3-Determinacy .” Alternatively: Π3-CA0 `“there is a β-model of ∆ 1 3-CA0 + Σ 0 3Determinacy.” The implication is not reversible. (The antecedent here may be replaced with Π3(Π 1 3)-CA0: Π 1 3 instances of Comprehension with only Π3-lightface def...
متن کاملSmoothness of Subdivision Surfaces with Boundary
Subdivision rules formesheswith boundary are essential for practical applications of subdivision surfaces. These rules have to result in piecewise C -continuous boundary limit curves and ensure C -continuity of the surface itself. Extending the theory of Zorin (Constr Approx 16(3):359–397, 2000), we present in this paper general necessary and sufficient conditions for C -continuity of subdivisi...
متن کاملSmoothness assessment of corneal stromal surfaces.
PURPOSE To assess the accuracy of the scanning electron microscopy (SEM) and present alternative approaches to quantify surface roughness based on numerical analysis. SETTING Department of Ophthalmology, Maisonneuve-Rosemont Hospital, University of Montreal, Montreal, Quebec, Canada. DESIGN Experimental study. METHODS Lamellar stromal cuts were performed on human corneas using a femtoseco...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2002
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(01)00163-3