منابع مشابه
Analyzing midpoint subdivision
Midpoint subdivision generalizes the Lane-Riesenfeld algorithm for uniform tensor product splines and can also be applied to non regular meshes. For example, midpoint subdivision of degree 2 is a specific Doo-Sabin algorithm and midpoint subdivision of degree 3 is a specific Catmull-Clark algorithm. In 2001, Zorin and Schröder were able to prove C1-continuity for midpoint subdivision surfaces a...
متن کاملGeneral Midpoint Subdivision
In this paper, we introduce two generalizations of midpoint subdivision and analyze the smoothness of the resulting subdivision surfaces at regular and extraordinary points. The smoothing operators used in midpoint and mid-edge subdivision connect the midpoints of adjacent faces or of adjacent edges, respectively. An arbitrary combination of these two operators and the refinement operator that ...
متن کاملA piecewise polynomial approach to analyzing interpolatory subdivision
The four-point interpolatory subdivision scheme of Dubuc and its generalizations to irregularly spaced data studied by Warren and by Daubechies, Guskov, and Sweldens are based on fitting cubic polynomials locally. In this paper we analyze the convergence of the scheme by viewing the limit function as the limit of piecewise cubic functions arising from the scheme. This allows us to recover the r...
متن کاملAnalyzing the Characteristic Map of Triangular Subdivision Schemes
Introduction In the last two decades many subdivision schemes for di erent purposes were devised see e g All these algorithms generate from an initial control net a sequence of nets which converges to a limiting surface Although su cient conditions for the convergence to a smooth limiting surface were given in and their rigorous application has been carried out only for some of the above mentio...
متن کاملDiscrete Midpoint Convexity
For a function defined on a convex set in a Euclidean space, midpoint convexity is the property requiring that the value of the function at the midpoint of any line segment is not greater than the average of its values at the endpoints of the line segment. Midpoint convexity is a well-known characterization of ordinary convexity under very mild assumptions. For a function defined on the integer...
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ژورنال
عنوان ژورنال: Computer Aided Geometric Design
سال: 2011
ISSN: 0167-8396
DOI: 10.1016/j.cagd.2011.08.002