منابع مشابه
Subdivision Schemes for Thin Plate Splines
Thin plate splines are a well known entity of geometric design. They are defined as the minimizer of a variational problem whose differential operators approximate a simple notion of bending energy. Therefore, thin plate splines approximate surfaces with minimal bending energy and they are widely considered as the standard “fair” surface model. Such surfaces are desired for many modeling and de...
متن کاملSubdivision Schemes for Variational Splines
The original theory of splines grew out of the study of simple variational problems. A spline was a function that minimized some notion of energy subject to a set of interpolation constraints. A more recent method for creating splines is subdivision. In this framework, a spline is the limit of a sequence of functions, each related by some simple averaging rule. This paper shows that the two ide...
متن کاملDraft: Subdivision Schemes for Variational Splines
The original theory of splines grew out of the study of simple variational problems. A spline was a function that minimized some notion of energy subject to a set of interpolation constraints. A more recent method for creating splines is subdivision. A spline is the limit of a sequence of functions, each related by some simple averaging rule. This paper shows that the two ideas are intrinsicall...
متن کاملThin-Plate Splines
2 The Calculus of Variations 2 2.1 Functionals of f and f ′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Functionals of f , f ′, and f ′′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Cubic Splines and Green’s Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Euler-Lagrange Equations for Multi...
متن کاملThin plate regression splines
I discuss the production of low rank smoothers for d ≥ 1 dimensional data, which can be fitted by regression or penalized regression methods. The smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thinplate spline smoothing problem, and are optimal in the sense that the truncation is designed to result in the minimum possible pe...
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ژورنال
عنوان ژورنال: Computer Graphics Forum
سال: 1998
ISSN: 0167-7055
DOI: 10.1111/1467-8659.00277