Refinable polycube G-splines
نویسندگان
چکیده
منابع مشابه
Refinable polycube G-splines
Polycube G-splines form a 2-manifold guided by a mesh of quadrilateral faces such that at most six quads meet at each vertex. In particular, this replicates the layout of the quad faces of a polycube. Polycube G-splines are piecewise bicubic and polycube Gspline surfaces are almost everywhere tangent-continuous (G) based on rational linear reparameterization. They can be constructed in two diff...
متن کاملStructure of Refinable Splines
A refinable spline is a compactly supported refinable function that is piecewise polynomial. Refinable splines, such as the well known B-splines, play a key role in computer aided geometric designs. Refinable splines have been studied in several papers, most noticably in [7] for integer dilations and [3] for real dilations. There are general characterizations in these papers, but these characte...
متن کاملClassification of Refinable Splines
A refinable spline is a compactly supported refinable function that is piecewise polynomial. Refinable splines, such as the well known B-splines, play a key role in computer aided geometric designs. So far all studies on refinable splines have focused on positive integer dilations and integer translations, and under this setting a rather complete classification was obtained in [12]. However, re...
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A refinable spline in R is a compactly supported refinable function whose support can be decomposed into simplices such that the function is a polynomial on each simplex. The best known refinable splines in R are the box splines. Refinable splines play a key role in many applications, such as numerical computation, approximation theory and computer aided geometric design. Such functions have be...
متن کاملCharacterization of compactly supported refinable splines
We prove that a compactly supported spline function of degree k satisses the scaling equation (x) = P N n=0 c(n)(mx?n) for some integer m 2, if and only if (x) = P n p(n)B k (x?n) where p(n) are the coeecients of a polynomial P(z) such that the roots of P(z)(z ? 1) k+1 are mapped into themselves by the mapping z ! z m , and B k is the uniform B-spline of degree k. Furthermore, the shifts of for...
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ژورنال
عنوان ژورنال: Computers & Graphics
سال: 2016
ISSN: 0097-8493
DOI: 10.1016/j.cag.2016.05.021