Linear subdivision is strictly a polynomial phenomenon
نویسندگان
چکیده
منابع مشابه
Polynomial Reproduction in Subdivision
We study conditions on the matrix mask of a vector subdivision scheme ensuring that certain polynomial input vectors yield polynomial output again. The conditions are in terms of a recurrence formula for the vectors which determine the structure of polynomial input with this property. From this recurrence, we obtain an algorithm to determine polynomial input of maximal degree. The algorithm can...
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In previous works a polynomial interpolation method for triangular meshes has been introduced. This interpolant can be used to design smooth surfaces of arbitrary topological type. In a design process, it is very useful to be able to locate the deformation made on a geometric model. The previously introduced interpolant has the so-called strict locality property: when a mesh vertex is changed, ...
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This paper presents a new algorithm for solving a system of polynomials, in a domain of . It can be seen as an improvement of the Interval Projected Polyhedron algorithm proposed by Sherbrooke and Patrikalakis [SP93]. It uses a powerful reduction strategy based on univariate root finder using Bernstein basis representation and Descarte’s rule. We analyse the behavior of the method, from a theor...
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Given a dilation matrix A : Z d → Z d , and G a complete set of coset representatives of 2π(A −− Z d /Z d), we consider polynomial solutions M to the equation g∈G M (ξ + g) = 1 with the constraints that M ≥ 0 and M (0) = 1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbol...
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We first present necessary and sufficient conditions for a linear, binary, uniform, and stationary subdivision scheme to have polynomial reproduction of degree d and thus approximation order d + 1. Our conditions are partly algebraic and easy to check by considering the symbol of a subdivision scheme, but also relate to the parameterization of the scheme. After discussing some special propertie...
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ژورنال
عنوان ژورنال: Computer Aided Geometric Design
سال: 1984
ISSN: 0167-8396
DOI: 10.1016/0167-8396(84)90013-x