Constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain
نویسندگان
چکیده
منابع مشابه
Constrained multi-degree reduction of Bézier surfaces using Jacobi polynomials
Article history: Received 9 March 2007 Received in revised form 16 June 2008 Accepted 20 October 2008 Available online 1 November 2008
متن کاملTesting Low-Degree Polynomials over
We describe an efficient randomized algorithm to test if a given binary function is a low-degree polynomial (that is, a sum of low-degree monomials). For a given integer and a given real , the algorithm queries at !" # points. If is a polynomial of degree at most , the algorithm always accepts, and if the value of has to be modified on at least an fraction of all inputs in order to transform it...
متن کاملA PTAS for the minimization of polynomials of fixed degree over the simplex - Extended abstract
One may assume w.l.o.g. that p(x) is a homogeneous polynomial (form). Indeed, as observed in [2], if p(x) = ∑d l=0 pl(x), where pl(x) is homogeneous of degree l, then minimizing p(x) over ∆ is equivalent to minimizing the degree d form p(x) := ∑d l=0 pl(x)( ∑n i=1 xi) . Problem (1) is an NP-hard problem, already for forms of degree d = 2, as it contains the maximum stable set problem. Indeed, f...
متن کاملA PTAS for the minimization of polynomials of fixed degree over the simplex
Abstract. We consider the problem of computing the minimum value pmin taken by a polynomial p(x) of degree d over the standard simplex ∆. This is an NP-hard problem already for degree d = 2. For any integer k ≥ 1, by minimizing p(x) over the set of rational points in ∆ with denominator k, one obtains a hierarchy of upper bounds p∆(k) converging to pmin as k −→ ∞. These upper approximations are ...
متن کاملConstrained multi-degree reduction of triangular Bézier surfaces using dual Bernstein polynomials
Abstract. This paper proposes and applies a method to sort two-dimensional control points of triangular Bézier surfaces in a row vector. Using the property of bivariate Jacobi basis functions, it further presents two algorithms for multi-degree reduction of triangular Bézier surfaces with constraints, providing explicit degree-reduced surfaces. The first algorithm can obtain the explicit repres...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2008
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.04.001