Degenerations of NURBS curves while all of weights approaching infinity
نویسندگان
چکیده
منابع مشابه
Degenerations of NURBS curves while all of weights approaching infinity
NURBS curve is widely used in Computer Aided Design and Computer Aided Geometric Design. When a single weight approaches infinity, the limit of a NURBS curve tends to the corresponding control point. In this paper, a kind of control structure of a NURBS curve, called regular control curve, is defined. We prove that the limit of the NURBS curve is exactly its regular control curve when all of we...
متن کاملReparametrization of NURBS Curves
In geometric design, it is often useful to be able to give an arc length reparametrization for NURBS curves, that keeps the curve a NURBS too. Since parametric rational curves, except for straight lines, cannot be parametrized by arc length, we developed a numerical method of approximating the arc length parametrization function. In this way it was possible to obtain a good parametrization of a...
متن کاملDegenerations of Curves in P3
In this paper we prove every connected, reduced curve in P3 of arithmetic genus 0, may be flatly smoothed. Moreover, we give a new example of a reduced singular curve in P3 which cannot be flatly smoothed. Introduction. This paper is concerned with the following question: Given a reduced, connected curve IcP3, when is X a degeneration of a smooth curve? More precisely, given such a curve X, whe...
متن کاملDegenerations of Symmetric Products of Curves
Denote C (d) ∆ the relative symmetric product of this family over ∆ , parameterizing effective divisors of degree d on fibres Ct for t 6= 0. We will construct a compactification H̃d of C (d) ∆ over ∆, such that H̃d has smooth total space and the fibre over t = 0 has simple normal crossing support. By studying the fibre over t = 0 of H̃d, we understand how the symmetric products of smooth curves de...
متن کاملDegenerations of elliptic curves and cusp singularities
This paper gives more or less explicit equations for all twodimensional cusp singularities of embedding dimension at least 4. They are closely related to Felix Klein’s equations for universal curves with level n structure. The main technical result is a description of the versal deformation of an n-gon in P. The final section contains the equations for smoothings of simple elliptic singularitie...
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: Japan Journal of Industrial and Applied Mathematics
سال: 2018
ISSN: 0916-7005,1868-937X
DOI: 10.1007/s13160-018-0301-4