On linear independence of T-spline blending functions

نویسندگان

  • Xin Li
  • Jianmin Zheng
  • Thomas W. Sederberg
  • Thomas J. R. Hughes
  • Michael A. Scott
چکیده

This paper shows that, for any given T-spline, the linear independence of its blending functions can be determined by computing the nullity of the T-spline-to-NURBS transform matrix. The paper analyzes the class of Tsplines for which no perpendicular T-node extensions intersect, and shows that the blending functions for any such T-spline are linearly independent.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Linear independence of the T-spline blending functions associated with some particular T-meshes

Based on the local refinement algorithm addressed in [18], we analyze the linear independence of the bi-cubic T-spline blending functions corresponding to particular T-meshes.

متن کامل

Some Properties for Analysis-suitable T-splines

Analysis-suitable T -splines (AS T -splines) are a mildly topological restricted subset of T -splines which are linear independent regardless of knot values [1–3]. The present paper provides some more iso-geometric analysis (IGA) oriented properties for AS T splines and generalizes them to arbitrary topology AS T -splines. First, we prove that the blending functions for analysis-suitable T -spl...

متن کامل

Aane Similarity of Reenable Functions in Memory of Professor Cheng M. T. with Great Respect

In this paper, we consider certain aane similarity of reenable functions and establish certain connection between some local and global properties of reenable functions, such as local and global linear independence , local smoothness and B-spline, local and global HH older continuity.

متن کامل

Quartic and pantic B-spline operational matrix of fractional integration

In this work, we proposed an effective method based on cubic and pantic B-spline scaling functions to solve partial differential equations of fractional order. Our method is based on dual functions of B-spline scaling functions. We derived the operational matrix of fractional integration of cubic and pantic B-spline scaling functions and used them to transform the mentioned equations to a syste...

متن کامل

On the linear independence of truncated hierarchical generating systems

Motivated by the necessity to perform adaptive refinement in geometric design and numerical simulation, the construction of hierarchical splines from generating systems spanning nested spaces has been recently studied in several publications [1,2,3,4]. Linear independence can be guaranteed with the help of the local linear independence of the spline basis at each level. We extends this framewor...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Computer Aided Geometric Design

دوره 29  شماره 

صفحات  -

تاریخ انتشار 2012