Knot insertion for Natural Splines

نویسندگان

  • Tom Lyche
  • Kyrre Strøm
چکیده

We derive knot insertion formulas for the B-spline basis for natural splines. We also show that this basis is totally positive and give necessary and su cient nesting conditions for uniqueness of interpolation. x

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

Local and Global Approaches to Fracture Mechanics Using Isogeometric Analysis Method

The present research investigates the implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics. NURBS and T-splines are two different computational geometry technologies which are studied in this work. Among the features of B-spline basis functions, the possibility of enhancing a B-spline basis with discontinuities ...

متن کامل

NURBS-Based Isogeometric Analysis Method Application to Mixed-Mode Computational Fracture Mechanics

An interaction integral method for evaluating mixed-mode stress intensity factors (SIFs) for two dimensional crack problems using NURBS-based isogeometric analysis method is investigated. The interaction integral method is based on the path independent J-integral. By introducing a known auxiliary field solution, the mixed-mode SIFs are calculated simultaneously. Among features of B-spline basis...

متن کامل

B-splines with arbitrary connection matrices

We consider a space of Chebyshev splines whose left and right derivatives satisfy linear constraints that are given by arbitrary non-singular connection matrices. We show that for almost all knot sequences such spline spaces have basis functions whose support is equal to the support of the ordinary B-splines with the same knots. Consequently, there are knot insertion and evaluation algorithms a...

متن کامل

Control curves and knot insertion for trigonometric splines

We introduce control curves for trigonometric splines and show that they have properties similar to those for classical polynomial splines. In particular, we discuss knot insertion algorithms, and show that as more and more knots are inserted into a trigonometric spline, the associated control curves converge to the spline. In addition, we establish a convex-hull property and a variation-dimini...

متن کامل

Non-uniform subdivision for B-splines of arbitrary degree

We present an efficient algorithm for subdividing non-uniform B-splines of arbitrary degree in a manner similar to the Lane-Riesenfeld subdivision algorithm for uniform Bsplines of arbitrary degree. Our algorithm consists of doubling the control points followed by d rounds of non-uniform averaging similar to the d rounds of uniform averaging in the Lane-Riesenfeld algorithm for uniform B-spline...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 1992