in the present research, implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics are investigated. nurbs and t-splines are two different computational geometry technologies which are studied in this work. among features of b-spline basis functions the possibility of enhancing a b-spline basis with discontinuities b...

Knot insertion is the operation of obtaining a new representation of a B-spline curve by introducing additional knot values to the defining knot vector. The new curve has control points consisting of the original control points and additional new control points corresponding to the number of new knot values. So knot insertions give additional control points which provide extra shape control wit...

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

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work f...

We derive the stability inequality ‖C‖ 6 γ ‖∑i cibi‖ for the B-splines bi from the formula for knot insertion. The key observation is that knot removal increases the norm of the B-spline coefficients C = {ci}i∈Z at most by a constant factor, which is independent of the knot sequence. As a consequence, stability for splines follows from the stability of the Bernstein basis.  2000 Elsevier Scien...

We give a new, simple algorithm for simultaneous degree elevation and knot insertion for B-spline curves. The method is based on the simple approach of computing derivatives using the control points, resampling the knot vector, and then computing the new control points from the derivatives. We compare our approach with previous algorithms and illustrate it with examples.  2004 Elsevier B.V. Al...

TECHNIQUE After drain insertion, a horizontal mattress suture is placed. A simple knot is placed distally half way along the two free ends. The two threads are wrapped tightly together the same way around the tube up to the level of the knot. The free ends of the knot are then passed proximally under the loop of the skin suture (Fig 1). The suture is pulled fi rmly, and the free ends are separa...

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...

This paper studies the merits of using knot interval notation for B-spline curves, and presents formulae in terms of knot intervals for common B-spline operations such as knot insertion, differentiation, and degree elevation. Using knot interval notation, the paper introduces MD-splines, which are B-spline-like curves that are comprised of polynomial segments of various degrees (MD stands for “...