In this paper, we describe a general class of C1 smooth rational splines that enables, in particular, exact descriptions ellipses and ellipsoids — some the most important primitives for CAD CAE. The univariate are assembled by transforming multiple sets NURBS basis functions via so-called design-through-analysis compatible extraction matrices; different allowed to have polynomial degrees weight...

Knots can occur in biopolymers such as DNA and peptides. In our previous study, we systematically investigated the effects of intra-chain interactions on knots and found that long-range repulsions can surprisingly tighten knots. Here, we use this knowledge to trap a knot into tight conformations in Langevin dynamics simulations. By trapping, we mean that the free energy landscape with respect t...

NURBS surfaces can be non-uniform and defined for any degree, but existing subdivision surfaces are either uniform or of fixed degree. The resulting incompatibility forms a barrier to the adoption of subdivision for CAD applications. Motivated by the search for NURBS-compatible subdivision schemes, we present a non-uniform subdivision algorithm for B-splines in the spirit of the uniform Lane-Ri...

BACKGROUND Suturing and knot tying are basic skills for surgeons. Performing these tasks laparoscopically can be a tedious, time-consuming endeavor associated with much frustration. We evaluated a mechanically assisted suture and pretied knot device (Quik-Stitch) for performing the basic tasks of suturing and knot tying. METHODS We performed a time study using 1) intracorporeal suturing and k...

We introduce disk matrices which encode the knotting of all subchains in circular knot configurations. The disk matrices allow us to dissect circular knots into their subknots, i.e. knot types formed by subchains of the global knot. The identification of subknots is based on the study of linear chains in which a knot type is associated to the chain by means of a spatially robust closure protoco...

Bjorklund, L. & Moberg, L. 1999. Modelling the inter-tree variation of knot properties for Pinus syluestris in Sweden. Studia Forestalia Suecica 207. 23 pp. ISSN 0039-3150. With the help of the Swedish Scots Pine Stem Bank, the variation of internal knot properties was studied between stems and stands in sections in which the vertical variation was small. By means of explanatory site, stand and...

Knot polynomials have been used to detect and classify knots in biomolecules. Computation of knot polynomials in DNA and protein molecules have revealed the existence of knotted structures, and provided important insight into their topological structures. However, conventional knot polynomials are not well suited to study RNA molecules, as RNA structures are determined by stem regions which are...

B-spline methods have several advantages over Bezier techniques. B-splines are piecewise polynomials that meet smoothly at their common boundaries independent of the location of the control points. This guaranteed smoothness allows designers to use low degree polynomial pieces to construct complicated freeform shapes. In addition, a control point of a B-spline curve or surface has no influence ...

This is an expository paper discussing some parallels between the Khovanov and knot Floer homologies. We describe the formal similarities between the theories, and give some examples which illustrate a somewhat mysterious correspondence between them.

To record what has happened, ancient people tie knots. | I ching, the Chinese classic of 1027{771 B.C. Knots are fascinating objects. When fastening a rope, the distinction between a knot and a \slip-knot" (one that can be undone by pulling) must have been recognized very early in human history. We even developed a subconscious about knots: When we are puzzled or troubled, we have a feeling of ...