OBJECTIVE In the past, knot-tying techniques have been evaluated and compared, but there has been a scarcity of objective scoring systems in these comparison studies. Using an objective scoring system, we aimed to compare 3 types of knots: intracorporeal flat-square knots, intracorporeal slip-square knots, and extracorporeal square-knots for their Knot Quality Scores (KQS) and their rates of sl...

Surface envelopes are tight, two-sided enclosures of composite spline surfaces. This paper shows how to construct the two hulls of the enclosure so that matched triangle pairs sandwich a given nonlinear, curved surface consisting of tensor-product Bézier patches. The main cost of the hull computation are 12 transversal line-plane intersections per vertex. The width of the enclosure, i,e. the di...

This paper addresses the problem of joint rate-distortion optimization of spline curves for optimal video object shape coding. It proposes a B-spline snake model which minimizes rate-distortion energy to find optimal spline coefficients. A continous model of a contour distortion is used which models the shape reconstruction error. A continous model of a coding bitrate is based on the relative i...

We explore algebraic characterizations of 2-knots whose associated knot manifolds fibre over lower-dimensional orbifolds, and consider also some issues related to the groups of higherdimensional fibred knots. Nontrivial classical knot groups have cohomological dimension 2, and the knot is fibred if and only if the commutator subgroup is finitely generated, in which case the commutator subgroup ...

The enamel knot, a transient epithelial structure, appears at the onset of mammalian tooth shape development. Until now, the morphological, cellular and molecular events leading to the formation and disappearance of the enamel knot have not been described. Here we report that the cessation of cell proliferation in the enamel knot in mouse molar teeth is linked with the expression of the cyclin-...

Knots occur in many areas of science and art. The mathematical field of Knot Theory studies an idealised form of knots by viewing them as closed loops in 3-space. They can be formally studied via knot drawings which are well-behaved projections of the knot onto the 2-D plane. Equivalence of knots in 3-space (ambient isotopy) can be encapsulated via sequences of diagram rewriting rules, called R...

Recursive subdivision is receiving a great deal of attention in the deenition of B-spline surfaces over arbitrary topology. The technique has recently been extended to generate interpolating surfaces with given normal vectors at the interpolated vertices. This paper describes an algorithm to generate recursive subdivision surfaces that interpolate B-spline curves. The control polygon of each cu...

Litherland has shown that if a knot is (+)-amphicheiral then its m-twist-spin is reversible. We show that, for classical knots, in many cases the converse holds. The irreversibility (sometimes called noninvertibility) of certain twist-spun knots has been established by Ruberman [10], using the Farber-Levine linking pairing and the Casson-Gordon invariants. More recently, alternative proofs of t...

Focus Research dealing with the manipulation of flexible objects has been on for a while. Most of the existing motion-planning algorithms that determine a trajectory from a start to the goal state revolve around traditional sampling-based and feedback control methods. What has not been done so far is the realisation of desired goal states from different initial states through reactive, global p...