The effect of knot modifications on the shape of B-spline and NURBS curves is discussed in this paper. Theoretical results include the description of the path of curve points, obtained by the modification of a knot value, and the examination of the one-parameter family of curves. It is shown that this family has an envelope which is a lower order B-spline or NURBS curve. Applying these results ...

A method for decompose the triangulated surface into quadrilateral patches using Morse theory and Spectral mesh analysis is proposed. The quadrilat-eral regions extracted are then regularized by means of geodesic curves and fitted using a B-splines creating a new grid on which NURBS surfaces can be fitted.

Extracting the human brain from magnetic resonance head scans is difficult because of its highly convoluted and nonuniform geometry. A technique based on Non-Uniform Rational B-Splines (NURBS) and energy minimising deformable models to extract the brain surface accurately from MR head scans is presented. The weighting parameter that comes with the NURBS definition is explored to attract the sur...

We address the problem of how to perform prescribed shape modification of NURBS curves merely by the modification of the weight of some of their control points. As is known, NURBS curves can be considered as central projections of nonrational B-spline curves. Making use of the property that there is an infinite number of nonrational B-spline curves the central projection of which is a given NUR...

We consider isogeometric functions and their derivatives. Given a geometry mapping, which is defined by an n-dimensional NURBS patch in R, an isogeometric function is obtained by composing the inverse of the geometry mapping with a NURBS function in the parameter domain. Hence an isogeometric function can be represented by a NURBS parametrization of its graph. We take advantage of the projectiv...

In this paper, we present the geodesic-like algorithm for the computation of the shortest path between two objects on NURBS surfaces and periodic surfaces. This method can improve the distance problem not only on surfaces but in R. Moreover, the geodesic-like algorithm also provides an efficient approach to simulate the minimal geodesic between two holes on a NURBS surfaces.

We present a scheme to construct C1 continuous toolpath for 5-axis pocketing of high speed machining. A continuous toolpath synthesis is proposed, that forms out circular segments of maximally inscribed sizes and linear segments connecting these circular segments. Extending earlier work that employed the Medial Axis Transform to compute these maximally inscribed circles for 2D planar pockets, t...

The only connected minimal surfaces foliated by circles and lines are domains on one of the following surfaces: the helicoid, the catenoid, the plane, and the examples of Riemann ([Ri] p329-33, [En] p403-6, [Ni] p85-6). All these surfaces are complete and embedded. Topologically they are planar domains: the helicoid is simply-connected, the catenoid is an annulus (conformally a twice-punctured ...

In this paper, we construct a complete invariant for stably homeomorphic classes of curves on compact oriented surfaces without boundaries and show that this is a finite type invariant for curves. In knot theory, it is still unknown whether finite type invariants completely classify knots (the Vassiliev conjecture). We consider the analogy to this conjecture for generic immersed curves: do fini...

Employing a unique dataset that covers households from six West African capitals, this paper provides new evidence on the demand for informal sector products and services. We first investigate whether demand linkages exist between formal and informal products and distribution channels, and whether there is an overlapping customer base, which would imply that both formal sector wage earners and ...