Powell-Sabin splines are C-continuous quadratic splines defined on an arbitrary triangulation. Their construction is based on a particular split of each triangle in the triangulation into six smaller triangles. In this article we give an overview of the properties of Powell-Sabin splines in the context of computer aided geometric design. These splines can be represented in a compact normalized ...

An extended isogeometric analysis (XIGA) approach is proposed for modeling fracturing in a fluid-saturated porous material. XIGA provides definition of the discontinuity independent underlying mesh layout, which obviates need knowing crack extension direction priori. Unlike Lagrange shape functions used standard finite element approach, non-uniform rational B-splines (NURBS) provide higher-orde...

This study presents a deep learning based methodology for both remote sensing and design of acoustic scatterers. The ability to determine the shape scatterer, either in context material or sensing, plays critical role many practical engineering problems. class inverse problems is extremely challenging due their high-dimensional, nonlinear, ill-posed nature. To overcome these technical hurdles, ...

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 ...

A system is presented for ray tracing trimmed NURBS surfaces. While approaches to components are drawn largely from existing literature, their combination within a single framework is novel. This paper also differs from prior work in that the details of an efficient implementation are fleshed out. Throughout, emphasis is placed on practical methods suitable to implementation in general ray trac...