Subdivision surfaces would find a greater number of applications if there was a scheme that included general degree NURBS as a special case. As a step towards such a scheme, we present a univariate refine and smooth subdivision algorithm that applies directly to regular regions of a surface and might, in future work, be generalised to incorporate extraordinary points. The algorithm is symmetric...

The representation, matching and analysis of objects of interest are of prime importance in shape-based retrieval systems. Considering that these systems involve analysis of various complex shapes, an accurate representation of free form shape is required. A simple and accurate shape representation procedure would ensure meaningful results from the shape-based retrieval systems. Motivated by th...

With the improving capabilities of Computational Fluids Dynamics (CFD) on predicting aerodynamic performance, these tools are now being increasingly used for aerodynamic design optimization in the aerospace industry. In this paper, an automated optimization framework is presented to address inviscid aerodynamic design problems. Key aspects of this framework include the use of the continuous adj...

We have developed algorithms and programs capable of efficiently parameterizing complex cultural heritage shapes including texture, which significantly reduces the data-set size. This is potentially significant for online viewing and interactive presentation and processing. The proposed approach is based on Non-uniform rational B-splines (NURBS) mathematical model which is also by itself suitab...

In this paper, we study high order methods for solving the time domain Maxwell equations using spline finite elements on domains defined by NURBS. Convenient basis functions for the discrete exact sequence of spaces introduced by Buffa et al [4] are exhibited which provided the same discrete structure as for classical Whitney Finite Elements. An analysis of stability of the time scheme is also ...

Abstract A real-time path generation method with Non Uniform Rational B Spline(NURBS) technology in the Computer Aided Design(CAD) field is presented and realized in a five-axis Computer Numerically Controlled(CNC) system. In this method, the tool path was represented into two NURBS curves, tooltip and tool-orientation spline curve, based on the same knot vector. The Cutter Location(CL) data wa...

This paper considers the problem of G1 curve interpolation using a special type of discrete logarithmic spirals. A ”logarithmic arc spline” is defined as a set of smoothly connected circular arcs. The arcs of a logarithmic arc spline have equal angles and the curvatures of the arcs form a geometric sequence. Given two points together with two unit tangents at the points, interpolation of logari...

A-splines are implicit real algebraic curves in Bernstein-B ezier (BB) form that are smooth. We use these in an algorithm for active contouring of images. One advantage of A-splines is that any change to the controlling weights only a ects the curve locally, which results in fast convergence. Our active A-splines are also level sets of a time-dependent function with the added exibility of a dyn...

Arc splines are G continuous curves made of circular arcs and straight-line segments. They have the advantages that the curvature of an arc spline is known and controlled at all but a finite number of points, and that the offset curve of an arc spline is another arc spline. Arc splines are used by computer-controlled machines as a natural curve along which to cut and are used by highway route p...

By making use of the advantages of non-uniform rational B-spline (NURBS) curves to represent spatial curves, an instruction format with double NURBS curves suitable for 5-axis coordinated real-time interpolation is presented to replace the current 5-axis coordinated linear interpolation method defective in low-speed, low-accuracy and enormous numerical control (NC) files in sculptured surface m...