A new kind of NURBS representation for periodic curves is introduced. The method for periodic curves is extended to derive a compact and symmetric representation of the sphere or the ellipsoid using a piecewise bi-quadratic NURBS surface with only eight distinct control vertices.

A general framework for the multi-scale topology optimisation (TO) of lattice structures (LSs) is presented in this work. The proposed method involves: Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces to represent pseudo-density field describing LS representative volume element (RVE) topology, Solid Isotropic Material with Penalisation (SIMP) approach and strain energy-based homogenisat...

Cranial implants, especially custom made are complex, important and necessary in craniofacial fracture restoration surgery. However, the classical procedure of manual design implant is time consuming complicated. Different computer-based techniques proposed by different researchers, including CAD/CAM, mirroring, reference skull, thin plate spline radial basis functions have been used for crania...

Isogeometric Analysis uses NURBS representations of the domain for performing numerical simulations. The first part of this paper presents a variational framework for generating NURBS parameterizations of swept volumes. The class of these volumes covers a number of interesting free-form shapes, such as blades of turbines and propellers, ship hulls or wings of airplanes. The second part of the p...

This paper mainly discusses the weight factor that influence on cubic NURBS interpolation curve shape. Based on the existing curve and surface interpolation, the thought, the criterion and the concrete steps of the convexity-preserving of the weight factor of cubic NURBS interpolation curve are provided, numerical examples are carried out by the computer simulation and the weights are controlle...

There has been a growing interest in controlled heat flux manipulation to increase the efficiency of thermal apparatus. Heat manipulators control and manipulate flow. A key effective performance these is their design. Such designs can be achieved by materials specially engineered have outstanding properties that not with natural (known as metamaterials or meta-structure), whose geometry materia...

In this paper, we propose an algorithm to construct 3-D surface model from a set of range data, based on non-uniform rational B-splines (NURBS) surface-fitting technique. It is assumed that the range data is initially unorganized and scattered 3-D points, while their connectivity is also unknown. The proposed algorithm consists of three stages: initial model approximation employing -means clust...

The non-uniform rational B-splines (NURBS) has been widely accepted as a standard tool for geometry representation and design. Its rich geometric properties allow it to represent both analytic shapes and free-form curves and surfaces precisely. Moreover, a set of tools is available for shape modification or more implicitly, object deformation. Existing NURBS rendering methods include de Boor al...

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.

In this paper we present a NURBS version of the rational interpolating spline with tension introduced in [2], and we extend our proposal to the rectangular topology case. In particular we present some rational interpolating techniques that enable us to reconstruct shape-preserving bivariate NURBS and allow us to interactively modify the resulting surface by a set of tension parameters.