Research on the integrated NC conceptual layout design (I-NCC) concerned with a broader area of interests. The key issues of I-NCC system are associated with NURBS and agent. Firstly, formulas for the derivatives and normal vectors of non-rational B-spline and NURBS are proved based on de BOOR’s recursive formula. Compared with the existing approaches targeting at the non-rational B-spline basi...

In this paper, we present a boundary integral based approach to isogeometric analysis and shape optimization. For analysis, it uses the same basis, Non-Uniform Rational B-Spline (NURBS) basis, for both representing object boundary and for approximating physical fields in analysis via a Boundary-Integral-Equation Method (BIEM). We propose the use of boundary points corresponding to Greville absc...

A surface extraction algorithm with NURBS has been developed for the mesh generation from the scattered data after a cell-based simulation. The triangulation of a surface is initiated with a step of describing the geometry along the polygonal boundary with multiple points. In this work, an NURBS surface can be generated with scattered data for each polygonal surface by employing a multilevel B-...

This paper proposes a method to improve the shortest path problem on a NURBS (Non-uniform rational basis spline) surfaces. It comes from an application of the theory in classic differential geometry on surfaces and can improve the distance problem not only on surfaces but in the Euclidean 3-space R . Keywords—shortest paths, geodesic-like method, NURBS surfaces.

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.

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...

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...

As a rule, an energy method is widely adopted for b-spline curve smoothing, but this method has the disadvantages such as massive calculation, computation complexity and low efficiency. Compared with the energy method, multi-resolution smoothing approaches nicely overcome these obstacles. Presently, some researches have been conducted on multi-resolution smoothing, but these efforts mainly aime...