The Isogeometric Analysis (IA) method is applied for structural topology optimization instead of the finite element method. For this purpose, the material density is considered as a continuous function throughout the design domain and approximated by the Non-Uniform Rational B-Spline (NURBS) basis functions. The coordinates of control points which are also used for constructing the density func...

Quadratic Powell-Sabin splines and their rational extension, the socalled NURPS surfaces, are an interesting alternative for classical tensor-product NURBS in the context of isogeometric analysis, because they allow the use of local refinements while retaining a Bspline like representation and exact description of conic sections. In this paper we present a simple and effective strategy to conve...

A new formulation of energy minimising splines, based on Non-Uniform Rational B-Spline (NURBS) curves, is presented. The existing snake models do not facilitate the local control of their shapes without increasing the number of control points. The introduction of NURBS renders more flexibility into the snake model due to the weighting parameters that are made to adapt according to the curvature...

There are currently no analytical methods available which determine the exact arc length for NURBS curves and for this reason, a smooth feedrate profilewith desired trajectory cannot be achieved. Numerical methods used to calculate the arc length are time-consuming processeswhichmake generating a feedrate profile with desired accelerations difficult in real-time. This paper introduces a look-ah...

We present an algorithm for interactive display of trimmed NURBS surfaces. The algorithm converts the NURBS surfaces to B ezier surfaces and NURBS trimming curves into B ezier curves. It tessellates each trimmed B ezier surface into triangles and renders them using the triangle rendering capabilities common in current graphics systems. It makes use of tight bounds for uniform tessel-lation of B...

Direct slicing of CAD models to generate process planning instructions for solid freeform fabrication may overcome inherent disadvantages of using stereolithography format in terms of the process accuracy, ease of file management, and incorporation of multiple materials. This paper will present the results of our development of a direct slicing algorithm for layered freeform fabrication. The di...

Abstract Nowadays, NURBS (Non-Uniform Rational B-Spline) method is widely used in CAD/CAM (Computer-Aided Design/Computer-Aided Manufacturing) to represent sculptured curves or surfaces. In this paper, we develop a 5-axis NURBS real-time interpolator and realize it in our developing CNC(Computer Numerical Control) system. At first, we use two NURBS curves to represent tool-tip and tool-axis pat...

NURBS are used mainly to represent 3D models, being included in standards like OpenGL (Phigs) and used in computer graphics and manufacturing systems, representing adequately, in a compact way, almost any shape. For this sake, NURBS algorithms are implemented in graphical processing units (GPUs) hardware, but its rigid processing architecture and power consumption makes it inadequate in embedde...

Interactive rendering of trimmed NURBS models is of great importance for CAD systems. For this the model needs to be transformed into a polygonal representation. This transformation can be either performed in a preprocessing step, at the cost of losing the capability to edit the surfaces, or on the fly during rendering. Since the number of frames per second is usually critical, efficient on the...