Derivatives are a very important tool of computations in an engineering practice on the graphics structures. B-Spline functions are defined recursively, so the direct computation is very difficult. In this article new direct proof of the formula used for simpler direct computation is shown. The paper also presents own method of programming derivatives of NURBS curves by means of the proven form...

A method is presented to interpolate real affine plane curves with second degree NURBS (Non Uniform Rational Bezier Splines). The curve into object is initially partitioned into an arbitrary number of arcs. Then each arc is approximated with a conic section passing thru its extremes, thru a third intermediate point and being tangent to the arc at the extremes. Each arc is then parameterized by ...

Given two distinct points S and E on a simply-connected domain (without holes) enclosed by a closed parametric curve, this paper provides an algorithm to find the shortest interior path (SIP) between the two points in the domain. SIP consists of portions of curves along with straight line segments that are tangential to the curve. The algorithm initially computes point-curve tangents and bitang...

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 describe a new approach for constructing patient-specific vascular geometries suitable for isogeometric fluid and fluid-structure interaction analysis of blood flow in arteries. We use solid NURBS (non-uniform rational B-splines) to define vascular geometries as well to perform analysis. It is argued in this paper that this new approach is a viable alternative to the finite element method, w...

Every curve or surface can be defined by a set of parametric functions. For instance, (x,y,z) coordinates of the points of the curve can be given by:) (), (), (t Z z t Y y t X x = = = t being the parameter and X, Y, Z being polynomial functions in t. If X, Y and Z are 1 st degree polynomials, a line segment will be defined. In that case, two knowns only (i.e. two points or a point and a slope) ...

In this paper, we present a novel non-uniform rational B-spline (NURBS) muscle system for the simulation of human facial expressions and talking animation based on features extracted from video sequences. We construct the facial muscles based on anatomical knowledge and NURBS models. We use 43 feature points to represent facial expressions and apply a lip contour extraction technique to determi...

According to the need of canopy visualization calculation in the digital plant research, we introduced a method, using Non-Uniform Rational B-Splines (NURBS) interpolation and multi-line segment splitting algorithm, to reconstruct the 3D morphological structure of maize leaf with a complexity controllable mesh. Using the data cloud obtained by digitizer, construct the surface of maize leaf by c...