Implementation of NURBS Curve Derivatives in Engineering Practice
نویسندگان
چکیده
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 formula which is implemented in German engineering software RFEM 3D.
منابع مشابه
An Improved N-dimensional NURBs-based Metamodel
Non Uniform Rational B-splines (NURBs) are proved to be very promising for metamodeling in engineering problems, because they have unique properties such as local modification scheme, strong convex hull property, and infinitely differentiability, etc. Since NURBs are defined by control points, knot vector, and weights associated with control points, the precision of NURBs is influenced by all o...
متن کاملSurface Fitting with NURBS - a Gauss Newton with Trust Region Approach
This paper shows a new approach for non-linear least squares fitting with NURBS as curves and surfaces to measured data by the Gauss-Newton method. A Trust Region algorithm is used to reach global convergence as well as variable substitution and simple bounds. Key–Words: Non-linear least squares, NURBS, curve and surface fitting, reverse engineering, optimisation, GaussNewton
متن کاملModifying free-formed NURBS curves and surfaces for offsetting without local self-intersection
This paper presents an algorithm of modifying free-formed NURBS curve/surface for offsetting without local self-intersecting. The method consists of (1) sampling a number of points from a progenitor curve/surface based on second derivatives; (2) checking the curvature or maximum curvature of the progenitor curve/surface at the sampled points; (3) inserting corresponding knots of sampled points;...
متن کاملAnalysis of thin plates by a combination of isogeometric analysis and the Lagrange multiplier approach
The isogeometric analysis is increasingly used in various engineering problems. It is based on Non-Uniform Rational B-Splines (NURBS) basis function applied for the solution field approximation and the geometry description. One of the major concerns with this method is finding an efficient approach to impose essential boundary conditions, especially for inhomogeneous boundaries. The main contri...
متن کاملDegenerations of NURBS curves while all of weights approaching infinity
NURBS curve is widely used in Computer Aided Design and Computer Aided Geometric Design. When a single weight approaches infinity, the limit of a NURBS curve tends to the corresponding control point. In this paper, a kind of control structure of a NURBS curve, called regular control curve, is defined. We prove that the limit of the NURBS curve is exactly its regular control curve when all of we...
متن کامل