On The NURBS Curves And Surfaces Approximation Algorithm To Constrained Data Set

Curves and Surfaces fitting to constrained data sets is an indispensable problem in CAD/CAM, which is also a common topic in industry design and manufacture. Constrained conditions consist of data interpolations (interpolations to data points or to one order and curvature at data points), shape-preserving interpolation and smoothing or fairing fitting.The NURBS curves and surfaces approximation to constrained data sets is discussed in this dissertation. The major works are as follows:Firstly, Based on simulated annealing algorithm and least square principle, a NURBS curves approximation algorithm to constrained discrete data sets is presented. The algorithm is simple and is easy to accomplish. The approximation extent is high.Secondly, Based on NURBS curves approximation algorithm, a NURBS surface approximation algorithm on discrete data sets is given.Thirdly, a shape-preserving parametric surface interpolation to data set is given.The constructed surface is C2 continuous on the whole domain, and is a piecewisecubic parametric polynomial on every subdomains. The interpolating surface can preserve the convexity, concavity, inflection property and monotonicity of the data set.In the end, each algorithm brought forward in the paper is exemplified, at the same time, error is discussed.