Research On Disk B-Spline Curves Interpolation And Knot Insertion Problem

In the Computer-aided Geometric Design (CAGD) prac-tice,we often encountered how to construct a interpolation curve todesign a curve's shape. The basic problem is to construct a curve (sur-face) to be strictly through the data points set(normally get from theactual measurement). However, because the means of measurementtechnology and the restrictions, in the measurement of data usuallywith error. In the two-dimensional case, the measurement data witherror is a series of small area on the plane,so the general interpolationproblem turn into how to carry out a series of small regional interpo-lation problem. In this paper,based on the B-spline curve theory,theinterpolation algorithm how to use disk B-spline curves to interpolatethrough these small regions was studied. Knot insertion algorithmis supported one of the most important technology of the B-spline'smethod. Through knot insertion, increase the ?exibility of surfacemodel, it's can prove that the variation diminishing property of B-spline curves, etc. In addition,the algorithm of knot insertion is thefoundation of degree elevation which is also one of the most impor-tant property of B-spline. In this paper, based on the general B-splinecurves we study the Disk B-spline curve knot insertion algorithm. It'smostly contains the following contents:Chapter 1 introduce the back-ground and research content of this paper, and illustrates the necessityfor introduction of disk arithmetic in the shape of curve (surface) de-scribing;The second chapter describes the definition and property theB-spline curves , and analyzed the interpolation algorithm of B-spline curve which had been existed;Chapter 3 introduces the Disk B-splinecurves, the definition and property of the Disk B-spline curves,andthe recursive algorithm of Disk B-spline curves. Chapter 4 introducea specific discussion how to use a Disk B-spline curve to interpolatethrough the measurement data with error, and the interpolation Diskthe B-spline curve has the good property of local and continuity,etc. .Chapter 5 based on the definition of Disk B-spline curves studies theknot insertion algorithm of Disk B-spline curves .