Dual Basis Of Even Degree J-NTP Bases And Its Applications

In2003, J.Delgado et put forward a new kind of basis functions with degree of n,which is normalized totally positive, and referred to as J-NTP basis. For given n+1control points, we can get a n degree curve by n degree J-NTP basis as mix functions,which has the property of shape preserving, and for all the evaluations with linearcomplexity.Considering the advantages of the J-NTP curve, we urgently need to study itsapplication in computer aided geometric design system, as the diversity of the basisfunctions in the CAGD system, we need to study the transformation between theJ-NTP basis and the other basis which is frequently used at first. Then, based onderivation of diffident order at the endpoint of even degree J-NTP bases, the dualbasis of J-NTP basis is represented, following which, the transformation formulabetween even degree J-NTP basis and the power basis or Bernstein basis is given.The result is significant in the further development of computer aided geometricdesign system.This thesis is divided into six chapters:The first chapter introduces the related background;The second chapter introduces the related knowledge, especially the property oftotally positive matrix;The third summarizes several kind of dual base of basis functions and itsapplications which the former research;The fourth mainly introduced the definitions and properties of the J-NTP basisand J-NTP curve;The fifth gives the dual basis representation of even degree J-NTP and itsapplications;The sixth summarizes the work of this paper, points out the deficiency of thisthesis,and puts forward some prospects for future work.