Based On Wavelet B-spline Curves And Surfaces, Local Multi-resolution Editing

The emergence of computer technology and the application of CAD/CAM enable people to breach the aboriginal manufacturing mode and to realize the leap from hand drawing to computer aided design. But with the continuous development of CAD/CAM technology, the demand to sculpting technology is becoming higher and higher, which forces people to find new more effective sculpting methods constantly. The emergence of wavelets analysis provides us a new idea for the solution of the above problem. For the reason that wavelet base has the property of multi-resolution, the wavelet technology has infiltrated through many science research fields gradually. In 1994, Finkelstein and Salesin applied wavelet technology to the field of surface, who inaugurated a new method for multi-resolution curve surface sculpting. From that time on, the idea of multi-resolution analysis has been widely applied to CAGD and many achievements have been obtained.In this thesis, the multi-resolution denotation and edition of quasi-uniform B-spline curve surface are expatiated in detail with a large quantity of cutlines. On mis basis, local multi-resolution edition of B-spline curve surface is put forward for the first time in this thesis. Traditional curve surface multi-resolution edition modifies or edit only in allusion to the whole curve (surface), which is not fit for more refined modification to curve surface in the latter step of geometric sculpting design. So local multi-resolution edition of B-spline curve surface is more meaningful. The basic idea is as follows. According to node-inserting algorithm, split the original B-spline curve (surface) and denote independently the portion of the curve or surface that needs to be modified. Then, multi-resolution edit the curve or surface and discuss the continuity join of all curve surfaces. Many aspects related to this problem are discussed andstudied in this thesis. For curves, a C1 or C2 continuity join condition of curvesegments is given after local multi-resolution edition. For surfaces, a G1 continuity join condition of surface segments is given after local multi-resolution edition.