Breakdown Of The Shape Of The Curve Control And Applications

This thesis studies modelling and application of subdivision curves. Subdivision method has become an important tool in computer graphics recently. To extend application areas (especially in the area of CAD) more widely, however, many problems have to be solved. The problems include modifying the local shape for subdivision curves and surfaces, the subdivision schemes for NURBS etc. The thesis investigates some effective modelling approaches for enhancing modelling ability of the subdivision methods.especially modifying the local shape for subdivision curves.The firstly we introduce a subdivision scheme for the uniform B-splines curves through the relation between the subdivision mark for B-splines and pascal' triangle. Then another subdivision scheme for uniform B-splines curves of odd degree with interpolatory restriction is constructed and we can adjust its part shape. We can find its effective modeling in modifying the local shape through the example for the subdivision scheme.The secondly NURBS have been identified as being a sensible standard for parametric surface descriptions, but the subdivision schemes for NURBS are still few. An algorithm for NURBS subdivision curves is first given. The algorithm based on the subdivision for the difference operator. It is very effective that we applied the algorithm in the free curve fitting and shape controlling. The properties of the curves by this method are the same as which of the parameter NURBS curves. The examples of generating circular arcs and circle are given in the last part of the third chapter.The thirdly we introduce an interpolatory subdivision scheme with modifying local shape restriction. Because when the parametric w of Dyn' four-point binary interpolating subdivision scheme is fixation then its shape isfixedness, Dyn' four-point binary interpolating subdivision scheme is short ofadjusting the shape of subdivision curves. A four-point binary interpolating subdivision scheme with modifying local shape is introduced, and then we give some examples for the subdivision curves and surfaces with modifying local shape. The algorithm is effective in geometric modelling. A four-point ternary interpolatory subdivision scheme with variable parameters is presented .It is shown that for a certain range of the variable parameters the resulting curves is convergence, C1 and C2, respectively. In the last we applied the subdivision theories to introduce an interpolatory subdivision scheme for curves with local shape modifications.