On Fast Generating Algorithm For Parametic Curves And Surfaces

RaPidly generatin curves and surfaces is always one of the basicproblems in CAGD. With the population and penetration of usingCMAM, efficiency and accuracy of generating curves and sdricesaffectS the range and dePth of using CADCAM system directly So itis necessary to discuss how to generatP curves and surfaces rapidlyTraditional algorithIns of generating curves and surfaces all adoptways of interpolation. According to generating algorithIns oninterpolation functions, .multiplication and division are used manytimes in the process of cariying out. So efficiency of algorithIns isrestricted. Based on the fast generating algorithIn for polynomial..parametric curves resented by Huang Youdu and Zhou Gongqin, thisdissertaion discuss raPidly generating for rational parametricpolynomial curves and parametric polyndmial surfaces thoroughiy Themain contributions are as follows:(1) Specific method was given to determine derivative boundary ofrational parametric polynomial curve. Dividing variable interval byderivative boundary the generated' curve is continuous andcomputation comPlexity is little.(2) A fast generating algorithIn fOr rational parametric polynomialIlcurve was presented. With this algorithm, computing one point on a n-degree rational parametric polynomial curve, only 2(n-l) times integer addition and one time integer division are required. So rational parametric polynomial curve can be generated quickly.(3)Rapidly generating parametric polynomial surface was discussed, a fast algorithm of generating parametric polynomial surface was given which is based on integer addition and subtraction. For a (m,n)-degree parametric polynomial surface , only (m+n-2) times integer addition and subtraction can be required to compute one point on surface, efficiency of the algorithm is rapidly improved.