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unifying representation of bézier curve and two kinds of generalized ball curves unifying representation of bézier curve and two kinds of generalized ball curves.pdf

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unifying representation of bézier curve and two kinds of generalized ball curves unifying representation of bézier curve and two kinds of generalized ball curves

ComputerAidedDrafting,DesignandManufacturing CADDM Volume22,Number2JJune2012,Page32 UnifyingrepresentatiOnofBrziercurveandtwokindsofgeneralizedballcurves ZHUXiaolin1)andWANGZhihu口 1)SchoolofMathematics，HefeiUniversityofTechnology，Hefei230009，China 2)SchoolofMathematicsandComputationSciences，AnqingNormalUniversiyt，246011，China Abstract：Thispaperpresentsanew basis，theW SB basis，whichunifiestheBernsteinbasis，W ang—BallbasisandSaid-Ballbasis， andthereforetheB6ziercurve，Wang-BallcurveandSaid—BallcurvearethespecialcasesoftheW SB curvebasedontheW SBbasis Inaddition，therelativedegreeelevationformula，recursivealgorithm andconversionfomr ulabetweentheW SB basisandtheBem- steinbasisraegiven． Keywords：basis；W SBcurve；Wang·Ballcurve；B6ziercurve；degreeelevationformula；recursivealgorithm 1．IntrOductiOn andZhu [14]gaveauniyfingrepresentationofthe B6ziercurveandhteW ang．Ballcurvein2008．This BallA．A．presentedthecubicBallbasisfunctions paper presents a new basis， the W SB basis inthesystem ofSURFin1974[1—2]．Wang[3】and (Wang—Said—B6zierbasis)，whichunifiestheBernstein Said 4『1generalizedthecubicBallbasisfunctionsto basis．hteWnag-BallbasisandhteSaid．Ballbasis， thecaseofanydegree，andthecurvesbasedonthese na d consturctsa new family ofcurves．the W SB basisfunctionsarecalledtheW ang—Ballcurveandthe curves，based onhteW SB basis，consequently，the Said．BallcurvebyHu 5『1．TheWang．Ballcurveand Said—B6ziercurves，Wang—Ballcurve，Said—BaUin[121 theSaid—Ballcurvehavemanypropertiessimilarto na dB6ziercurveare the specialcasesofthenew thatoftheB6ziercurve 6『—81，suchas，stabilityof curves．Thenew