混合空間標準B-基的存在性證明和它的一種求法.pdf

1、復旦大學碩士學位論文混合空間標準B基的存在性證明和它的一種求法姓名：葛焰明申請學位級別：碩士專業(yè)：應用數學指導教師：吳宗敏2002.5.22AbstractInCAGD，theparametriccurvescanberepresentedby：P(，)=∑尸口，(r)，where』=O尸)‰cR“，日。(t))二isthebasisofsomefunctionalspace，forexample：Bemsteinbasis，Bspin

2、ewhicharecallednormalizedBbasis(see11)inEMainar，JMPenaf19991andEMainarf200l1Butthecommonbasis，suchas：Bemsteinbasis，B—spine，havedisadvantagesinpractice，forexampletheyfailtoexpressthecycloidandthehelixforthecircles、theyhav

3、eexactrepresentationwiththerationalB6zierctlrves，butcalculationfortherepresentationisdifficultSoPotmann[1994]andZhang[1996]studiedthespace：span1，f，cos(t)，sin(t))；EMainar[2001】investigatedthespacesspanl，，，cos(t)，sin(t)，co

4、s(2t)，sin(2t)andspan1，r，r2，cos(t)，sin(t)Firstly，inthispapertheexistenceofnormalizedBbasisofthespace：span1，t，r。，cos(O，sin(t)，一，cos(kt)，sin(kt)isprovedAnalgorithmtoconstructthisnormalizedB—basisisgiventooThealgorithmconsis

5、tsoftwosteps：f1)GeneratetheBbasis(see11)withallitemtiveforrnulaf2)GeneratethenormalizedB—basisbasedonthepropertiesofB—basisSecondlysomepropertiesofthecurveswhichareexpressedbythenormalizedBbasisinthisspacearediscussedSom

6、eofthemaresimilartothepropertiesofthecurvesexpressedbyBernsteinbasis，Bspine，suchas：(1)Endpointinterpolationproperty(2)BoundarytangentpropertyFurthermorewederiveaparticularpropertyforthecurveswhichareexpressedbythenormali

7、zedB—basisinthisspace，thatisf2tand∑d』Bj(t)expresstheJOidenticalCUrve，where∽)譬匕R2；螞(f，1：2。kdenotethenormalizedBbasisofthespace：span1，f，，，7，cos(t)，sin(t)，，cos(kt)，sin(kt)，f∈【O，口】，BⅣ)描l2kistheBernsteinbasisFinallywegivesome