基于指导向量构造隐式曲线英文

1、基于指导向量构造隐式曲线（英文）9第卷第期4 0 1 2 v o 14 0 n ol 2? a? f? ie? i fc i ec e ade c iig? f c ii ia2010 年 12 月 dec2010?aricleld0253-277820 1012-1211-14c? b a? a12 2 2x uc h e ndon g d e n gj ianon g c ii e nf a 1 a iy a n gz h o? a n gif s nu? n3 1 5 2 1 1 c?2d mu? s? t? ch? 2 3 0 0 2 6 ca b a? am ch o d? a? p

2、 r o p oe d? oc o n? rc? analgebrai ccref r o m? h eg ie nc o nr o lp o i n eb ae d onh eid a n c ee co ro fh eco nr o 1 o 1 ondefi n e d bhee o i n aro oe da fe r g? pg? p?ppd e r ii nh eere? ere? i o n andanalini?roeri ei? aa 1 i e do c o n? rci n ag p g? pp? p p? gi ne r p o 1ain g ere? h oe?ha p

3、 cc a nb cm od i f i e deai 1. t h em eh o de anbed i r e cig ene r a1 ie d? o?con? rc? i m p 1 i c ir f a c ekcagdalebraic ere eomericconi ni? i d a n c ee co r? gg? gc l cb? 0 1 7 44 2 0 2 4 13? d a? d o i 1 03 9 6 9i? no 2 5 3 - 2 7 7 82 0 1 01 20 0 1j9a m ssb? caa200065d17基于指导向量构造隐式曲线12 2 2徐晨东邓建

4、松陈发来杨周旺宁波大学理学院浙江宁波小国科学技术大学数学系安徽合肥13 1 5 2 1 1 22 3 0 0 2 6摘要提hit 一种基于由给定控制多边形定义的指导向量 构造隐式代数曲线的方法同时推导了所生成的代数曲线的表达式 并具体分析了其性质这种方法可以用来构造插值曲线而且 曲线的形状很容易修改与调整此外该方法也可直接推广用于构 造隐式曲而关键词计算机辅助儿何设计代数曲线儿何连续指导向量a n d i m 1 i c im eh o d. t h e a r a m er i c m eh o d? p? po ii 3h aeb een?ideli ne? i g ae dh i 1 e

5、? h ea ni m p o ra n o p i co fcomp?erai dedimpl i c i? m eh o d? h aer e c e ie d i n c r e ai n g a? e ni o n4eomericdeincagdandcom?errahicinrecene a r. c o m a r e dih a r a m ee rggpg p p? p9cgi?eomericmodel i nh oem aor?rfaceiml i c ir f a c ccc ciallalcbraicggjpp?gcomponenarefree-fro mere? a n

6、 d r f a c e r f a c ep 1 aa ni m p o ra n? r o 1 ei nc o n? rci n g5dein andmodel i na c c o r d i noh eobecihcomle? o o 1 og? g gj? pp gr e r ee nai o nm o d e 1 i ne c h n iec anbethefol 1 oi n areomereearcheabohep gq gc 1 a? i f i e di no oc ae g o r i ep a r a m er i cm eh o di m p 1 ic i?m eh

7、odtnl 984sederberg?ed r2 009-07- 06r2009-1 1-03?fa sp p o re dbn ai o n a ik eb ai cr ee a r c h 9 7 3 p r o g r a mofchina2004cb318000nsfc6053306060872 0 9 5h e?special ie dr ee a r c hfn df or?hedocoralprogra mofhigheredcaion20060358055an dsb j c c? f on d ai o ni nningbounierikl09046?baxuchenclon

8、gcorrepondinga?horborninl977phdlec?rereearchf icldcagd&cge-mai 1? c h e n d o n gn b. e d. c n?中国科学技术大学学报第卷121240?6?i e c eie alebraic ere in eomericmodel i ni m r oe dandeandedinrefl822beca?epg gg p? p? 一？r e f7 b r ohf o ra r dh e c o n c co f fn ci o n a lh cc m eh o de a n o n 1 a 1 idea lih

9、i m 1 e rgp?pp 1 i nedic e d?h ep r o p e ri e? of? h ep ara bo1ici?aionc o nide r i ngh ed i r e c? d ei gnm eh o dof?fn ci o n a 1? p 1 i n e a n da p p 1 i e d? h e m? o r f a c e i m p 1 i c ir f a c c? ii 1 1? a la b 1 cb 1 c n d i n d ci naa? 1 c m e nr ef8 t hia e r co nc e nraeo nalebraiccre

10、gg? pppp g?diced? h edeer m i nai o nm eh o do f? h ec o na cand rfacedeinandmodelinecificallong g p?p o i n o rc o na c? cree di np 1 a c co f? h ch cd i r c c? c o n? rci onofalgebrai cere? f r o m? h e?a r a b o 1 i c i n b 1 e ndindeini ndeai 1r e f9 ie n c onroloin?einomekindof i n ii a 1p? g g

11、? g? p? g?r oe dh e c o neio fh ik i n d o fl i n e. r e fr a d i e ni n f o r m ai ontheradieninf ormaionh ap? p g? gl 0 p r oi d e da? c m ai ca. n a 1? i? o f? a r i o? b c e n? i d e 1 e di ng e o m er i cm o d e 1 ingand?kin d? o ffn ci o n a 1? p 1 inemehod?anded?hemin d r i a id ei g n c ha h

12、 er e c o n? rci o no fi nh emo oh inmanil ai o n o f g b 1 endi n acreo r?rfac e? h cm ooh i no f c o m cr i c? gp? gg? gcr e fl1 r eene d a? f f icienobecheadmenofimaea n dh ep p? jj? gr e p r ee nai onnameda-pacho fa? r ia r i ae d e f o r m ai o no f? h a p e. n oa d ah e? e c h n i qeo 1 n o m

13、i a lih i n aer a h e d r o nt oo leh cinolinradi e n? e co r f 1 oh am a d e a 1 oo fpgg?rfaceinerecionroblemrefl2?edaachi ee men? inmedical imaemanaemen?! ice? pggp r o j e ci on ?ech ni qer e fl 3 p r oi d e daqie d aar e c o n? rci ondiconi no deform aio no fcomprehc nica p p r oach?o?olingh eb

14、lendinggraphic? an dee n? ae rf o r e c a? in gb? a? f a rarob lemofalebrdic?rfacef ir?diedbref?ek n oc o n? rci nalebraic crca n dp? ggg?14therearemanohermehodini ml i c i r f a c eb ae d o ni d a n c ee co rae c i a 1 k i n dp g? p?moldin g?c ha? csgmehodradialb ai? fn ci o n o fg r a d i e necor?

15、def ine db? h eg ie nc o nr o 1?m eh o d p a ri c 1 e? e m a n d? oo np o lg o n i? an e? m eh o cl? h a? h a? n o? b e e nu? a 1 lh c m eh o do f a r a m er i c crc r ee a r c h c d cpd ci na r ei n? iief o rea m 1 e i no r d e r? o orc o n? rci o nm eh o do fi m 1 i c i? ere? andg p p?c h a n g e?

16、 h ecreh a p eeo nln eed?oadj?rface?here i nh a h ef o 1 1 oi n g c h a r a ce r i? i c? h e oii o n o fo m e c o nr o 1 o i n b? iit h e i n? ia c o nr o 1 o 1 o nh ea m eihh eppppg?r e r e? a b 1 eh a? h oe i m 1 i c im eh o do f ere rc? r e o fh e a r a m ee r crea nd?rfacegppd ei g n e di np r a

17、 ci c ea r ea 1 1? ih o in? iiet h ef in a 1 i m p 1 i c i? ere? aif ieheendpoin?conrolthi?limiimplici? ere? andrface?ini ne r p o 1 ai o nc o n d ii ona n dl i e? i ni d e? h ec o neh e f o r mofracicalal icaionthereforehehl 1 o fh e c o nr ololonimila roh e pp ppgd o fi m 1 i c i? crca n d r f a c

18、 cc o n? rci o n a r a m ee rb? i e ra n db - s 1 in ecre? t h e? p p pm eh o d? ihg e o m er i c in? iie n e a n de a? a m on? o fc a 1 cl ai o ni? r e 1 aie 1? m a 1 1 b e i n g am a n il ai o n ia nr e n? ak a n dh e r ei 1 1 b ea d r ai c r o r a m m in r o b 1 e mih ea 1 ip gqp g gp? q?b r i hr

19、 oe c? i n r a ci c er e? r i ci o nic anbechaned i noo 1i n aeo fgp p? p g? go n ef c ai b 1 e? ai o? r a nf o r mp a r a m er i c 1 i n e a re qai o n ihat e de e d - r a n k? r f a c e? i no? h ec o r r epondin gimplici?iem thethereof?hi?pape ri? o r g a n ie da? follofir?mehodofimlic iiai o n o

20、f a r a m er i c f i r ei 1 1 in r o de eh e r o b 1 e mh a n e e d? o p? ppr face? aie ninrefl5laerrefl6bedcal?ihandhcnia inideaoformehodgf i r p r o p oe d? h em oi n g 1 in ea n dm oi n g? r f a c e t h e nep r o p oe? h ea p p r o a c hi nd ea i li n c id i n gm eh o do m a k eh e i m 1 i c iiai

21、 on r o c e? me hh e c r e ai o n o fh ei d a n c ee co rh o? o m c c? pp? gm o r c e f f i c i e nb h im eh o d c ol d b eh e i ne r o 1 ai o n c o n d ii o n a n dh eo 1? i ono fhepheoreical limproedrefl7decribed?he o pi m iai o nm o d e 1a fe r? h a? ed e r ie? h em eh o cla h e b ai h e o r? h i

22、 c h? a? frh e r cp r c? i o no f? h ei m p 1 i c i? crca n da n a 1? ei?第期1 2 c o n? rci ngimplici? ere? b ac do ngi d a n c e? c co rl 2 1 3?r o e ri e. a loei 1 1 ieo m e ea m 1 e? op p? g? p?1 1 1 r aeh e e f f e c. fin al lh e e neral iai o n o fg? h i? a p p r o a c h? oc o n? rc? i m p 1 i c

23、ir f a c e? a n d? h ereplacemen?of?he?ol?ion?pac eb? h e? e no rr o dcbl in ei 1 1 b e ie np- p g2 cf lcaagienomeconroloin?onecancon? rep?a a r a m er i c ere b? c h c 1 a? i c a 1 m eh o dap?f o 1 1 oi n o be rai onandreflecionforaieng? gb? i e ro rb -p 1 i n eo? hah ecrei? proidedimlic icreh e c

24、o r r e ondin r a d i e n?ecorp? p gg? ih? o m eg o o dp r o p e ri ec ha? e n cl p o i nc a nb eo ba i n e da? anpoin?in idef iniionin e r o 1 ai o ned o 1 o calconroldereeraiinp p -ggr e i o n f i2h o? a n e 1 1 ii c ere an d i?g g? peomericaff ineinarianceco nehl 1g?r a d i e n? e co r f ieldnear

25、bonheoherhandg? a r i ai o nd i m i n ih i n g a n d? oo nsa ri n g f r o m? h ipgereo m? h ec o nrc o n? rci o n1 n m e ni o nloehdaameric?rfacon defde c a noeo m ckef o r r ai n e dbher e ao ni n do f?oec onr o 1a b 1 eg?e co rf i e 1 dci c a 1 a 1 i c ai o ne.p pp p gh ah ar o e r d e f iniionaea

26、cho i ni n h e a r e a?p pph e? e 1 lk n onn u r b sa r o ndca nbeco n? rce dt h i? e co rfieldlnreccnca ra? mcnionedbeforeinipl i c i? h ol db ea b 1 e? or e f 1 e c h ec o nr o lp o lg on r f a c eh ae b e en m o r e a ndmor ei del? edin? hap ea ndcha ngea ndc a nb er e g a r d e da h eeomericmode

27、l i ntheref oreadei nmehodof gg? g?rolonaionofheconroloin?eeomericp gp? gi m p 1 icirface?i? needed? hie hi? ep e ce d? ob ei n f o r m ai o n? o? h ca r e an e a r ben a m c? h c? c co rc o ne n i e n? e n og hf o rb oh? heoreicalanal?i?ando f? h i? f i e 1 da h egi dan c e? e co ra m ing racicalal

28、icaion. frh ermorehc?rface pp p?ha?healebraic ere id e f i n e d aele? g? qe n e r ae dbh i? m eh o d? h ol di n h e r i h oef i n egc a n e? h oe a r a m ee r? oh a? h eg? p 1?p r o p e ri c? o f? h ec 1 a? icpar a m ericr fac ca?mehalgebrai ccrei? f on d edbfi? i n ghi?kindof?ao? i b 1 ell e r ee?

29、 a rb d in h emeh o dpg?gi d a n c e? e co rf i e 1 da nelmeei n g cerainofheim1i c icre con? rci o n p?incrolaioncondiio nac n d o i n t h ii? h cp pino r d e r? of a c i 1 iae? h er ee a r c hea m eb ai ci d e ao for? aod ei n? h ei m 1 i c i? ere g ph a h ecre? ob ec o n? rce di? p 1 an a rg ie n

30、?+lc onr o 1 oin?on e c a ne ai 1 e p ogc onrololonalcde?andninorma lpgg? 1? c cor?correondinlafol loee? 1 p gf ilw ih? h eec on d ii on?en e e d? ogc o n? rc? a ni m p 1 ici? algebrai ccreo fd e g r e e? bp1? 1? ? h e r c bi? a r oo fb ae? o f? h e lgpolnomia 1 r i n pp? g?f. 2aa? ade? o? h ep a ri

31、 cl a r i? o f? h ei m p 1 i c ialebraic ere iin od i f f i cl?oi m a ineh ag gconi deringha?algebrai cere? o fh ighi c o n?rci o nroc ei1 lb eo bi o? le rp d e g r e ch acc ompleopological rc? r c h ichd if fe r e n? f r o m? h a? o f? h ep a r amer i co neor ii nco nen ienforboha nalia ndal i c ai

32、 onppcon? rci o n m eh o d im a i n 1 b ae d o nh e? e? ol d e? h eo 1 no m i a lereo fl o? d e r e epg中国科学技术大学学报第卷12 14 4 0conor eel le? 3h e nh e ere? d e r e e ier e? i o n o fh ei dan c ee co r? gp g 2?1 - 2 + 1+ 21 0 an dbar ep oer? e2?2? lb ae? h e r e ih emini ma ir adicoerinal1?heg2 2 3 22 3

33、?1? c o nr o lp o i nf r om? h ece nr oidof? hems o?ha l aer? e? i 1 la lo e? e norr o de? b -1in eheaboede f iniion o fh ei d a n c ee co r ip p? g?fn ci o n? o f? n i f o r mn o d c? a h e? o 1? i o n? p a c ei n d eendenofheconrololoncal eppg?n e e r o oeh earoachi ndeai 1? i np p? p p g ea21c o

34、ni d e rf orc o nr o lp o i n aae cificcamleincldinhccon? rci o n o fpp g f o 1 1 oh egi d a n c e? e co rh o om e e h e 1 0 1 2 10 -1 _i ne r p o 1 ai o nc o n d ii o n? a n d? h e? o 1? i o no f? h e 2 5 - 11 - 1 5? 23oi m iai o n m o d c lpt h c n? h cc o nr o lp o lg o na n d? h ec o r r ep ondi

35、ng?21g a i d a nceecordef in e d b e2 a r eh ongqfirec o n? re h egi d a. n c e? e co rf i e 1 di nf i3? g? ? ac cordi noh oe+ 1 c o nr o 1 goinihc onrololonaledep 0 pgga n dni n o r m a le cor 1? lc o r r e ondinl iiereholdreflec?hep gg e o m er i ci n f orm aio no f? h ec onrolp olg oncom m e ndab

36、l.f o ri n? ancehegi dan c e?e cori nhen e ihborhoodofomcoi na? h c c o nr o lg po 1 o nh old b ei m i 1arohe n o t m a lecoto fpg h a? c onr o lp o lgon ale d g e? h e re?hep oin?ilo c ae di fh e e ni r e c o nr o 1 o 1 o n ir e a r d e d aa npg? gi m 1 i c icre def inedbaiec eie 1 i n e a r fn ci

37、o np? p h e n i n gh eg r a d i e n e co r? o f? h i? fn ci o na h ef 3c? a? agi d a n c c? c co r? i? a? i m p 1 ca n dd i r c c? m ch o dh oee r a lh ohh ik i n d o fi d a n c ee co rl nf a c? h egi dan c e? e co rc a na lo? a k eggoh e r d e f iniionf oreamle? iniec eiem a i na i na 1 m o? a 1 lh

38、 e c o m cr i c i n f o r m ai o n o fh e? p g pg?fn ci o n o r eendicreefnciont her e1 aiec o nr o lp o lgoni?i?obio?ifa rfro m? h egradieneco r o fh e creh a?ehoeobi1 da fer a 11idie riof?he?idan c c? c co rd c finiioni? ap?gi? o o f a ih f loh einiialco ndiion. onheohercha r a ce r i? i co f? h i

39、? crec o n? rci on m eh o dh a n dh i? d e f i n iiondoe?no?faci 1 iaee ih e r? h e 22eifonl h e r a d i e nf ieldofhealebraic erec a 1 cl ai o no r? h cd c r iai o n? gg?therefor ee? eh e f o 1 1 oi n m e a? r eoiak e do f i? h ei dan c ee co r f i e 1 d g gdef i n eh ei d a n c ee co r i? r e ae d

40、 ad e f i n e dbh ec o nro lo i n e? a boch ecrc?g ph c?e i g he dae r a g co f?hc?ni?no r m a 1? e cor e g m en? i? a1 1? e p a r aef r o m? hec onr o1o fe a c heo nr o lpo lg o na le d g eh e r e? h e? eig hpo lgo nt h i? i? ha r d? oan a 1? ci p r o p e ri e?fn ci o n ia n a? e nai onfn cionabohe

41、edeoanohino fracicalal icai on. ii e n c eg g? pp p1 e nh? a n d? h ed i? a n c e b e? e e n? h eh e ere? h ol d i ne r o 1 aeh e e n d o i ng? p? pp o i n a n d? h cm i d p o i n? o f? h a? c o nr o 1 frh c rmoreheradi e n e co r? o f? a?g oo ion a 1 e d ef o r ea m 1 e? inh e g a i a npggp g? a n

42、da r er e qi r e d? ob ep e r p e n cl i cl a r? o? h el i n ea? c nai onfnciononccane?hefol 1 oi n g? gc g m c n? a n d r ep e cie 1. w r ii n g a 1 10 1- 1?第期1 2 c o n? rci ngimplici? ere? b ae do ngi d a n c e? e co rl 2 1 5? h ee c o n d ii o na m i nh a? h e r e a r ef in a 1 er e? i o n o fh e

43、 ere iaf o 1 1 o g? p3 2con d ii o na lo eh e r h e r e? i no05 2500 800 626554?g? 一+ +2 2?ep r e? i o30 0 00 9 40 00 1 3 63 t h ecrehf o r? h ea ep r e? i o o n? a r c? 一+-1 2 4 71 11 2 5 5 51 1 1+-+ 06 7892 55251 3+-+02 345782 21 2 3 4 6 11 0 2 3 4 51 2 5 5 5 58 9 1 4 3 7n? eh ae 002 2 4 205 93 9

44、05 4 5a p ei h oni nf ib oeea m p 1 e21h9 1 700 8 0 1 4 1 6- +200 5 9 0 1 2 0+- -200 4 7 4 4 2 2? +? +?g4 0 1e?pecificn? o f? h eee n d p o i n?in e r p o 1 ai o nc o ndii_1 0 +2 3 +4 5 +7+- of. 4a? a? baa?6 7 8 92 5 5 2 5 1 2 523 0? aa fe r c o n? rci nh e r o e ri d a n c ee co rg? p pgin h i? e c

45、i o nei 1 1 r ee n? h e el i c if i e 1 d? on ec a ng e h eo pi m iai o np r o b 1 e m? ihp? per e? i o n o fh e i m 1 i c icre a n dh e r e 1 ea n? o m ee qa 1 i? c o n? r a in b e 1 o? ba p p r oi m ai n g p ph e f i e 1 dihh e r adienfieldofhe ere i nh eh e o r ei c a la n a li i aa n a li nh eoi m iai o ng? gpdef i n ii o n r e i o nh ac oc ra 1 lhcconroloin?pro blem4theproceo foh e r p e? o f? h eg p? o 1? i o na c e f o r ea m 1 ee no r r o dcbn d e r?