计算机辅助口腔修复体模型的缝合算法_英文_

计算机辅助口腔修复体模型的缝合算法_英文_ Com puter a ided st itch ing approach for den ta l re stora t ion m ode ls Y uan T ian ran D a i N ing C heng X iaosheng L iao W enhe ()C o llege of M echan ica l and E lec trica l Eng inee ring, N an jing U n ive rs ity of A e ronau tics and A s tronau tics, N an jing 210016, C h ina Abstrac t: A cco rd ing to the b io2cha rac te ris tics of the low e r and )cu t to extract the upp er cavity su rface of the resto ra tion; 5 Stitch the upp er and lower cavity su rface to ob ta in a su rface upp e r cav ity su rfaces of den ta l res to ra tion, a s titch ing app roach is p a tch, wh ich m ake s the cavity of the re sto ration watertigh t. p rop osed based on a v irtua l z ipp e r w o rk ing m echan ism and a m in im iza tion of the su rface to ta l cu rva tu re ene rgy, w h ich is used F ig. 1 ske tche s the typ ica l p rocess of the comp u te r aided de2 to reso lve the s titch ing p rob lem s ex is ting du ring com p u te r2a ided sign fo r in lay, wh ich is a lso adap tab le to crown. des ign fo r den ta l res to ra tions. F irs t, the tw o bounda ries co rresp ond ing to the low e r and upp e r su rfaces a re triangu la ted based on the z ipp e r w o rk ing m echan ism to gene ra te the in itia l s titch ing su rface p a tch, of w h ich the edges a re d is tribu ted un ifo rm ly be tw een the bounda ries. S econd ly, the in itia l s titch ing su rface p a tch is subd iv ided and defo rm ed to recons truc t an F ig. 1 Illus tra tion of the com p u te r a ided in lay res to ra tion de2 op tim ized su rface p a tch acco rd ing to the b io2cha rac te ris tics of the ( ) ( ) ( ) s ign. a 3D in lay p rep a ra tion; b Fea tu re line de tec ting; c The tee th. The op tim ized su rface p a tch is m in im a lly d is tingu ishab le ( ) low e r cav ity su rface; d The upp e r cav ity su rface af te r be ing loca ted; f rom the su rround ing m esh in sm oo thness and dens ity, and it can ( ) eIn lay res to ra tion and its co rresp ond ing v irtua l w ea r s titch the upp e r and low e r cav ity su rfaces na tu ra lly. The exp e rim en ta l resu lts show tha t the den ta l res to ra tions ob ta ined by In g rap h ics, the effo rts in su rfaces s titch ing techn iques can the p rop osed m e thod can sa tisfy bo th the shap e aes the tic and the be app rox im a te ly c lass if ied in to th ree m a jo r ca tego ries, [ 8 ] [ 9 ] [ 10 ] f itting accu racy, and m ee t the requ irem en ts of c lin ica l o ra l nam e ly subd iv is ion , im p lic it and p a ram e tric su rfaces . [ 8 ] m ed ic ine. The subd iv is ion schem es need g iven bounda ry cu rves, Key words: den ta l res to ra tion; m ode l s titch ing; subd iv is ion and c ross2bounda ry de riva tives and in itia l con tro l ne ts. B ecause it is d iff icu lt to accu ra te ly so lve the bounda ry de riva tives fo r defo rm a tion; v irtua l z ipp e r d isc re te su rfaces, it becom es d iff icu lt to p e rfo rm the s titc2 h ing op e ra tion be tw een the triangu la r m eshes us ing the sub2 he in lay and crown re sto ration s in den tal p ro sthe sis are d iv is ion schem es. The im p lic it su rface 2based s titch ing m e th2 u sed to resto re the shap e and function of the tee th, wh ich[ 9 ] T od m os tly uses vo lum e tric techn iques and rad ia l bas is a re dam aged o r affec ted by too th defects, such a s carie s, m a l2 func tions fo r su rface in te rp o la tion to recons truc t the s titch ing fo rm ation, crack s and hypodon tia. The trad itional re sto ration s su rface. The s titch ing resu lt is g loba lly op tim ized, and can2 m ak ing m e thod is a tim e con sum ing and labo r2in ten sive wo rk. no t ref lec t the loca l cha rac te ris tics. The p a ram e tric su rface2 The p atien ts have to exp e rience wea r2rewo rk ing m any tim e s [ 10 ] based m e thod uses cons tra in ts such as con tro l p o in ts and befo re ach ieving a re sto ra tion w ith sa tisfacto ry fitting accu ra2 shap e inf luenc ing tangen t m agn itudes to cons truc t a v irtua l cy. W ith the deve lopm en t of comp u ter techno logy, the 3D s titch ing su rface f irs t, and then ob ta ins the f ina l triangu la r den ta l model can be ea sily ob ta ined via d iffe ren t k ind s of in2 [ 122 ]s titch ing su rface th rough m app ing o r re 2sam p ling tech2 tra2 o r extra2o ral m ea su rem en t m ethod s. CAD /CAM ha s n iques. The p a ram e tric2based s titch ing m e thod changes the been in troduced to den tistry d iscip line and grea t success ha s connec t re la tionsh ip of the o rig ina l su rface, w h ich m akes the been ach ieved in clin ical app lica tion s of o rthodon tic s a s well [ 326 ]s titch ing su rface seem unna tu ra l. a s o ra l and m axillofac ial su rgeries. The CAD /CAM den ta l B ecause the bounda ries co rresp ond ing to the upp e r and system has simp lified the p rocedu re s of the resto ra tion p ro2 low e r cav ity su rfaces a re long and w ith sha rp bend ing chan2 duc tion p roce ss th rough d igitizing, comp u ter a ided de sign and ges, it is d iff icu lt to ob ta in a s titch ing p a tch w h ich can sa tis2 virtual wea ring, and m anufactu ring. The design ing p rocess fo r fy bo th the shap e aes the tic and the f itting accu racy by us ing in lay and c rown resto ra tion s are d ivided app roxim ate ly in to [7 ] the ex is ting m e thods. The s titch ing resu lts of the upp e r and ) ) five step s: 1 P rep a re and d igitize the too th mode l; 2 D etec t low e r su rfaces have a g rea t inf luence on w he the r the res to ra2 ) the fea tu re line of the in lay o r c rown p rep ara tion; 3 Extrac t tion can be used in c lin ica l app lica tion successfu lly o r no t. In the lowe r cavity su rface of the in lay o r c rown re sto ration u sing th is p ap e r, acco rd ing to the b io 2cha rac te ris tics of the low e r ) the fea tu re line; 4 R econ struct the occlu sal su rface wh ich co r2 and upp e r cav ity su rfaces, w e p rop ose a s titch ing a lgo rithm re spond s to the m issing p a rt of the too th, and then locate and based on a z ipp e r w o rk ing m echan ism and a m in im iz ing to2 Rece ived 2009 202 220. ta l cu rva tu re func tion of the su rface p a tch, w h ich can recon2 ) ( (B iogra ph ie s: Yuan T ian ran 1982 —, m a le, g radua te; D a i N ing co rresp ond2 s truc t a su rface p a tch sa tisfy ing the na tu ra l a ttribu tes of the ) ing au tho r, m a le, assoc ia te p rofesso r, da i n ing @ nuaa. edu. cn. - too th. Foun da t ion item s: The N a tiona l H igh Techno logy R esea rch and D eve lop 2 ) () (m en t P rog ram of C h ina 863 P rog ram N o. 2005AA 420240 , the Key S c i2 1 V irtua l Z ipp e r and S titch ing A lgo rithm )(ence and Techno logy P rog ram of J iangsu P rov ince N o. B E2005014 . C ita t ion : Yuan T ian ran, D a i N ing, C heng X iaosheng, e t a l. C om p u te r a ided s W h ile the z ipp e r is be ing c losed, the th ree ne ighbo ring titch ing app roach fo r den ta l res to ra tion m ode ls [ J ]. J ou rna l of S ou theas t U tee th of the z ipp e r in con tac t w ith each o the r fo rm the shap e ( ) () n ive rs ity Eng lish Ed ition , 2009, 25 3 : 330 2334. z ipp e r w o rk ing and it w ill add one triang le in its m ov ing d i2 of a triang le. B ecause the bounda ries of the low e r and upp e r rec tion fo r each s tep. A f te r the z ipp e r m oves one s tep f rom cav ity su rfaces a re nea r to each o the r in sp a tia l loca tion. ( ) ( ) S im ila r in shap e, w ith nea rly equa l leng ths and num be r of the in itia l s ta te in F ig. 2 b to tha t in F ig. 2 c , w e ob ta in a 1 2 () ve rtices, each bounda ry can be seen as a v irtua l c ircu la r z ip 2 new c losed bounda ry B B = B + B , and then the ad d ad d s titc h s titc h p e r w ith the ve rtices as the “tee th ”. The “tee th ”con tac t in2 z ipp ing p rocedu re can a lso be seen as the triangu la tion of fo rm a tion of the v irtua l z ipp e r is rep resen ted by a line seg2 B unde r the cond ition tha t the triang les of the triangu la tion add m en t, w hose ends a re the bounda ry ve rtices. Th ree ne ighbo r2 w h ich a re used to c lose the bounda ry has to sa tisfy the fo l2 ing line segm en ts connec ted w ith each o the r consecu tive ly a t low ing p re requ is ites: the end fo rm a triang le. B ased on the above assum p tions, w e ) 1 The ve rtices of the triang le have to com p rise th ree con2 can im ita te the z ipp e r w o rk ing m echan ism to z ip the upp e r secu tive ve rtices of B , and the triang le shou ld be o rien ted a dd and low e r cav ity su rfaces. The d iffe rence be tw een the rea l cons is ten tly w ith the face ts a long the bounda ries. 12 and v irtua l z ipp e r used in s titch ing the su rface is tha t the ) 2 Each bounda ry of B and B has to ow n a t leas t one s titc h s titch “tee th ”of the v irtua l z ipp e r can be in con tac t w ith m o re ve rtex of the triang le, bu t a t m os t tw o. than tw o “tee th ”s im u ltaneous ly, and rem a in so du ring the c lose op e ra tion. The triang les in the s titch ing p a tch ob ta ined above a re jus t connec tions be tw een the bounda ry ve rtices, and have to be subd iv ided and defo rm ed to ob ta in an op tim ized su rface p a tch. It can ref lec t the loca l cha rac te ris tics of the co rre2 sp ond ing too th p a rt and sa tisfy the f itting accu racy, and it is m in im a lly d is tingu ishab le f rom the su rround ing m esh in sm oo thness and dens ity. B ecause the su rface of a hea lthy too th m ode l is cu rva tu re con tinuous, w e use the bounda ry cu rva tu re info rm a tion as a cons tra in t to cons truc t an op ti2 m ized su rface p a tch, w h ich m in im izes the to ta l cu rva tu re ene rgy. The fo llow ing s tep s desc ribe the p rocedu re of the s titch ing a lgo rithm : ) 1 Z ip the upp e r and low e r cav ity su rface a long the bounda ries to gene ra te the in itia l s titch ing su rface p a tch; ) 2 S ubd iv ide and defo rm the in itia l s titch ing su rface p a tch acco rd ing to the bounda ry info rm a tion in o rde r to ob ta in a su rface p a tch w h ich can m a tch the dens ity and sm oo thness of the su rround ing m esh. 111 D ef in itions The 3D den ta l m ode l is rep resen ted by us ing a w a te rtigh t o r tw o 2m an ifo ld triangu la r m esh. L e t M be a tw o 2m an ifo ld 3 triangu la r m esh co rresp ond ing to su rface S em bedded in R , and V = { v, v, ?, v} deno tes the se t of ve rtices in M. W e 1 2 n ( ) ( )def ine NV ias one 2ring ne ighbo rs of ve rtex vand N Ti 1 i 1 ( ) F ig. 2 M echan ism of the v irtua l z ipp e r. a B ounda ries to be as the se t of triang les tha t sha re ve rtex v. The bounda ry ( ) is titched; b The m ov ing d irec tion and loca tion of the v irtua l z ipp e r; ( ) cA f te r m ov ing fo rw a rd one s tep edge is an edge tha t on ly connec ts to one triang le, and a bounda ry ve rtex is a ve rtex tha t is ad jacen t to a bounda ry 11212 W e igh t ru le and z ipp e r c los ing edge. A bounda ry of the m esh is a c losed loop of bounda ry W hen w e use the triangu la tion concep t to rea lize the v ir2 b 3 edges. L e t vrep resen t the bounda ry ve rtex. The bounda ry is i Ω tua l z ipp e r, w e def ine : B?L as the w e igh t func tion.b b b deno ted by the sequence of ve rtices B = { v, v, ?, v}. 1 2 n Ω H e re, L is the w e igh t se t andass igns a w e igh t fo r each tri2 ( ) ang le w ith th ree consecu tive ve rtices of B. N Tide2 1 112 G ene ra tion of the in itia l s titch ing p a tch b b b ( )Ω ( ) i. L e t v, v, vbe the no tes the se t s ize of N T1 i - 1 i i + 1 11211 In itia liza tion of the v irtua l z ipp e r bb b ( ) w e igh t of the triang le v , v, v,and the w e igh t ru le is i - 1 i i + 1 L e t m eshand m eshdeno te the tw o m eshes co rresp ond2 1 2 desc ribed as fo llow s: bb b ing to the upp e r and low e r cav ity su rfaces to be s titched. ) ( )1 If a ll the th ree ve rtices of the triang le v , v, v i - 1 i i + 1 1 2 B and B a re the co rresp ond ing s titch ing bounda ries as 1 2 s titc h s titc h be long to B o r B s im u ltaneous ly, w h ich does no t sa tis2 s titc h s titc h 1bbb 21 1 1 ( ) 2 a w he re B show n in F ig. = { v , v , ?, v} and Bs titc h 1 2 m s titch fy the p re requ is ites p resen ted above, the triang le shou ld be 1 bbbb2 2 2 1 b b b= { v, v, ?, v}. G iven ve rtex von B , the c loses t ve r2 1 2 k i s titch ) Ω( , v, v= - ?. g iven the low es t cho ice p rio rity:vi - 1 i i + 1 2 b2 bb b tex von B is cons ide red as the o the r end of the “b ridge” j s titch ) ( 2 If the triang le v )sa tisf ies the p re requ is ites , v, vi - 1 i i + 1 bb1 2 ( )vv. The bounda ries a re b ridged as show n in F ig. 2 b . i j ( ) i?8, the w e igh t func tion is p resen ted above and N T1 B ecause the bounda ries a re c ircu la r, w e ob ta in tw o opp os ite com p u ted acco rd ing to the p e rim e te r l of the triang le. If ( ) m ov ing d irec tions m a rked w ith a rrow s in F ig. 2 b a t the ( )N Ti> 8, the triang le shou ld be added w ith a h ighe r 1 ( ) sam e s ta rting loca tion. F ig. 2 c show s the w ay of the v irtua l cho ice p rio rity in o rde r to ob ta in an in itia l s titch ing p a tch 3 w ith edges un ifo rm ly d is tribu ted be tw een the bounda ries. Ω) t:?Rbe a fam ily of the sm oo th su rface. u and v a re the ( Then the w e igh t func tion is su rface p a ram e te rs a t tim e t. W hen the su rface fam ily S u, ) v, tevo lves a long the g rad ien t2descen t d irec tion d riven by ( )l - iN T?8 1 the su rface ene rgy, w e can so lve the fo llow ing geom e try b b b Ω( ) ( ) )(v, v, v= N T i1 i - 1 i i + 1 1 f low to ob ta in the su rface w ith m in im a l p o ten tia l ene rgy g iv2 ( ) N Ti> 8 1 8 ()en by E S . W e app ly the fo llow ing p rocedu re to im p lem en t the v irtu2 )(3 ()= - A E S S? a l z ipp e r c los ing p rocess: 2 12)(4 Δ() ()A E S = - FN , F = - H - 2H H - K ) S 1 P rep rocess the bounda ries B and B to ob ta in a s titch s titch new c losed bounda ry B , and inse rt the triang les gene ra ted a dd ( w he re Sis the tim e de riva tive of S w ith resp ec t to t. N t, u, ?0 to the su rface p a tch M w h ich is in itia lly em p ty. C om p u te a ll ) ( )() vis the un it no rm a l of su rface S u, v, t. To so lve 3 nu2 the w e igh ts acco rd ing to the w e igh t func tion g iven above fo r ) (m e rica lly, the tim e de riva tive te rm in 3 is app rox im a ted by each triang le w ith th ree consecu tive ve rtices of B , and in2 a dd its fo rw a rd d iffe rence app rox im a tion se rt the w e igh ts in to L in w h ich the w e igh t is so rted by us ing τ( ) ( )an AVL tree. S t +, u, v- S t, u, v ()S? ?5 ) τ2 G e t the m ax im um lf rom L and inse rt its co rresp ond2 m ax b b b 0( ) ing triang le v, v, vin to M . R em ove the w e igh ts of i - 1 i i + 1 W e ob ta in a d isc re te su rface evo lu tion p rocess by Eqs. b b b b b b b ) Ω( ) Ω ( Ω ( the triang les v, v, v, v, v, vand v,i - 2 i - 1 i i - 1 i i + 1 i ()() 4 5 , and b b b b ) v, vf rom L tha t inc lude ve rtex v.E lim ina te ve rtex v i + 1 i + 2 i ib b b b b b ( τ) ( )S t +, u, v- S t, u, v f rom B , and then B= { v, v, ?, v, v, v, v, ?, add H 1 2 i - 2 i - 1 i + 1 i + 2 )(6 ()= - A E S b b b b b b b τ) ( )( v}. C om p u te the w e igh ts v, v, v, v, v, v n i - 2 i - 1 i + 1 i - 1 i + 1 i + 2 b b b b b b Ω ( ) Ω ( ) of the triang les v, v, vand v, v, v,i - 2 i - 1 i + 1 i - 2 i - 1 i + 1 )(( ττ) ( ) 7 S t +, u, v= S t, u, v+FN) and inse rt them in to L. Execu te s tep 2 ite ra tive ly un til the [ 13 ] ΔW hen, H and K a re d isc re tized by M eye r e t a l. , the ( ) )( ve rtex num be r of B is less than th ree see F ig. 3 b . S ad d () d isc re te evo lu tion of su rfaces 7 can be app rox im a ted by a m esh up da ting p rocess, w h ich is p e rfo rm ed ite ra tive ly un til it ( ) ( ) ) ( reaches a s teady 2s ta te see F igs. 3 c and d : + 1 k k k k k ()τ 8 v= v+F n i i i i k + 1 k + 1 ( )F ig. 3 Exam p le of the m o la r too th m ode l s titch ing. aM ode l w he re v is the ve rtex of M ob ta ined af te r k s tep s of the i 1 ( ) ( ) to be s titched; b In itia l s titch ing su rface p a tch; c A f te r subd iv is ion ) ( up da ting p rocess 8 f rom the in itia l s ta te M , w h ich ap 2 ( ) and defo rm a tion; d S titch ing resu lts ()p rox im a tes S 0, u, v. 113 S ubd iv is ion and defo rm a tion 2 Exp e rim en ta l R esu lts and A na lys is The triang les in the in itia l s titch ing p a tch a re jus t the con2 The m iss ing p a rts of the occ lusa l su rface a re usua lly ob2 ( ) ) ( nec tions be tw een the bounda ry ve rtices see F ig. 3 b and ta ined th rough ed iting the s tanda rd c row n, w h ich is s to red in have to be subd iv ided and defo rm ed to ob ta in an op tim ized the s tanda rd c row n da tabase, and the fea tu re line of the p rep 2 su rface p a tch w h ich can sa tisfy the f itting accu racy and is a ra tion can be recogn ized and ex trac ted accu ra te ly and eff i2 m in im a lly d is tingu ishab le f rom the su rround ing m esh in c ien tly by us ing ex is ting m e thods in com p u te r g rap h ics. A s sm oo thness and dens ity. In th is p ap e r, the subd iv is ion p roce2 ( ) ( ) ( ) can be seen f rom F ig. 3 b , F ig. 4 b and F ig. 5 b , the ed2 du re is p e rfo rm ed by adop ting the a lgo rithm p resen ted by ges of the in itia l s titch ing su rface p a tch gene ra ted based on [ 11 ] 0 1 Pfe if le and S e ide l on M to ob ta in a p a tch M tha t app rox2 the z ipp e r m echan ism a re d is tribu ted be tw een the bounda ries ( ) )( im a tes the dens ity of the su rround ing m esh see F ig. 3 c . even ly, and the w e igh t ru le p resen ted above can avo id the In com p u te r g rap h ics and the geom e try m ode ling f ie ld, the s itua tion of se lf2in te rfe rence eff ic ien tly du ring triangu la tion. 2 2 ( ) ( ) ( ) F ig. 3 c , F ig. 4 c and F ig. 5 c show the f ina l resu lts of () κκto ta l cu rva tu re func tiona l E S = +dA is w ide ly used1 2 κ the s titch ing su rface w h ich m a tch the dens ity and the con ti2 κκto fa ir a su rface p a tch w ith a f ixed bounda ry. H e re,and 1 2nu ity of the su rround ing m eshes and the loca l cha rac te ris tics deno te the p rinc ip a l cu rva tu res of the su rface, resp ec tive ly, of the s titch ing reg ion can be recove red accu ra te ly. The f it2 and dA is the su rface a rea e lem en t. W e gene ra lize the fa iring ting accu racy be tw een the p rep a ra tion and its co rresp ond ing [ 12 ] m e thod p resen ted by Yosh izaw a and B e lyaev to defo rm res to ra tion is m os tly conce rned in c lin ica l app lica tion. B e2 1 the su rface p a tch M , w h ich is based on the to ta l cu rva tu re cause the bounda ry ve rtices of the low e r cav ity su rface and func tiona l and can p roduce h igh qua lity shap es. The co rre2 the fea tu re line ve rtices of the p rep a ra tion a re in one2to 2one sp ond ing Eu le r2L ag range equa tion w h ich cha rac te rizes the co rresp ondence, the bounda ry no rm a l info rm a tion is subs titu2 () m in im ize rs of E S is g iven by ted by the no rm a l info rm a tion of the fea tu re line in o rde r to 2m ake su re tha t the defo rm ed su rface p a tch can a lso s titch Δ (()) H + 2H H- K= 0 2 S sm oo th ly ac ross the fea tu re line w ith the p rep a ra tion. B e2 w he re H and K a re the m ean and G auss ian cu rva tu res, re2 cause the s titch ing op e ra tion is d irec tly app lied on the Δ( sp ec tive ly; is the L ap lace 2B e ltram i op e ra to r. L e t S u, v, m eshes, and it does no t need to be conve rted in to N u rbs o r a S ( ) tu red ob jec t in F ig. 5 e dem ons tra te tha t the a lgo rithm B 2sp line su rface, w e can reduce the des ign com p lex ity and can im p rove the accu racy of the con tac ting reg ion. The v irtua l ach ieve sa tisfac to ry resu lts. ( ) ( ) w ea r s im u la tions in F ig. 4 d , F ig. 5 d and the m anufac2 ( ) F ig. 4 S titch ing p rocess fo r in lay res to ra tion. aFea tu re line de tec tion, and the co rresp ond ing low e r and upp e r cav ity su rface af te r be ing ( ) ( ) loca ted; b The in itia l s titch ing su rface p a tch and its co rresp ond ing res to ra tion; cThe su rface p a tch af te r be ing subd iv ided and defo rm ed, and ( ) its co rresp ond ing res to ra tion; d V irtua l w ea r ( ) F ig. 5 S titch ing p rocess fo r c row n res to ra tion. aFea tu re line de tec tion, and the co rresp ond ing low e r and upp e r cav ity su rface af te r be2 ( ) ( ) ing loca ted; bThe in itia l s titch ing su rface p a tch w ith its su rround ing triang les, and its co rresp ond ing res to ra tion; cThe su rface p a tch af te r be2 ( ) ( ) ing subd iv ided and defo rm ed, and its co rresp ond ing res to ra tion; d V irtua l w ea r; eM anufac tu red ob jec t 3 C onc lus ion Referen ce s In th is p ap e r, w e p resen t a s titch ing app roach to reso lve [ 1 ] H a jee r M J, M ille tt D T, A youb A F, e t a l. A pp lica tions of the s titch ing p rob lem s ex is ting du ring com p u te r a ided de2 3D im ag ing in o rthodon tics [ J ]. J ou rna l of O r thodon tics, s ign fo r in lays and c row ns, such as d is to rtions and f itting () 2004, 31 1 : 62270. inaccu rac ies. The key of the p rop osed app roach is to recon2 [ 2 ] R udo lp h H , L u tha rd t R G , W a lte r M H. C om p u te r2a ided s truc t a su rface p a tch, w h ich can s titch the low e r and upp e r ana lys is of the inf luence of d ig itiz ing and su rfac ing on the cav ity su rfaces sm oo th ly and na tu ra lly. The exp e rim en ta l re2 accu racy in den ta l CAD / CAM techno logy [ J ]. C omp u te rs in su lts show tha t the in lay and c row n res to ra tions ob ta ined by () B io logy a nd M ed ic ine, 2007, 37 5 : 5792587. [ 3 ] B a rnfa the r K D P, B run ton P A. R es to ra tion of the upp e r the p rop osed m e thod can sa tisfy the requ irem en ts of c lin ica l TM o ra l m ed ic ine bo th in v irtua l w ea r s im u la tion and in the den ta l a rch us ing L avaa ll2ce ram ic c row n and b ridgew o rk () [ J ]. B r itish D en ta l J ou rna l, 2007, 202 12 : 731 2735. m anufac tu ring s tage. A t the sam e tim e, the p rop osed m e th2 [ 4 ] Touchs tone A , Ph illip s R J. S im p lify ing CAD / CAM D en tis t2 od in th is p ap e r is no t on ly res tric ted to the f ie ld of den ta l ) ( ry [ EB /OL ]. 2005 211209 [ 2009 201 210 ]. h ttp : / /www. res to ra tions, bu t a lso it can be used to cons truc t com p lex tucsonsm ile. com / a rtic les / cad2cam 2den tis try. p df. ob jec ts w h ich sha re a ll the fea tu res of the o rig ina l m ode l [ 5 ] G a rino F. The o rthodon tic 3D w o rld: the bas ic ro le of the o r2 bu t d iffe r f rom the o rig ina l m ode ls in the f ie lds of gam es, ) ( thodon tis t [ EB /OL ]. 2007 208 201 [ 2009201 210 ]. h ttp : / / v irtua l rea lity, and so on. www. d rga rino. it / p ics / up load /O rtho tribune. p df. () [ 6 ] B e ttega G , Payan Y, M o lla rd B , e t a l. A s im u la to r fo r m ax il2 2005, 21 11 : 915 2927. lofac ia l su rge ry in teg ra ting 3D cep ha lom e try and o rthodon tia [ 11 ] Pfe if le R , S e ide l H P. T riangu la r B 2sp lines fo r s titch ing and () f illing of p o lygona l ho les [ C ] / / P roceed ings of G rap h ics [ J ]. C om p u te r A ided Su rge ry, 2000, 5 3: 156 2165. va rious In te rfa ceπ96. To ron to, O n ta rio, C anada, 1996: 186 2193. 7 ] A do lp h S , G u rke S. M ode ling of a f itting in lay f rom [ info rm a tion [ C ] / / P roceed ings of V is ion, M ode ling, a nd V i2 [ 12 ] Yosh izaw a S , B e lyaev A G. Fa ir triang le m esh gene ra tion w ith d isc re te e las tica [ C ] / / P roceed ings of G eom e tr ic M od2 sua liza tion 2001. S tu ttga rt, G e rm any, 2001: 309 2316. e ling a nd P rocess ing. R iken, S a itam a, J ap an, 2002: 119 2123. [ 8 ] B ie rm ann H , M a rtin I. C u t2and 2p as te ed iting of m u lti2reso lu2 tion su rface [ J ]. ACM T ra nsa c tions on G rap h ics, 2002, 21 [ 13 ] M eye r M , D esb run M , S ch rode r P, e t a l. D isc re te d iffe ren tia l () 3: 330 2338. geom e try op e ra to r fo r triangu la ted 22m an ifo lds [ C ] / / P ro2 [ 9 ] Zou W H , D ing Z, Ye X Z, e t a l. In te rac tive p o in t c loud ceed ings of the 26 th A nnua l C onfe rence on C om p u te r b lend ing by d rag2and 2d rop [ J ]. J ou rna l of Zhe jia ng U n ive rs i2 G rap h ics a nd In te ra c tive Techn iques. L os A nge les, U SA , () ty: Sc ience A, 2007, 8 10: 163321641. 1999: 3172324. [ 10 ] L iu Y S , Zhang H. M esh b lend ing [ J ]. V isua l C om p u te r, 计算机辅助口腔修复体模型的缝合算法 袁天然戴宁程筱胜廖文和 () 南京航空航天大学机电学院 , 南京 210016 摘要 :针对计算机辅助口腔修复体设计中的缝合问题, 根据修 复体腔底表面和上表面的生物医学特征 , 提出了一种基于拉链啮合机制和最小化全曲率能量函数的缝合算法. 该算法首先采用由局部最优化权值驱动的虚拟拉 链 , 对修复体腔的底表面和上表面边界进行拉合 , 得到对应的初始缝合曲面片. 其次 , 对初始缝合曲面片进行细 分优化 , 并根据牙齿的生理医学特性 , 对缝合曲面片进行变形调整 , 构造出符合实际生理医学特征的缝合曲面 片 , 实现修复体腔底表面和上表面的光滑连续缝合. 实验结果表明 , 利用所提方法设计出的修复体在形态和配合 精度上 , 均能满足临床口腔医学要求. 关键词 : 口腔修复体; 模型缝合 ; 细分变形; 虚拟拉链 中图分类号 : TP391