ISO INTERNATIONAL STANDARD

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1 INTERNATIONAL STANDARD ISO First ition Inustrial automation systms an intgration Prouct ata rprsntation an xchang Part 511: Application intrprt construct: Topologically boun surfac Systèms 'automatisation inustrill t intégration Rprésntation t échang onnés prouits Parti 511: Construction intrprété: Surfac élimité topologiqumnt Rfrnc numbr ISO :2001(E) ISO 2001

2 PDF isclaimr This PDF fil may contain mb typfacs. In accoranc with Aob's licnsing policy, this fil may b print or viw but shall not b it unlss th typfacs which ar mb ar licns to an install on th computr prforming th iting. In ownloaing this fil, partis accpt thrin th rsponsibility of not infringing Aob's licnsing policy. Th ISO Cntral Scrtariat accpts no liability in this ara. Aob is a tramark of Aob Systms Incorporat. Dtails of th softwar proucts us to crat this PDF fil can b foun in th Gnral Info rlativ to th fil; th PDF-cration paramtrs wr optimiz for printing. Evry car has bn takn to nsur that th fil is suitabl for us by ISO mmbr bois. In th unlikly vnt that a problm rlating to it is foun, plas inform th Cntral Scrtariat at th arss givn blow. ISO 2001 All rights rsrv. Unlss othrwis spcifi, no part of this publication may b rprouc or utiliz in any form or by any mans, lctronic or mchanical, incluing photocopying an microfilm, without prmission in writing from ithr ISO at th arss blow or ISO's mmbr boy in th country of th rqustr. ISO copyright offic Cas postal 56 CH-1211 Gnva 20 Tl Fax copyright@iso.ch Wb Print in Switzrlan ii ISO 2001 All rights rsrv

3 Contnts Pag 1 Scop Normativrfrncs Trms,finitionsanabbrviations Trms fin in ISO Trms fin in ISO Trms fin in ISO Othrfinitions Abbrviations EXPRESSshortlisting Funamntal concpts an assumptions aic topologically boun surfac schma ntity finition: avanc fac... 8 Annx A (normativ) Short nams of ntitis AnnxB(normativ) Informationobjctrgistration B.1 Documntintification B.2 Schmaintification AnnxC(informativ) Computr-intrprtabllistings AnnxD(informativ) EXPRESS-Giagrams Inx Figurs Figur D.1 aic topologically boun surfacexpress-giagrampag1of Figur D.2 aic topologically boun surfacexpress-giagrampag2of Figur D.3 aic topologically boun surfacexpress-giagrampag3of Figur D.4 aic topologically boun surfacexpress-giagrampag4of Figur D.5 aic topologically boun surfacexpress-giagrampag5of Figur D.6 aic topologically boun surfacexpress-giagrampag6of Figur D.7 aic topologically boun surfacexpress-giagrampag7of Figur D.8 aic topologically boun surfacexpress-giagrampag8of Tabls Tabl A.1 Short nams of ntitis ISO 2001 All rights rsrv iii

4 Forwor ISO (th Intrnational Organization for Stanarization) is a worlwi fration of national stanars bois (ISO mmbr bois). Th work of prparing Intrnational Stanars is normally carri out through ISO tchnical committs. Each mmbr boy intrst in a subjct for which a tchnical committ has bn stablish has th right to b rprsnt on that committ. Intrnational organizations, govrnmntal an non-govrnmntal, in liaison with ISO, also tak part in th work. ISO collaborats closly with th Intrnational Elctrotchnical Commission (IEC) on all mattrs of lctrotchnical stanarization. Intrnational Stanars ar raft in accoranc with th ruls givn in th ISO/IEC Dirctivs, Part 3. Draft Intrnational Stanars aopt by th tchnical committs ar circulat to th mmbr bois for voting. Publication as an Intrnational Stanar rquirs approval by at last 75 % of th mmbr bois casting a vot. Attntion is rawn to th possibility that som of th lmnts of this part of ISO may b th subjct of patnt rights. ISO shall not b hl rsponsibl for intifying any or all such patnt rights. This Intrnational Stanar is organiz as a sris of parts, ach publish sparatly. Th structur of this Intrnational Stanar is scrib in ISO Each part of this Intrnational Stanar is a mmbr of on of th following sris: scription mthos, implmntation mthos, conformanc tsting mthoology an framwork, intgrat gnric rsourcs, intgrat application rsourcs, application protocols, abstract tst suits, application intrprt constructs, an application mouls. This part is a mmbr of th application intrprt construct sris. A complt list of parts of ISO is availabl from th Intrnt: < Annxs A an B form a normativ part of of this part of ISO Annxs C an D ar for information only. iv ISO 2001 All rights rsrv

5 Introuction ISO is an Intrnational Stanar for th computr-intrprtabl rprsntation an xchang of prouct ata. Th objctiv is to provi a nutral mchanism capabl of scribing prouct ata throughout th lif cycl of a prouct inpnnt from any particular systm. Th natur of this scription maks it suitabl not only for nutral fil xchang, but also as a basis for implmnting an sharing prouct atabass an archiving. This Intrnational Stanar is organiz as a sris of parts, ach publish sparatly. Th parts of ISO fall into on of th following sris: scription mthos, intgrat rsourcs, application intrprt constructs, application protocols, abstract tst suits, implmntation mthos, an conformanc tsting. Th sris ar scrib in ISO This part of ISO is a mmbr of th application intrprt construct sris. An application intrprt construct (AIC) provis a logical grouping of intrprt constructs that supports a spcific functionality for th usag of prouct ata across multipl application contxts. An intrprt construct is a common intrprtation of th intgrat rsourcs that supports shar information rquirmnts among application protocols. This ocumnt spcifis th application intrprt construct for topologically boun surfac. This is th final raft of a 500 sris part ition of th AIC for th finition of a fac with xplicit topology an fully fin gomtry. Th fac an g gomtry inclus both lmntary an fr-form gomtry. ISO 2001 All rights rsrv v

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7 INTERNATIONAL STANDARD ISO :2001(E) Inustrial automation systms an intgration Prouct ata rprsntation an xchang Part511: Applicationintrprtconstruct: Topologicallyboun surfac 1 Scop This part of ISO spcifis th intrprtation of th itgrat rsourcs to satisfy th rquirmnt for th finition of a fac with xplicit topological bouns an fully fin gomtry. Th following ar within th scop of this part of ISO 10303: 3D gomtry; B-splin curvs an surfacs; conics; lmntary curvs; lmntary surfacs; polylins; pcurvs; sculptur surfacs; surfac curvs rfrncing pcurvs; swpt surfacs; twist curvs; unboun gomtry; gomtric transformations; us of topology to boun gomtric ntitis. Th following ar outsi th scop of this part of ISO 10303: 2D gomtry othr than for th finition of a pcurv in th paramtr spac of a surfac; ciso 2001 Allrightsrsrv 1

8 boun curvs othr than polylins an B-splin curvs; boun surfacs othr than B-splin surfacs; offst curvs an surfacs. 2 Normativ rfrncs Th following normativ ocumnts contain provisions which, through rfrnc in this txt, constitut provisions of this part of ISO For at rfrncs, subsqunt amnmnts to, or rvisions of, any of ths publications o not apply. Howvr, partis to agrmnts bas on this part of ISO ar ncourag to invstigat th possibility of applying th most rcnt itions of th normativ ocumnts inicat blow. For unat rfrncs, th latst ition of th normativ ocumnt rfrr to applis. Mmbrs of ISO an IEC maintain rgistrs of currntly vali Intrnational Stanars. ISO/IEC8824-1: 1998, Informationtchnology -AbstractSyntax Notation On (ASN.1): Spcification ofbasicnotation. ISO : 1994, Inustrial automation systms an intgration - Prouct ata rprsntation an xchang - Part 1 : Ovrviw an funamntal principls. ISO : 1994, Inustrial automation systms an intgration - Prouct ata rprsntation an xchang - Part 11 : Dscription mthos: Th EXPRESS languag rfrnc manual. ISO : 1994, Inustrial automation systms an intgration - Prouct ata rprsntation an xchang - Part 41 : Intgrat gnric rsourcs: Funamntals of prouct scription an support. ISO : 1994, Inustrial automation systms an intgration - Prouct ata rprsntation an xchang - Part 42 : Intgrat gnric rsourcs: Gomtric an topological rprsntation. ISO : 1994, Inustrial automation systms an intgration - Prouct ata rprsntation an xchang - Part 43 : Intgrat gnric rsourcs: Rprsntation structurs. ISO :1996, Inustrialautomationsystmsanintgration-Prouctatarprsntationan xchang - Part 202: Application protocol: Associativ raughting 3 Trms, finitions an abbrviations 3.1 Trms fin in ISO For th purposs of this part of ISO 10303, th following trms fin in ISO apply. application; 2 ciso 2001 Allrightsrsrv

9 application contxt; application protocol; implmntation mtho; intgrat rsourc; intrprtation; prouct ata; 3.2 Trms fin in ISO For th purposs of this part of ISO 10303, th following trms fin in ISO apply. axi-symmtric; bounary; bouns; coorinat spac; curv; opn curv; orintabl; surfac; topological sns. 3.3 Trms fin in ISO For th purposs of this part of ISO 10303, th following trm fin in ISO applis application intrprt construct (AIC) a logical grouping of intrprt constructs that supports a spcific functionality for th usag of prouct ata across multipl application contxts. 3.4 Othr finitions ciso 2001 Allrightsrsrv 3

10 avanc fac A fac fin on a surfac. This fac is a finit portion of th surfac that has its bounaris fully fin using topological ntitis with associat gomtric curvs. Th surfac gomtry is rquir to b ithr an lmntary surfac, or a swpt surfac, or a B-splin surfac sculptur surfac A bi-paramtric fr-form surfac. In this part of ISO a sculptur surfac is rprsnt by a B-splin surfac swpt surfac A surfac obtain by translating or rvolving a curv twist curv A paramtric curv in thr-imnsional spac. In this part of ISO a twist curv is rprsnt by a B-splin curv. 3.5 Abbrviations For th purposs of this part of ISO 10303, th following abbrviations apply. AIC Application Intrprt Construct AP Application Protocol 4 EXPRESS short listing This claus spcifis th EXPRESS schma that uss lmnts from th intgrat rsourcs an contains th typs, ntity spcializations, an functions that ar spcific to this part of ISO NOTE 1 Thr may b subtyps an itms of slct lists that appar in th intgrat rsourcs that ar not import into th AIC. Constructs ar liminat from th subtyp tr or slct list through th us of th implicit intrfac ruls of ISO Rfrncs to liminat constructs ar outsi th scop of th AIC. In som cass, all itms of th slct list ar liminat. Bcaus AICs ar intn to b implmnt in th contxt of an application protocol, th itms of th slct list will b fin by th scop of th application protocol. This application intrprt construct provis a consistnt st of gomtric an topological ntitis for th finition of a fac with fully fin gomtry an xplicit topology fining th bounaris. Th prmissibl typs of fac gomtry inclu lmntary surfacs an B-splin surfacs. Egs ar rquir to hav thir gomtry fin by curvs, that may inclu pcurvs. Th highst lvl ntity in this AIC is avanc fac which is a spcialis typ of fac surfac (s ISO ). Th ruls on this ntity nsur that th topology an gomtry ar fully fin. 4 ciso 2001 Allrightsrsrv

11 EXPRESS spcification: *) SCHEMA aic_topologically_boun_surfac; USE FROM gomtry_schma (axis2_placmnt_2, axis2_placmnt_3, bzir_curv, bzir_surfac, b_splin_curv_with_knots, b_splin_surfac_with_knots, cartsian_point, circl, composit_curv_on_surfac, conical_surfac, cylinrical_surfac, gnrat_toroial_surfac, irction, llips, gomtric_rprsntation_contxt, hyprbola, lin, parabola, pcurv, plan, polylin, quasi_uniform_curv, quasi_uniform_surfac, rational_b_splin_curv, rational_b_splin_surfac, sphrical_surfac, surfac_curv, surfac_of_linar_xtrusion, surfac_of_rvolution, swpt_surfac, toroial_surfac, uniform_curv, uniform_surfac, vctor); USE FROM topology_schma (g, g_curv, g_loop, fac_boun, fac_outr_boun, fac_surfac, orint_g, path, vrtx_loop, vrtx_point); USE FROM rprsntation_schma ciso 2001 Allrightsrsrv 5

12 (finitional_rprsntation, paramtric_rprsntation_contxt); USE FROM masur_schma (paramtr_valu); (* NOTE 2 Th ntitis g, path an swpt surfac ar xplicitly intrfac, i.., inclu in th USE FROM lists, to allow ruls in th avanc fac ntity to accss attributs of ths ntitis. For th us of this AIC ths ntitis shall only b instantiat as on of thir subtyps. NOTE 3 Th schmas rfrnc abov can b foun in th following parts of ISO 10303: gomtry schma ISO topology schma ISO rprsntation schma ISO masur schma ISO Funamntal concpts an assumptions Th following ntitis ar intn to b inpnntly instantiat in th application protocol schmas that us this AIC: avanc fac; axis2 placmnt 2; axis2 placmnt 3; bzir curv; bzir surfac; b splin curv with knots; b splin surfac with knots; cartsian point; circl; conical surfac; finitional rprsntation; gnrat toroial surfac; cylinrical surfac; 6 ciso 2001 Allrightsrsrv

13 irction; g curv; g loop; llips; fac boun; fac outr boun; fac surfac; gomtric rprsntation contxt; hyprbola; lin; parabola; paramtric rprsntation contxt; pcurv; plan; polylin; quasi uniform curv; quasi uniform surfac; rational b splin curv; rational b splin surfac; sphrical surfac; surfac of linar xtrusion; surfac of rvolution; toroial surfac; uniform curv; ciso 2001 Allrightsrsrv 7

14 uniform surfac; vctor; vrtx loop; vrtx point. An application protocol that uss this AIC shall rquir that all th abov ntitis ar support. An application protocol that uss this AIC shall rquir that a fac ntity is instantiat as an avanc - fac. 4.2 aic topologically boun surfac schma ntity finition: avanc fac An avanc fac is a spcial typ of fac surfac that has aitional constraints to nsur that th gomtry is irctly an compltly fin. Th avanc fac is th top lvl ntity that is us to formulat th prcis maning of a topologically boun surfac corrsponing to th scop of this AIC. An avanc fac is rquir to b fully boun by g loopsorbyvrtx loops. At most on of th bouns of th fac may b of typ fac outr boun NOTE boun. For som typs of clos or partially clos surfacs, it may not b possibl to intify a uniqu outr EXAMPLE 1 Any g loop onaplansurfacmaybustofinafac outr boun provi it is not nclos in any othr loop in th fac. EXAMPLE 2 A circular loop on a cylinrical surfac cannot fin a fac outr boun sinc it os not nclos a clos omain in th surfac. EXPRESS spcification: *) ENTITY avanc_fac SUBTYPE OF (fac_surfac); WHERE WR1 : SIZEOF ([ AIC_TOPOLOGICALLY_BOUNDED_SURFACE.ELEMENTARY_SURFACE, AIC_TOPOLOGICALLY_BOUNDED_SURFACE.B_SPLINE_SURFACE, AIC_TOPOLOGICALLY_BOUNDED_SURFACE.SWEPT_SURFACE ] * TYPEOF(fac_gomtry)) = 1; WR2 : SIZEOF(QUERY (lp_fbns <* QUERY (bns <* bouns AIC_TOPOLOGICALLY_BOUNDED_SURFACE.EDGE_LOOP IN 8 ciso 2001 Allrightsrsrv

15 TYPEOF(bns.boun)) NOT (SIZEOF (QUERY (o <* lp_fbns.boun\path.g_list NOT( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.EDGE_CURVE IN TYPEOF(o\orint_g.g_lmnt)))) = 0))) = 0; WR3 : SIZEOF(QUERY (lp_fbns <* QUERY (bns <* bouns AIC_TOPOLOGICALLY_BOUNDED_SURFACE.EDGE_LOOP IN TYPEOF(bns.boun)) NOT (SIZEOF (QUERY (o <* lp_fbns.boun\path.g_list NOT (SIZEOF ([ AIC_TOPOLOGICALLY_BOUNDED_SURFACE.LINE, AIC_TOPOLOGICALLY_BOUNDED_SURFACE.CONIC, AIC_TOPOLOGICALLY_BOUNDED_SURFACE.POLYLINE, AIC_TOPOLOGICALLY_BOUNDED_SURFACE.SURFACE_CURVE, AIC_TOPOLOGICALLY_BOUNDED_SURFACE.B_SPLINE_CURVE ] * TYPEOF(o.g_lmnt\g_curv.g_gomtry)) = 1 ) )) = 0))) = 0; WR4 : SIZEOF(QUERY (lp_fbns <* QUERY (bns <* bouns AIC_TOPOLOGICALLY_BOUNDED_SURFACE.EDGE_LOOP IN TYPEOF(bns.boun)) NOT(SIZEOF(QUERY (o <* lp_fbns.boun\path.g_list NOT(((( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.VERTEX_POINT IN TYPEOF(o\g.g_start)) AND ( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.CARTESIAN_POINT IN TYPEOF(o\g.g_start\vrtx_point.vrtx_gomtry)))) AND (( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.VERTEX_POINT IN TYPEOF(o\g.g_n)) AND ( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.CARTESIAN_POINT IN TYPEOF(o\g.g_n\vrtx_point.vrtx_gomtry))) ))) = 0))) = 0; WR5 : SIZEOF(QUERY (lp_fbns <* QUERY (bns <* bouns AIC_TOPOLOGICALLY_BOUNDED_SURFACE.EDGE_LOOP IN TYPEOF(bns.boun)) AIC_TOPOLOGICALLY_BOUNDED_SURFACE.ORIENTED_PATH IN TYPEOF(lp_fbns.boun))) = 0; WR6 : (NOT ( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.SWEPT_SURFACE IN TYPEOF(fac_gomtry))) OR (SIZEOF ([ AIC_TOPOLOGICALLY_BOUNDED_SURFACE.LINE, AIC_TOPOLOGICALLY_BOUNDED_SURFACE.CONIC, AIC_TOPOLOGICALLY_BOUNDED_SURFACE.POLYLINE, AIC_TOPOLOGICALLY_BOUNDED_SURFACE.B_SPLINE_CURVE ] * TYPEOF(fac_gomtry\swpt_surfac.swpt_curv)) = 1); WR7 : SIZEOF(QUERY (vlp_fbns <* QUERY (bns <* bouns AIC_TOPOLOGICALLY_BOUNDED_SURFACE.VERTEX_LOOP IN TYPEOF(bns.boun)) NOT(( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.VERTEX_POINT IN TYPEOF(vlp_fbns\fac_boun.boun\vrtx_loop.loop_vrtx)) AND ( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.CARTESIAN_POINT IN TYPEOF(vlp_fbns\fac_boun.boun\vrtx_loop. loop_vrtx\vrtx_point.vrtx_gomtry)) ))) = 0; WR8 : SIZEOF (QUERY (bn <* bouns NOT (SIZEOF([ AIC_TOPOLOGICALLY_BOUNDED_SURFACE.EDGE_LOOP, AIC_TOPOLOGICALLY_BOUNDED_SURFACE.VERTEX_LOOP ] * ciso 2001 Allrightsrsrv 9

16 TYPEOF(bn.boun)) = 1))) = 0; WR9 : SIZEOF(QUERY (lp_fbns <* QUERY (bns <* bouns AIC_TOPOLOGICALLY_BOUNDED_SURFACE.EDGE_LOOP IN TYPEOF(bns.boun)) NOT (SIZEOF (QUERY (o <* lp_fbns.boun\path.g_list ( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.SURFACE_CURVE IN TYPEOF(o\orint_g.g_lmnt\g_curv.g_gomtry)) AND (NOT (SIZEOF (QUERY (sc_ag <* o.g_lmnt\g_curv.g_gomtry\ surfac_curv.associat_gomtry NOT ( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.PCURVE IN TYPEOF(sc_ag)))) = 0)))) = 0))) = 0; WR10 : ((NOT ( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.SWEPT_SURFACE IN TYPEOF(fac_gomtry))) OR ((NOT ( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.POLYLINE IN TYPEOF(fac_gomtry\swpt_surfac.swpt_curv))) OR (SIZEOF(fac_gomtry\swpt_surfac.swpt_curv\polylin.points) >= 3))) AND (SIZEOF (QUERY (lp_fbns <* QUERY (bns <* bouns AIC_TOPOLOGICALLY_BOUNDED_SURFACE.EDGE_LOOP IN TYPEOF(bns.boun)) NOT (SIZEOF (QUERY (o <* lp_fbns.boun\path.g_list ( AIC_TOPOLOGICALLY_BOUNDED_SURFACE.POLYLINE IN TYPEOF(o\orint_g.g_lmnt\g_curv.g_gomtry)) AND (NOT (SIZEOF (o\orint_g.g_lmnt\ g_curv.g_gomtry\polylin.points) >= 3)))) = 0))) = 0); END_ENTITY; (* Formal propositions: WR1: Th gomtry us in th finition of th fac shall b rstrict. Th fac gomtry shall b an lmntary surfac, swpt surfac, orb splin surfac. WR2: Th gomtry of all bouning gs of th fac shall b fully fin as g curvs. WR3: Th typs of curv us to fin th gomtry of gs shall b rstrict to lins, conics, polylins, surfac curvs, or b splin curvs. WR4: All vrtics us in th fac finition shall b of typ vrtx point with gomtry fin by a cartsian point. WR5: Th us of orint paths in th finition of th g loopsofthavanc fac is prohibit. WR6: If th fac gomtry is of typ swpt surfac thn th swpt curv us in th finition shall b of typ lin, conic, polylin,orb splin curv. WR7: For any vrtx loop us to boun th fac th loop vrtx shall b of typ vrtx point an th gomtry shall b fin by a cartsian point. WR8: Th fac bouns shall b fin by ithr g loopsorvrtx loops. 10 ciso 2001 Allrightsrsrv

17 WR9: If a surfac curv is us as part of a fac boun thn th associat gomtry attribut shall rfrnc pcurvs not surfacs. WR10: If a polylin is us ithr to fin a swpt surfac or as part of a fac boun, it shall contain at last thr points. Informal propositions: IP1: Any instanc of avanc fac which has th gomtry of a complt sphrical surfac shall b bounby a vrtx loop locat at th point whr th z axis of th placmnt coorinat systm lavs th surfac of th sphr, (i. at th North Pol of th sphr). EXPRESS spcification: *) END_SCHEMA; -- n AIC_TOPOLOGICALLY_BOUNDED_SURFACE SCHEMA (* ciso 2001 Allrightsrsrv 11

18 Annx A (normativ) Short nams of ntitis Tabl A.1 provis th short nams of ntitis spcifi in th EXPRESS listing of this part of ISO Rquirmnts on th us of th short nams ar foun in th implmntation mthos inclu in ISO Tabl A.1 Short nams of ntitis Entity nam Short nam ADVANCED FACE ADVFAC 12 ciso 2001 Allrightsrsrv

19 Annx B (normativ) Information objct rgistration B.1 Documnt intification To provi for unambiguous intification of an information objct in an opn systm, th objct intifir f iso stanar part(511) vrsion(1) g is assign to this part of ISO Th maning of this valu is fin in ISO/IEC , an is scrib in ISO B.2 Schma intification To provi for unambiguous intification of th aic topologically boun surfac in an opn information systm, th objct intifir f iso stanar part(511) vrsion(1) objct(1) aic-topologically-boun-sufac(1) g is assign to th aic topologically boun surfac schma (s 4). Th maning of this valu is fin in ISO/IEC , an is scrib in ISO ciso 2001 Allrightsrsrv 13

20 Annx C (informativ) Computr-intrprtabl listings This annx provis a listing of th EXPRESS ntity nams an corrsponing short nams as spcifi in this Part of ISO without commnts or othr xplanatory txt. This annx is availabl in computr-intrprtabl form an can b foun at th following URLs: Short nams: EXPRESS: If thr is ifficulty accssing ths sits contact ISO Cntral Scrtariat or contact th ISO TC 184/SC4 Scrtariat irctly at: sc4sc@cm.nist.gov. NOTE Th information provi in computr-intrprtabl form at th abov URLs is informativ. Th information that is contain in th boy of this part of ISO is normativ. 14 ciso 2001 Allrightsrsrv

21 Annx D (informativ) EXPRESS-G iagrams Figurs D.1 through D.8 corrspon to th EXPRESS gnrat from th short listing givn in claus 4 using th intrfac spcifications of ISO Th iagrams us th EXPRESS-G graphical notation for th EXPRESS languag. EXPRESS-G is fin in annx D of ISO NOTE 1 Th following slct typs ar intrfac into th AIC xpan listing accoring to th implicit intrfac ruls of ISO Ths slct typs ar not us by othr ntitis in this part of ISO gomtric st slct; trimming slct; vctor or irction. NOTE 2 Th ruls on avanc fac xclu th instantiatiation of som ntitis which ar implicitly intrfac an, thrfor, shown in th iagrams. Ths ntitis ar mark with a in th iagrams. ciso 2001 Allrightsrsrv 15

22 2,5 loop 2,6 path 2,1 fac 2,2 fac boun 2,3 vrtx 2,4 g contxt typ 1 rprsntation contxt gomtric rprsntation contxt spac coorinat imnsion contxt intifir nam contxt of itms paramtric rprsntation contxt itms S[1:?] topological rprsntation itm 3,2 placmnt 4,1 curv 3,1 surfac 2,7 g curv 2,8 fac surfac 2,9 vrtx point rprsntation rprsntation itm nam irction ratios L[2:3] coorinats L[1:3] 4,4 finitional rprsntation irction point cartsian point gomtric rprsntation itm 1 vctor or irction 4,5 vctor 1,1 (3,4) 1,2 (2,3) 1,3 (3,4,6,7) 1,4 (6,7) Figur D.1 aic topologically boun surfac EXPRESS-G iagram pag1of8 16 ciso 2001 Allrightsrsrv

23 avanc fac fac gomtry fac surfac 2,8 (1) 3,4 sam sns surfac orint orintation fac 1 fac 2,1 (1) bouns S[1:?] fac outr 2,2 (1) fac boun boun orintation boun loop 2,5 (1) 1 g list orint path L[1:?] g vrtx loop g loop vrtx loop 2,6 (1) 2,3 (1) g start 1 vrtx g g n vrtx point 2,4 (1) 2,9 (1) g curv sam sns 1,2 point vrtx gomtry 4,2 curv orintation g lmnt g gomtry rvrsibl topology rvrsibl topology itm 2,7 (1) Figur D.2 aic topologically boun surfac EXPRESS-G iagram pag2of8 ciso 2001 Allrightsrsrv 17

24 gomtric st slct 3,1 (1) 1,2 point 3,4 (2,8) surfac 1 4,5 vctor 4,2 curv xtrusion axis swpt curv surfac of linar xtrusion 1,1 irction swpt surfac 1 axis (DER) z surfac of rvolution axis position axis1 placmnt pl[3:3](der) 5,1 lmntary surfac axis rf irction 3,2 (1) placmnt location axis 2 placmnt 3 boun surfac 1,3 cartsian point 3,3 (4,5) rf irction 7,1 b splin surfac axis 2 placmnt 2 trimming slct 3,5 (4) pl[2:2](der) Figur D.3 aic topologically boun surfac EXPRESS-G iagram pag3of8 18 ciso 2001 Allrightsrsrv

25 circl boun curv 1 polylin points LIST[2:?] 1,3 cartsian point finitional rprsntation 4,4 (1) 8,1 6,1 surfac lin b splin curv curv 8,2 ir composit curv vctor 4,3 (8) orintation magnitu 1,1 irction pcurv llips conic raius smi axis 1 smi axis 2 basis surfac 3,4 surfac rfrnc to curv 4,2 (2,3,8) curv 1 position parabola 4,1 (1) axis2 placmnt focal ist ISO :2001(E) pnt 1,3 cartsian point 4,5 (3) 3,3 axis2 placmnt 3 3,5 axis2 placmnt 2 smi axis hyprbola smi imag axis Figur D.4 aic topologically boun surfac EXPRESS-G iagram pag4of8 ciso 2001 Allrightsrsrv 19

26 5,1 (3) lmntary surfac position 3,3 axis2 placmnt 3 1 plan conical surfac sphrical surfac cylinrical surfac toroial surfac smi angl raius raius raius slct outr major raius gnrat toroial surfac minor raius Figur D.5 aic topologically boun surfac EXPRESS-G iagram pag5of8 20 ciso 2001 Allrightsrsrv

27 clos curv gr (DER) uppr inx on control points (u) slf intrsct wights ata L[2:?] (DER) wights L[0:u] 6,1 (4) b splin curv rational b splin curv curv form control points list L[2:?] (DER) control points A[0:u] b splin curv form 1,3 cartsian point 1,4 cartsian point multiplicitis knot L[2:?] b splin curv with knots uniform curv 1 quasi uniform curv bzir curv uppr inx on knots (DER) knots L[2:?] knot spc knot typ Figur D.6 aic topologically boun surfac EXPRESS-G iagram pag6of8 ciso 2001 Allrightsrsrv 21

28 u clos v clos slf intrsct (DER) u uppr (DER) v uppr wights ata L[2:?] OF L[2:?] (DER) wights A[0:u uppr] OF A[0:v uppr] 7,1 (3) rational b splin surfac 1,3 cartsian point control points list L[2:?] OF L[2:?] b splin surfac 1,4 cartsian point surfac form u gr v gr control points A[0:u uppr] OF A[0:v uppr] (DER) b splin surfac form knot u uppr (DER) knot v uppr (DER) b splin surfac with knots u multiplicitis L[2:?] u knots L[2:?] v knots L[2:?] v multiplicitis L[2:?] knot typ uniform surfac knot spc 1 quasi uniform surfac bzir surfac Figur D.7 aic topologically boun surfac EXPRESS-G iagram pag7of8 22 ciso 2001 Allrightsrsrv

29 slf intrsct 8,2 (4) composit curv * composit * curv on surfac sgmnts L[1:?] (DER) basis surfac S[0:2] 3,4 surfac foun itm sam sns composit * curv sgmnt parnt curv curv 4,2 4,2 curv associat gomtry L[1:2] 4,3 pcurv pcurv or surfac transition curv 3 surfac * transition co 8,1 (4) surfac curv (DER) basis surfac S[1:2] prfrr surfac curv rprsntation * not: xclu by rul on avanc fac mastr rprsntation 3,4 surfac Figur D.8 aic topologically boun surfac EXPRESS-G iagram pag8of8 ciso 2001 Allrightsrsrv 23

30 Inx avanc fac: finition :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::4 avanc fac AIC iagrams :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::17 AIC EXPRESS short listing ntity ::::::::::::::::::::::::::::::::::::::::::::::::::::::::9 AIC short listing - topologically boun surfac :::::::::::::::::::::::::::::::::::::::::::::::4 AIC: finition ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::3 sculptur surfac: finition :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::4 swpt surfac: finition :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::4 twist curv: finition :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::4 24 ciso 2001 Allrightsrsrv

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32 ICS Pric bas on 24 pags ISO 2001 All rights rsrv