IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?INOEOOO I?IAEAI IAOEIIAOAeOAAIIss ?I.A.I.I?AeAI?IIAI

Neni?aa THe?y Aiaoie??aia

OAeE
519.6:514.1

IAOAIAOE*IA IIAeAEUe OA IAOIAe ?ICA’ssCAIIss

IIOEI?CAOe?EII? CAAeA*? ?ICI?UAIIss I?AAEEUeIEO IIIAIEOOIEE?A

C O?AOOAAIIssI IIOEAIE II*AOEIAEO AeAIEO

01.05.02 ( iaoaiaoe/ia iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee

Aaoi?aoa?ao aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Oa?e?a ( 1998

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia o Oa?e?anueeiio aea?aeaaiiio oaoi?/iiio oi?aa?neoao?
?aae?iaeaeo?ii?ee, I?i?noa?noai ina?oe Oe?a?ie

Iaoeiaee ea??aiee: /eai-ei?aniiiaeaio IAI Oe?a?ie, aeieoi? oaoi?/ieo
iaoe, i?ioani?

Noiyi TH??e A?eai?iae/,
?inoeooo i?iaeai iaoeiiaoaeoaaiiy

?i.A.I.I?aeai?iiai IAI Oe?a?ie,
caa?aeoaa/ a?aeae?eo iaoaiaoe/iiai

iiaeaethaaiiy oa iioeiaeueiiai
i?iaeooaaiiy

Io?oe?ei? iiiiaioe:

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? sseiaeaa Na?a?e
Anaaieiaeiae/, Oi?aa?neoao aioo??oi?o ni?aa IAN Oe?a?ie, ia/aeueiee
oaeoeueoaoo oi?aae?iiy oa ?ioi?iaoeee;

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe ?ana?aa Ethaeieea A?eai???aia,
Iieoaanueeee aea?aeaaiee oaoi?/iee oi?aa?neoao ?i. TH.Eiiae?aothea,
noa?oee aeeeaaea/ eaoaae?e aeui? iaoaiaoeee

I?ia?aeia onoaiiaa:

Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao, eaoaae?a ia/enethaaeueii?
iaoaiaoeee oa iaoaiaoe/ii? e?aa?iaoeee, I?i?noa?noai ina?oe Oe?a?ie,
i.Aei?i?iiao?ianuee

Caoeno a?aeaoaeaoueny 25 aa?aciy 1999 ?. i 16 aiaeei? ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.180.01 a ?inoeooo? i?iaeai
iaoeiiaoaeoaaiiiy ?i. A.I.I?aeai?iiai IAI Oe?a?ie ca aae?anith: 310046,
Oa?e?a-46, aoe. Aei.Iiaea?nueeiai, 2/10.

C aeena?oaoe??th iiaeia iciaeiieoeny o a?ae?ioaoe? ?inoeoooo i?iaeai
iaoeiiaoaeoaaiiy ?i. A.I.I?aeai?iiai IAI Oe?a?ie ca aae?anith: 310046,
Oa?e?a, aoe. Aei.Iiaea?nueeiai, 2/10.

Aaoi?aoa?ao ?ic?neaiee 22 ethoiai 1999 ?.

A/aiee nae?aoa? niaoe?ae?ciaaii? a/aii? ?aaee

eaiaeeaeao oaoi?/ieo iaoe
Caeoeaa A.I.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Aeena?oaoe?eia ?iaioa ? iaia?a?aiei i?iaeiaaeaiiyi
aeine?aeaeaiue caaea/ aaiiao?e/iiai i?iaeooaaiiy ( caaea/, iia’ycaieo c
ia?aoai?thaaiiyi aaiiao?e/ii? ?ioi?iaoe??. Aei aeaiiai eeano
a?aeiinyoueny, cie?aia, caaea/? iioeiaeueiiai ?ici?uaiiy aaiiao?e/ieo
ia’?eo?a, ui aeieeathoue i?e ?ice?i? iaoa??ae?a, i?iaeooaaii?
?aae?iaeaeo?iiieo ieao, oaoi?/ieo nenoai, ?ic?iaoe? ieai?a i?iieneiaeo
i?aei?e?inoa, ?ici?uaii? iaeaaeiaiiy, aaioaae?a, oiui.

?ioa?an aei caaea/ ?ici?uaiiy aecia/a?oueny, c iaeiiai aieo, aeoaea
oe?ieei niaeo?ii i?aeoe/ieo canoinoaaiue, a c ?ioiai ( neeaaei?noth oa
iao?ea?aeuei?noth iiaoaeiae iaoaiaoe/ieo iiaeaeae, iaiao?aeieo aeey ?o
aaeaeaaoiiai iieno.

Iiiaeeii?noue ii/aoeiaeo aeaieo, ye? aeeth/athoue ?ioi?iaoe?th i?i
oi?io, ?ici??e aaiiao?e/ieo ia’?eo?a, oaoiieia?/i? iaiaaeaiiy oa
ooieoe?th oe?e?, ii?iaeaeothoue aaeeeo e?euee?noue iioei?caoe?eieo
caaea/ ?ici?uaiiy. Aea iacaaaeath/e ia ??ciiiai?oi?noue oeeo caaea/, an?
aiie iiaeooue aooe noi?ioeueiaai? oaeei /eiii: iaiao?aeii ?ici?noeoe
aeai? aaiiao?e/i? ia’?eoe o aeai?e iaeano? c o?aooaaiiyi oaoiieia?/ieo
iaiaaeaiue oae, uia ooieoe?y oe?e? aeinyaaea aeno?aiaeueiiai cia/aiiy.

Aei inoaiiueiai /ano ?ica’ycaiiy caaea/ iioeiaeueiiai ?ici?uaiiy aoei
ci???ioiaaii, a iniiaiiio, ia aeei?enoaiiy ?aeaae?ciaaieo iaoaiaoe/ieo
iiaeaeae iaoa??aeueieo ia’?eo?a oa ?o aca?iiae?e, eiee iioeaee caaeaiiy
ii/aoeiaeo aeaieo ia a?aoiaothoueny. A aiane?aeie oiai, ui iiaa eaea i?i
iioei?caoe?ei? caaea/?, aeieea? i?iaeaia oi/iino?, no?eeino? oa
a??ia?aeiino? io?eio?ieo ?acoeueoao?a.

Iio?aaa o ae??oaii? cacia/aii? i?iaeaie ii?iaeeea iaiao?aei?noue
noai?aiiy iiaiai iaoaiaoe/iiai aia?aoo. ?i noaei caii/aoeiaaia o 1992
?ioe? /eaiii-ei?aniiiaeaioii IAI Oe?a?ie TH.A.Noiyiii iiaa canoinoaaiiy
?ioa?aaeueiiai aiae?co a aaiiao?e/iiio i?iaeooaaii? ( ?ioa?aaeueia
aaiiao??y.

Aeaia aeena?oaoe?y i?enay/aia i?eeeaaeaiith aeaiaio?a oe??? iiai?
oai??? aei ?ica’ycaiiy iioei?caoe?eii? caaea/? ?ici?uaiiy i?aaeeueieo
i???ioiaaieo iiiaieooiee?a c o?aooaaiiyi iioeaie ii/aoeiaeo aeaieo.

?iaioa aeeiiaia o a?aeiia?aeiino? c oaiaoeeith oa caaaeueiei ieaiii
aeine?aeaeaiue, ui i?iaiaeeeenue ia eaoaae?? i?eeeaaeii? iaoaiaoeee
Oa?e?anueeiai aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo ?aae?iaeaeo?ii?ee ? o
a?aeae?e? iaoaiaoe/iiai iiaeaethaaiiy oa iioeiaeueiiai i?iaeooaaiiy
?inoeoooo i?iaeai iaoeiiaoaeoaaiiy ?i. A.I.I?aeai?iiai IAI Oe?a?ie a
ia??iae 1992(1998 ??.

Iaoith aeena?oaoe?eii? ?iaioe ? iiaoaeiaa iaoaiaoe/ii? iiaeae?
iioei?caoe?eii? caaea/? ?ici?uaiiy i?aaeeueieo i???ioiaaieo
iiiaieooiee?a c o?aooaaiiyi iioeaie ii/aoeiaeo

aeaieo oa ?ic?iaea iaoiaea ?? ?ica’ycaiiy.

Iniiai? caaea/? aeine?aeaeaiiy aeeth/athoue:

( iinoaiiaeo iioei?caoe?eii? caaea/? ?ici?uaiiy i?aaeeueieo i???ioiaaieo
iiiaieooiee?a o iai?aiane?i/aii?e nioc? (ui iaaeae?, aeey nei?i/aiiy,
iaceaa?oueny nioaith) c o?aooaaiiyi iioeaie ii/aoeiaeo aeaieo;

( iiaoaeiao iaoaiaoe/ii? iiaeae? cacia/aii? caaea/? a ?ioa?aaeueiiio
aeaeyae? (iaaeae? ( ?ioa?aaeueii? iaoaiaoe/ii? iiaeae?) c aeei?enoaiiyi
aeaiaio?a ?ioa?aaeueii? aaiiao???;

( iiaeaiiy ?ioa?aaeueii? iaoaiaoe/ii? iiaeae? a a?eoiaoe/iiio
aaee?aeiaiio i?inoi??;

( ?ic?iaeo iaoiaeo ?ica’ycaiiy iinoaaeaii? caaea/? ia aac? iaoiae?a,
i?ecia/aieo aeey ?ica’ycaiiy caaea/ aaiiao?e/iiai i?iaeooaaiiy;

( noai?aiiy eiiieaeno i?ia?ai, ui ?aae?cothoue iaoiae ?ica’ycaiiy.

Iaoeiaa iiaecia ?acoeueoao?a aeena?oaoe?eii? ?iaioe:

( iaoaiaoe/ia iiaeaeue iioei?caoe?eii? caaea/? ?ici?uaiiy i?aaeeueieo
iiiaieooiee?a o nioc?, ui iiaoaeiaaia ia iniia? iiiyoue ?ioa?aaeueii?
aaiiao???, iaaea? iiaeeea?noue ?aoe?iiaeueiei /eiii a?aoiaoaaoe iioeaee
ii/aoeiaeo aeaieo (ia iia’ycai? c ia/enethaaeueieie i?ioeanaie);

( cai?iiiiiaaia iiaeaiiy ?ioa?aaeueii? iaoaiaoe/ii? iiaeae? a
a?eoiaoe/iiio aaee?aeiaiio i?inoi?? aeicaiey? aiaeii/an a?aoiaoaaoe
iioeaee ii/aoeiaeo aeaieo ? canoiniaoaaoe aeia?a a?aeii? iaoiaee
iioei?caoe?? oa aaiiao?e/iiai i?iaeooaaiiy;

( aeine?aeaeai? aeanoeaino? iiaoaeiaaii? iaoaiaoe/ii? iiaeae? o aeaeyae?
aeiaaaeaieo oai?ai iaaeathoue iiaeeea?noue aeei?enoaoe aeey ?ica’ycaiiy
iinoaaeaii? caaea/? iaoiaee iiiaie?eoa??aeueii? iioei?caoe?? oa iaoiae
a?eie ? iaae;

( ?ic?iaeai? aoaeoeai? i?aaeea a?aen?eaiiy aacia?niaeoeaieo aa?oei
aea?aaa ?ica’yce?a caaea/? oa aeiaaaeai? oai?aie i?i aeno?aiaeuei?
aeanoeaino? e?i?eiie ooieoe?? oe?e? ia iaeano? i?eionoeieo ?ica’yce?a
aeicaiey? iiaeeo?eoaaoe iaoiae a?eie ? iaae.

I?aeoe/ia cia/aiiy io?eiaieo ?acoeueoao?a iieyaa? a ?ic?iaoe? oa
?aae?caoe?? ia IAII eiiieaeno i?ia?ai aeey ?ica’ycaiiy iioei?caoe?eii?
caaea/? ?ici?uaiiy i?aaeeueieo i???ioiaaieo iiiaieooiee?a c o?aooaaiiyi
iioeaie ii/aoeiaeo aeaieo. Noai?aiee i?ia?aiiee eiiieaen «Regular
interval polygons» (RIP) iiaea aooe aaciina?aaeiuei cacoiniaaiee i?e
i?iaeooaaii? aoae?aaeueieo ia’?eo?a, o?ainii?oieo cania?a,
?aae?iaeaeo?iiieo ieao, i?e ?ica’ycaii? i?iaeaie ?aoe?iiaeueiiai
?ici?uaiiy iaeaaeiaiiy o oeaoao oa aeiiii?/iiio ieaioaaii?.
Eiiieaen RIP iiaea oaeiae aeei?enoiaoaaoeny i?e ?ic?iaoe? noai
ia??cee iaoaeo o iaoeiiaoaeoaaii?, i?e ?ice?i? oeaiei oa oe??
a?aeiia?aeii o oaeno?euei?e oa acooo?a?e i?iieneiainoyo, ui aeicaiey?
a?aoiaoaaoe iioeaee ii/aoeiaeo aeaieo, i?aeaeuoaaoe aoaeoeai?noue
aeei?enoaiiy ??cieo iaoa??ae?a, a oaeiae nei?i/oaaoe /an ae??oaiiy
cacia/aiieo caaea/.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? ?acoeueoaoe
aeine?aeaeaiue aeiiia?aeaeenue:

( ia nai?ia?? iaoeiai? ?aaee IAI Oe?a?ie c i?iaeaie «E?aa?iaoeea»
«Iaoaiaoe/i? iaoiaee aaiiao?e/iiai i?iaeooaaiiy» (i.Oa?e?a, 1994 ?.);

( ia nai?ia?ao a?aeae?eo iaoaiaoe/iiai iiaeaethaaiiy oa iioeiaeueiiai
i?iaeooaaiiy ?inoeoooo i?iaeai iaoeiiaoaeoaaiiy IAI Oe?a?ie (i.Oa?e?a,
1996, 1998 ??.);

( ia nai?ia?? «Iaoaiaoe/i? iiaeae? oa iaoiaee iioei?caoe?? nenoai c
aeene?aoieie aeaea?aeaie o?ce/ieo iie?a» eaoaae?e i?ia?aiiiai
caaacia/aiiy ia/enethaaeueii? oaoi?ee AEeoiie?nueeiai
?iaeaia?ii-oaoiieia?/iiai ?inoeoooo (i.AEeoiie?, 1998 ?.);

( ia nai?ia?? eaoaae?e i?eeeaaeii? iaoaiaoeee Oa?e?anueeiai aea?aeaaiiai
oaoi?/iiai oi?aa?neoaoo ?aae?iaeaeo?ii?ee (i.Oa?e?a, 1998 ?.);

( ia nai?ia?? iaoeiai? ?aaee IAI Oe?a?ie c i?iaeaie «E?aa?iaoeea»
«Nenoaiiee aiae?c, iaoaiaoe/ia iiaeaethaaiiy ? i?eeiyooy ??oaiue o
nioe?aeueii-aeiiii?/ieo oa oaoi?/ieo nenoaiao» (i.Oa?e?a, 1998 ?.).

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?? aeeeaaeaii o 4 noaooyo.

Iniaenoee aianie aeena?oaioa a ?iaioe, iioae?eiaai? o ni?aaaoi?noa? ?
oaeei. A noaoo? [1] aaoi? cae?eniea iiaoaeiao iaoaiaoe/ii? iiaeae?
caaea/? ?ici?uaiiy i?aaeeueieo i???ioiaaieo iiiaieooiee?a c o?aooaaiiyi
iioeaie ii/aoeiaeo aeaieo a ?ioa?aaeueiiio aeaeyae?. A ioae?eaoe?? [3]
aeena?oaioii cai?iiiiiaaiee oa iaa?oioiaaiee iaoiae ?ica’ycaiiy
cacia/aii? caaea/? ye aeaie?eoa??aeueii? caaea/? i?i?i?caoe??, iaaaaeai?
?acoeueoaoe aenia?eiaio?a.

No?oeoo?a oa ianya aeena?oaoe??. Aeena?oaoe?y neeaaea?oueny c? anooio,
i’yoe ?icae?e?a, aeniiae?a oa nieneo aeei?enoaieo aeaea?ae. Iiaiee ianya
aeena?oaoe?? noaiiaeoue 117 noi??iie, na?aae ieo 101 noi??iea oaenoo, 23
?enoiee, 4 oaaeeoe? oa 206 iaeiaioaaiue e?oa?aoo?e.

INIIAIEE CI?NO ?IAIOE

O ia?oiio ?icae?e? c?iaeaii iaeyae e?oa?aoo?e, i?enay/aii? caaea/ai
aaiiao?e/iiai i?iaeooaaiiy, cie?aia, ?ia?o, ni?yiiaaieo ia ?ica’ycaiiy
aeaiaei??ieo iioei?caoe?eieo caaea/ ?ici?uaiiy. Aeine?aeaeaiiyi
oeueiai eeano caaea/ caeiaeeny ? caeiathoueny aaaaoi a/aieo, o oiio
/ene? ?aa/ia A.E., Noiyi TH.A., A?eue I.?., Eiiye A.I., sseiaeaa
N.A., Niaeyeia N.A., Iiaiaeeeiaa I.A., Sweeney P.E., Dyckhoff H.,
Dowsland K.A., Beasley J.E., Li Zh., Milenkovic V. oa ?i. Ooo oaeiae
iaaaaeaii ia?ae?e iniiaeo ioae?eaoe?e c ?ioa?aaeueiiai aiae?co, ui
i?noeoue ?iaioe, i?enay/ai? iiaoaeia? ?ioa?aaeueieo a?eoiaoee (Moore
R.E., Kaucher E., Markov S.M., Sendov B., Ianoa?ia A.I., Cthc?i A.N. oa
?i.), aeine?aeaeaiith ?ioa?aaeueieo iao?eoeue (Kulisch U., Hansen
E., Alefeld G., Herzberger J. oa ?i.), iaoiaeai ?ica’ycaiiy nenoai
e?i?eieo oa iae?i?eieo ?ioa?aaeueieo ??aiyiue (Rohn J.,

Hansen E., Rump S.M., Neumaier A., Krawczyk R., Moore R.E.,
Eaeieeia N.A., Oa?ee

N.I., Eaea?a A.A. oa ?i.), ia/eneaiith ?ioa?aaeueieo ?ioaa?ae?a oa
iio?aeieo (Ratschek H., Schroder G., Nickel K., Moore R.E. oa ?i.) ?
o.?i. Iaaeaii ei?ioeo aiioaoe?th ioae?eaoe?e Noiyia TH.A. c aeeeaaeaiiyi
iniia iiaiai canoinoaaiiy ?ioa?aaeueiiai aiae?co a aaiiao?e/iiio
i?iaeooaaii? ( ?ioa?aaeueii? aaiiao???, a oaeiae aeacai? ?iaioe
?iiaiiai? O.?. oa ?ana?ai? E.A. c i?eeeaaeaiiy aeaiaio?a oe??? oai???
aei ?ica’ycaiiy iioei?caoe?eieo caaea/ ?ici?uaiiy c o?aooaaiiyi iioeaie
ii/aoeiaeo aeaieo. E??i oiai, iaa?oioiaaiee aea?? iai?yieo
aeine?aeaeaiue.

O ae?oaiio ?icae?e? cae?eniaii iinoaiiaeo caaea/? ?ici?uaiiy
i?aaeeueieo i???ioiaaieo iiiaieooiee?a o nioc? c o?aooaaiiyi iioeaie
ii/aoeiaeo aeaieo; iaaaaeai? icia/aiiy oa aiae?oe/iee iien ?ioa?aaeueii?
nioae e i?aaeeueiiai ?ioa?aaeueiiai iiiaieooieea.

Aeeeaaeaii iniiai? iieiaeaiiy ae?oaiai ?icae?eo aeieeaaei?oa.

?icaeyaea?oueny iioei?caoe?eia caaea/a ?ici?uaiiy a oae?e iinoaiiaoe?.

aoea i?i?iaeueiith.

Ca iaoaiaoe/i? iiaeae? aaiiao?e/ieo ia’?eo?a, ui iathoue ci?ii?
iao?e/i? oa?aeoa?enoeee, ye? ii?iaeaeothoueny iioeaeaie ii/aoeiaeo
aeaieo, iae?athoueny ?ioa?aaeuei? iiiaeeie, eio?? ?icaeyaeathoueny ye
oi/eia? iiiaeeie ?ioa?aaeueieo i?inoi??a.

,

} oaeei /eiii:

.

Ia iniia? iiiyooy iioeeiai ?ioa?aaeueiiai m-eooieea aaaaeaii ianooiia
icia/aiiy.

nenoaie ?ioa?aaeueieo ia??aiinoae

aea

;

,

a?aeiia?aeii aecia/athoue i?aaeeuei? m-eooieee.

Aeei?enoiaoth/e icia/aiiy ?ioa?aaeueiiai i?yiieooieea, i?aaeeueiiai
?ioa?aaeueiiai m-eooieea oa a?aoiaoth/e ii/aoeia? aeai? iinoaaeaii?
caaea/?, ?ioa?aaeueio nioao ( iiaeia iienaoe ye

( = int ( ( fr (,
(1)

aea

( ye

, (2)

aea

;

,

int (() ( aioo??oi?noue iiiaeeie ((), fr (() ( ?ioa?aaeueia iaaea
iiiaeeie (().

.

O o?aoueiio ?icae?e? iiaoaeiaaii ?ioa?aaeueio iaoaiaoe/io iiaeaeue
iioei?caoe?eii? caaea/? ?ici?uaiiy i?aaeeueieo i???ioiaaieo
iiiaieooiee?a o nioc? c o?aooaaiiyi iioeaie ii/aoeiaeo aeaieo;
cae?eniaii iiaeaiiy ?ioa?aaeueii? iaoaiaoe/ii? iiaeae? caaea/? a
a?eoiaoe/iiio aaee?aeiaiio i?inoi??, yea aeicaiey?, c iaeiiai aieo,
a?aooaaoe iioeaee ii/aoeiaeo aeaieo, a c ?ioiai ( aeei?enoaoe aeey
?ica’ycaiiy ai?iaiaai? iaoiaee iioei?caoe??.

(2) a ?ioa?aaeuei?e nioc? ( (1) iiaea?ii o aeaeyae? no?oeoo?e e?i?eieo
?ioa?aaeueieo ia??aiinoae

, (3)

( iaa?? ?ioa?aaeueieo ia??aiinoae:

iieno?ii no?oeoo?ith e?i?eieo ?ioa?aaeueieo ia??aiinoae

, (4)

( iaa?? ?ioa?aaeueieo ia??aiinoae aeaeyaeo:

o aeiaaeeo, eiee m ( ia?ia, oa iaa?? ?ioa?aaeueieo ia??aiinoae aeaeyaeo:

,

o aeiaaeeo, eiee m ( iaia?ia;

,

,

,

,

,

,

C o?aooaaiiyi (3), (4) iaoaiaoe/ia iiaeaeue iinoaaeaii? caaea/? ia?
aeaeyae:

, (5)

], (6)

aea

,

.

.

caiaeeoueny aei iaai?o:

:

(8)

:

o aeiaaeeo, eiee m ( iaia?ia,

.

(6) aoaea oaeei:

]. (10)

A?aei?oeii aeaye? iniaeeaino? iiiaeeie ID: ID ( int ID, ID ( cl ID (cl
(() ( caieeaiiy iiiaeeie (() ), ID a caaaeueiiio aeiaaeeo iaca’ycia,
iaiaiaaeaia oa iaiioeea, fr ID (fr (() ( iaaea iiiaeeie (() )
eoneiai-e?i?eia.

. Oiae?, a ?acoeueoao? cacia/aiiai ia?aoiaeo, iaoaiaoe/ia iiaeaeue (5)
iaaoaa? aeaeyaeo:

, (11)

.

, iaoaiaoe/ia iiaeaeue (11) ni?aiaaea? c iaoaiaoe/iith iiaeaeeth
?aeaae?ciaaii? iioei?caoe?eii? caaea/? ?ici?uaiiy i?aaeeueieo
iiiaieooiee?a o nioc?.

O /aoaa?oiio ?icae?e? aeine?aeaeai? aeanoeaino? iaoaiaoe/ii? iiaeae?
iioei?caoe?eii? caaea/? ?ici?uaiiy i?aaeeueieo i???ioiaaieo
iiiaieooiee?a o nioc? c o?aooaaiiyi iioeaie ii/aoeiaeo aeaieo o
aeaeyae? aeiaaaeaieo oai?ai, eio?? iaaeathoue iiaeeea?noue
aeei?enoiaoaaoe aeey ?? ?ica’ycaiiy iaoiaee iiiaie?eoa??aeueii?
iioei?caoe?? oa iaoiae a?eie ? iaae.

Aeey ?ica’ycaiiy aeaie?eoa??aeueii? caaea/? (11) ?icaeyaea?oueny
aeiiii?aeia caaea/a:

inf l.
(12)

(ID

Caaea/a (12) ?ica’yco?oueny iaoiaeii a?eie ? iaae, iiaeeo?eiaaiei aeey
iioei?caoe?eieo caaea/ aaiiao?e/iiai i?iaeooaaiiy.

Ia?aae iiaoaeiaith aea?aaa ?ica’yce?a aaaaeai? ianooii? icia/aiiy.

iaceaa?oueny inaaaeiiiiaia?aiiith iiiaeeiith aei??iino? s, yeui aiia
caaea?oueny aeia?eueiith no?oeoo?ith (* e?i?eieo ia??aiinoae (na?aae
yeeo iiaeooue aooe ye no?ia?, oae ? iano?ia? ia??aiino?).

Iicia/eii /a?ac T* iaa?? ??aiyiue, eio?? a?aeiia?aeathoue an?i
ia??aiinoyi no?oeoo?e (*.

, yeui ?? eii?aeeiaoe ? ?ica’yceii nenoaie ia iaio ye s ??aiyiue iaai?a
T*, na?aae yeeo s e?i?eii iacaeaaeieo.

.

Oai?aia 2. Ooieoe?y oe?e? l caaea/? (12) aeinyaa? naiai aeiaaeueiiai
i?i?ioio a inaaaeiaa?oei? iiiaeeie ID.

C o?aooaaiiyi oai?aie 2 a (12) inf iiaeia cai?ieoe ia min:

min l.
(13)

(ID

+8n) ( iaa?? ??aiyiue, ye? a?aeiia?aeathoue ia??aiinoyi, ui aa?ooue
o/anoue a iien? ID (10). Aeey ?ica’ycaiiy caaea/? (13) aeei?enoiao?oueny
no?aoaa?y iiaoaeiae nenoai ??aiyiue ?c iaai?o O, eio?? iienothoue an?
inaaaeiaa?oeie iaeano? ID.

No?oeoo?a aea?aaa ?ica’yce?a ia? aeayeo niaoeeo?eo, coiiaeaio
iniaeeainoyie ??aiyiue, ui aoiaeyoue aei iaai?o O. A naia, ye
aeaeii c (7) ( (9), ??aiyiiy, eio?? i?noyoue ci?ii?

, aei?noei ca’ycai?

i?ae niaith, ooai?thth/e nenoaie. A?aoiaoth/e oea, aeai?eoi iiaoaeiae
aea?aaa ?ica’yce?a iieno?oueny oaeei /eiii.

c iaioeueiaeie eiao?oe??ioaie a?aeiia?aeii, yeui ? ( ia?ia.

c iaioeueiaeie eiao?oe??ioaie a?aeiia?aeii.

E?euee?noue nenoai ??aiyiue, iiaoaeiaaieo ia (2n+1)-iio ??ai? aea?aaa
?ica’yce?a, aei??aith? aaee/ei?

Aeey nei?i/aiiy e?eueeino? nenoai ??aiyiue, ye? iaiao?aeii ?ica’ycoaaoe
ia inoaiiueiio ??ai? (a oaeiae ia a?eueo aenieeo ??aiyo), cai?iiiiiaaiee
iaa?? i?aaee a?aen?eaiiy aacia?niaeoeaieo aa?oei aea?aaa ?ica’yce?a.

Iiaa?oath/enue aei caaea/? (11), aaiaeeii oae? iicia/aiiy:

= min l ;
(14)

(ID

;

(ID

= min l ,

(ID*

}.

?icaeyaea?oueny caaea/a:

; (15)

(ID’

(ID( l ( l’},

].

] aoa ?aeeiei c oi/i?noth aei aea?aaeaioiino? (a cia/eoue, ?
aoaeoeaiei), aeinoaoiuei aeeiiaiiy oaei? oiiae: iiiaeeia

(w ( g }, (16)

aea

( ID},

, i =1,2,

iiaeiia aooe iioeeith.

. Iiiaeeia cl ID iieno?oueny no?oeoo?ith e?i?eieo ia??aiinoae

, (17)

aea

;

; (18)

( ( neiao?e/ia iao?eoey aei??iino? v ( v, i?e/iio

, (=(+1,…,k,

a an? ?io? aeaiaioe iao?eoe? ( aei??aiththoue 1.

Eiao?oe??ioe, ui aoiaeyoue aei ia?oeo 4n ia??aiinoae iaai?o (18),
ia/eneththoueny ca oi?ioeaie:

= 1,

,

.

Aeae?, yeui ?iaeaene (, (, ( iia’ycai? ni?aa?aeiioaiiyi:

,

oi

aea

( = k(( ( 1) + (, ( = ( ( n(( ( 1) + 0,5((( + 1).

Ia?aoo?,

.

a (18), e??i iienaieo aeua, aei??aiththoue 0.

, aai iienoaaoeny no?oeoo?ith e?i?eieo ia??aiinoae

,

aea

.

, aai iai?aieiueiith a i?e.

)=(.

Oai?aia 4. Iiiaeeia W* (16) iioeea.

. Oiae? iaeanoue i?eionoeieo ?ica’yce?a caaea/? (15) iaaoaa? aeaeyaeo:

}.

. Oiio

}.

Oaeei /eiii, ?ica’ycaiiy caaea/?

)

(ID

caiaeeoueny aei ?ica’ycaiiy caaea/?

(ID

aecia/a?oueny ca?aeii c (14).

A i’yoiio ?icae?e? iaaaaeai? ?acoeueoaoe oanoiaeo i?eeeaae?a ?iaioe
i?ia?aiiiai eiiieaeno «Regular interval polygons», yeee ?aae?co? iiooe
iioeiaeueiiai ?ica’yceo iinoaaeaii? caaea/? iiaeeo?eiaaiei iaoiaeii
a?eie ? iaae, a oaeiae iiooe ?? iaaeeaeaiiai ?ica’yceo iaoiaeii
iine?aeiaii-iiiaeeiieiai ?ici?uaiiy c ianooiiei ia?aai?ii. C iaoith
i?iaaaeaiiy ii??aiyeueiiai aiae?co caeiaooeo ?acoeueoao?a aeey oeo
naieo oanoiaeo i?eeeaae?a ciaeaeai? iioeiaeuei? ?ica’ycee ?aeaae?ciaaii?
iioei?caoe?eii? caaea/? ?ici?uaiiy i?aaeeueieo iiiaieooiee?a, oi/i?
ieaei? oa aa?oi? ioe?iee iioeiaeueiiai ?ica’yceo iinoaaeaii? caaea/?.

INIIAI? AENIIAEE II ?IAIO?

1. Iiaoaeiaaia ?ioa?aaeueia iaoaiaoe/ia iiaeaeue iioei?caoe?eii? caaea/?
?ici?uaiiy i?aaeeueieo i???ioiaaieo iiiaieooiee?a o nioc? c o?aooaaiiyi
iioeaie ii/aoeiaeo aeaieo.

2. Cae?eniaia iiaeaiiy ?ioa?aaeueii? iaoaiaoe/ii? iiaeae? caaea/? a
a?eoiaoe/iiio aaee?aeiaiio i?inoi??.

3. Aeine?aeaeai? aeanoeaino? io?eiaii? iaoaiaoe/ii? iiaeae? o aeaeyae?
aeiaaaeaieo oai?ai, eio?? iaaeathoue iiaeeea?noue aeei?enoiaoaaoe aeey
?? ?ica’ycaiiy iaoiaee iiiaie?eoa??aeueii? iioei?caoe?? oa iaoiae a?eie
? iaae.

4. Cai?iiiiiaaia iiaeeo?eaoe?y iaoiaeo a?eie ? iaae aeey
?ica’ycaiiy caaaeaii? caaea/? c? neaey?iith ooieoe??th oe?e?,
iiaoaeiaaii aea?aai ?ica’yce?a oa noi?iiaaiee iaa?? i?aaee a?aen?eaiiy
aacia?niaeoeaieo aa?oei oeueiai aea?aaa.

5. ?ic?iaeaiee i?ia?aiiee eiiieaen «Regular interval polygons», yeee
?aae?co?: iiooe iioeiaeueiiai ?ica’yceo iinoaaeaii? caaea/?
iiaeeo?eiaaiei iaoiaeii a?eie ? iaae; iiooe ?? iaaeeaeaiiai ?ica’yceo
iaoiaeii iine?aeiaii-iiiaeeiieiai ?ici?uaiiy c ianooiiei ia?aai?ii.

Ii??aiyeueiee aiae?c io?eiaieo ?acoeueoao?a iaaea? iiaeeea?noue c?iaeoe
aeniiaie, ui iiaoaeiaaia a aeena?oaoe?ei?e ?iaio? ia iniia? iiiyoue
?ioa?aaeueii? aaiiao??? iaoaiaoe/ia iiaeaeue iioei?caoe?eii? caaea/?
?ici?uaiiy i?aaeeueieo iiiaieooiee?a o nioc? aeicaiey? ?aoe?iiaeueii
a?aooaaoe iioeaee ii/aoeiaeo aeaieo.

IIOAE?EIAAI? I?AOe? CA OAIITH AeENA?OAOe??

1. Noiyi TH.A., ?iiaiiaa O.A., Nuniaaa TH.A. Iaoaiaoe/aneay iiaeaeue
iioeiecaoeeiiiie caaea/e ?aciauaiey i?aaeeueiuo iiiaioaieueieeia n
o/aoii iia?aoiinoae enoiaeiuo aeaiiuo // Aeii. IAI Oe?a?ie.( 1998. ( ?5.
( N.104-111.

2. Nuniaaa TH.A. Iaoaiaoe/aneay iiaeaeue e iaoiae ?aoaiey
iioeiecaoeeiiiie caaea/e ?aciauaiey i?aaeeueiuo iiiaioaieueieeia n
o/aoii iia?aoiinoae enoiaeiuo aeaiiuo // ?aaeeiyeaeo?iieea e
eioi?iaoeea.( 1998. ( ?2. ( N.43-50.

3. Noiyi TH.A., ?iiaiiaa O.A., Nuniaaa TH.A. Iioeiecaoeeiiiay caaea/a
?aciauaiey i?aaeeue-iuo eioa?aaeueiuo iiiaioaieueieeia // Aeii. IAI
Oe?a?ie. ( 1998. ( ?9. ( N.114-120.

4. Iaoaiaoe/aneay iiaeaeue e iaoiae ?aoaiey caaea/e ?aciauaiey
i?aaeeueiuo i?eaioe?iaaiiuo iiiaioaieueieeia a iieina / Nuniaaa TH.A.;
Ei-o i?iae. iaoeiino?. IAI Oe?aeiu. ( Oa?ueeia, 1996. ( 20 n. ( ?on. (
Aeai. a AEIEOE 22.01.96, ?242(A96 // Aiio. a ae. Iaoaiaoeea, ?5, 1996.

Neni?aa TH.A. Iaoaiaoe/ia iiaeaeue oa iaoiae ?ica’ycaiiy
iioei?caoe?eii? caaea/? ?ici?uaiiy i?aaeeueieo iiiaieooiee?a c
o?aooaaiiyi iioeaie ii/aoeiaeo aeaieo. ( ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.05.02 ( iaoaiaoe/ia
iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee. ( ?inoeooo i?iaeai
iaoeiiaoaeoaaiiy ?i. A.I.I?aeai?iiai IAI Oe?a?ie, Oa?e?a, 1998.

Aeena?oaoe?th i?enay/aii ?ica’ycaiith iioei?caoe?eii? caaea/?
?ici?uaiiy i?aaeeueieo iiiaieooiee?a o nioc? c o?aooaaiiyi iioeaie
ii/aoeiaeo aeaieo. C aeei?enoaiiyi aeaiaio?a iiaiai canoinoaaiiy
?ioa?aaeueiiai aiae?co a aaiiao?e/iiio i?iaeooaaii? iiaoaeiaaia
iaoaiaoe/ia iiaeaeue oeacaii? caaea/?. Cai?iiiiiaaiee i?ea?iaeueiee
i?aeo?ae aei ?? ?ica’ycaiiy ia iniia? niieo/aiiy iaoiae?a
iiiaie?eoa??aeueii? iioei?caoe?? oa iiaeeo?eiaaiiai iaoiaeo a?eie ?
iaae. ?ic?iaeaiee i?ia?aiiee eiiieaen, yeee ?aae?co? iiooe iioeiaeueiiai
oa iaaeeaeaiiai ?ica’yce?a caaea/?, ui ?icaeyaea?oueny.

Eeth/ia? neiaa: iaoaiaoe/ia iiaeaethaaiiy, aaiiao?e/ia i?iaeooaaiiy,
?ioa?aaeueiee aiae?c, iioei?caoe?y, ?ici?uaiiy, iaoiae a?eie ? iaae,
iioeaee ii/aoeiaeo aeaieo.

Nuniaaa TH.A. Iaoaiaoe/aneay iiaeaeue e iaoiae ?aoaiey iioeiecaoeeiiiie
caaea/e ?aciauaiey i?aaeeueiuo iiiaioaieueieeia n o/aoii iia?aoiinoae
enoiaeiuo aeaiiuo. ( ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii

niaoeeaeueiinoe 01.05.02 ( iaoaiaoe/aneia iiaeaee?iaaiea e
au/eneeoaeueiua iaoiaeu. ( Einoeooo i?iaeai iaoeiino?iaiey
ei.A.I.Iiaeai?iiai IAI Oe?aeiu, Oa?ueeia, 1998.

Aeenna?oaoeey iinayuaia ?aoaieth iioeiecaoeeiiiie caaea/e ?aciauaiey
i?aaeeueiuo iiiaioaieueieeia a iieina n o/aoii iia?aoiinoae enoiaeiuo
aeaiiuo. N eniieueciaaieai yeaiaioia iiaiai i?eeiaeaiey eioa?aaeueiiai
aiaeeca a aaiiao?e/aneii i?iaeoe?iaaiee iino?iaia iaoaiaoe/aneay
iiaeaeue oeacaiiie caaea/e. I?aaeeiaeai i?eaeiaeueiue iiaeoiae e aa
?aoaieth ia iniiaa ni/aoaiey iaoiaeia iiiaie?eoa?eaeueiie iioeiecaoeee e
iiaeeoeoee?iaaiiiai iaoiaea aaoaae e a?aieoe. ?ac?aaioai i?ia?aiiiue
eiiieaen, ?aaeecothuee iiene iioeiaeueiiai e i?eaeeaeaiiiai ?aoaiee
?anniao?eaaaiie caaea/e.

Eeth/aaua neiaa: iaoaiaoe/aneia iiaeaee?iaaiea, aaiiao?e/aneia
i?iaeoe?iaaiea, eioa?aaeueiue aiaeec, iioeiecaoeey, ?aciauaiea, iaoiae
aaoaae e a?aieoe, iia?aoiinoe enoiaeiuo aeaiiuo.

Sysoyeva Yu.A. Mathematical model and solution method of an
optimization placement problem of regular polygons taking into account
errors of initial data. ( Manuscript.

Thesis for a candidate’s degree (physics and mathematics) by speciality
01.05.02 ( mathematical modelling and numerical methods. ( The Institute
for Problems in Machinery named by A.M.Pidgorny of National Academy of
Science of Ukraine, Kharkov, 1998.

The dissertation is devoted to solving of an optimization placement
problem of regular polygons into the given strip taking into account
errors of initial data. A mathematical model of the problem by using of
elements of the new application of interval analysis in geometrical
design has been built. To solve the problem an original approach based
on a combination of methods of multicriteria optimization and the
modification of the branch and bound algorithm is suggested. The program
complex which realizes searching for the optimal and the approximate
solutions of the problem has been developed.

Key words: mathematical modelling, geometrical design, interval
analysis, optimization, placement, branch and bound algorithm, errors of
initial data.

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