INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING AND TECHNOLOGY (IJARET) AN APPLIED TWO-DIMENSIONAL B-SPLINE MODEL FOR INTERPOLATION OF DATA

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1 INTERNTINL JURNL F DVNCED RESERCH IN ENGINEERING ND TECHNLGY IJRET Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME ISSN 97-8 Pr ISSN le Vole Ie Jl-Deeer. - IEME: Jorl I For :.778 Clled GISI IJRET I E M E N PPLIED TW-DIMENSINL B-SPLINE MDEL FR INTERPLTIN F DT Med Z Cvl Egeerg Dere Fl o Teolog d Egeerg Yo Uver Yo IRN d@l...r BSTRCT Te lerre o e erolo o d le e oe or e roo o d eell or ree deo d. Te ree eod o erolo wo-deol Lgrge wo-deol le d wo-deol el le re veged. I e ree d ew odel w wo-deol B-le ro ee develoed. Te reeed odel e dvge o l d ll w ree o e vole o oero llo d g o-or d o-er d. Tree role were eleed or e eg d verg e odel w e qre rrgee o e d d o-or dro. Te rel de odel le ee d lle or e wo-deol erolo o d. Te odel e geerled or o-reglr d o-or dro o d w rel oded re r or e goverg ler e o eqo. Keword: roo B-le le erolo Lgrge eod I. INTRDUCTIN Te erolo odel re led oderl ll re o egeerg ve. Ele re e evlo o re re d vole o o-or d rreglr oe deero o vole o g llg d ee er wor d egeerg rveg. Vole o re oogr d orolog or ll d vlle. Here erolo e o d odel o w e d o ereore; or L. I roo ro e odel rve doe o eerl ro e d o. Te l eod o erolo re eled del Foel 997 Coll D Kl 5 Noedl d Wrg d Z 9. Te eod or wo-deol

2 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME erolo egeerg lerre re o reqe. Te o or odel re re Lgrge eod B-le eod wo-deol le eod d el wo-deol le eod. Te rodo o e er old el e re o e role revo wor roe d e oro o e er. Te oe o e eo e rovded o derd el o e er.. Lgrge Meod Te Lgrge eod or e e geero o oe-deol Lgrge orlo or wo-deol erolo role Der 99 d Brde d Fr. For role w e o 9 rle d ε { 9} Fgre. Te wo-deol Lgrge eqo ollow L Fg: Sle d dro Te wo-deol Lgrge odel led er o ll. Te degree d order o e Lgrge olol ree e er o d o ree. Tereore rel e ollo d evor o e goverg rve. Hee e Lgrge rve gve g lo d devo ro e rel rve or e o ewee e d or ode. Tereore e odel o lle d ee or ge egeerg d.. B-le roo Meod B-le eod ve ee eeded e 97. Te deged B d or B o e ll e o ro e le. B-le eod re ol ed or rve d re oer gr. Te d d rd degree B-le w re ed eevel or roo o d re le lle or e erolo o d. W oe odo d orreo e B-le odel ell e eod d rd degree e led or erolo o ge d rlrl or oe-deol erolo role. Te d d rd degree B-le olol e ed or roo o orol o L Se d S 5 d Sloo

3 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME P L [ ]{ } B P L ] [ ] [ q q [ ][ ][ ] { } B B T [ ][ ][ ][ ] [ ] { } B Z B T T T Te ove B-le rve wll o ro rog e orol o er e. Te l d erl o q d q o e B-le rve w re o o e oed ro Eq.. Te wo-deol B-le e oed ro e rod o Eq. wo deo [ ]{ } [ ]{ } [ ] T B B 5 Were [ ]. Ug e ler roro ro d o d ; reevel or e or B-le re Fg. e gr eqo rel ollow 7 were d 8

4 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME q Fg: D dro or B-le re ewor o d w orol o P rog P row d ol w or d ree. Fro e ove ewor o - - lol B-le gr or e e oed w ve o le o e elee de. Te l gr w o o lol gr e - - erl o q. I e d o rer o oe erl o o q e l gr wold e wo-deol B-le w oed e erolo eod. Hee e l gr roe ll e d o. For e del o eod e o o erl o o d er oorde reer o Sloo. Te q e deered w ree o vle Eq. 8. [ ] Te erolo wo-deol B-le o ewor d w e d or d reqre ore eqo order o e qee o e goverg e o eqo. However rele o e degree o olol B-le odered. Te ove er eqo old e oed g e odr odo. Te govered ler e o eqo d o odgol e. I ler odel o rl or role vg ge d o.. Two-deol C Sle Meod T eod oed e rod o wo le eqo dreo d Eq g d o l e 9 Were le w dee or e reglr elee d reer. Toe reer re oed g e ollowg o eqo o e orer o e elee. 5

5 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME ± ± g Te ove eqo o o or e elee re wre d oed ogeer o or odgol ler e o eqo. B ddg e goverg odr odo o e ove ler e oleeed o ler e o eqo w qe olo. T eod o olo gve e o log e ode d le o e elee de.. El Two-deol C Sle Meod el wo-deol erolo odel ee develoed Z e lo o e ove wo-deol le eod. He led or ewor o d e reglr dro. Te erolo eqo w leeed odel ollow Te oee o 9 re oed g o o e elee de. Te o o eqo o o or o d eqo o o or e r rl dervve log e d ode o e elee Eq. d. W vg e ove rl dervve e role qe d o o eqo d ow w e olved ell o eer o or ler e o eqo. I o e e rl dervve re o vlle e

6 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME [ ] L ode e reoved or eled g erl dervve roe. Te oee o 9 o Eq. e deered ro e ollowg eqo. Were d re leg d wd o elee ; reevel. For ge e o d w ll e egeerg role e ove odel le d reqre le llo oero w ree o e oer eod o wo-deol erolo. Te ol lo or odel deerg e rl dervve w ree o d e ode d e old e roed e goverg eod. II. MDEL FRMULTIN Te odel e geero o B-le eod wo deol ereore; eer o el re revew o e oe-deol B-le.. e-deol B-le T odel eled ore del Slo d rel ded. Te B-le rve o o ere o B-le o re lerl deede do [ ] 5 were ] [ / / d e er o elee. E B- le o o o or olol o Eq..

7 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME oerwe Te ollowg eqo led or B-le o or reg ll d o orderr Z 9. e e 7 Were d. 78. Fg. ow e B-le o or Eq. 7. Fg: B-le o I order o rooe e r d ee o B-le eod wo o d re dded o Eq. 5 or ddg e ee o odr odo. Te oee d e lled w ree o e B-le rve odr o ordg o e ollowg eqo. 8 9 er g dervve ro 9 e wre e B-le o d Eq. 8

8 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME e were. I e e w e oee or e l odr o e e oed. e W regrdg o d e dervve e r d e l o re o vlle d old e roed. T odel gve rdgol ler e o eqo w deo w o e dgol ere d o e dgol d dgol ooe. Te oed ler e o eqo e o olve. T e doe To lgor. Te ove odel rel oo rve or d o vg oler dro d or elee. Te odel lo e eeded or d o o-or elee leg.. Two-deol B-le Te wo-deol B-le odel e geero o oe-deol odel wo dreo d ldrl oorde ollow e e ρ l l [ ] were er o ode vg oorde. Eq. or l / e [ ] Were elee leg. Te wo-deol B-le Eq. 5 or d ρ / d eql d ; reevel. Te eeve rd or B-le o o Eq. 5. Fg. d 5 ow e gr o Eq. 5 d oor le. 5 Fg: Two-deol B-le o gr 9

9 Ierol Jorl o dved R 8Pr ISSN 97 99le Fg: 5 Two-d Soe ere e d o w re o ll over e e w deo B-le o or were e ol er ode le oder qre elee w Te vle o B-le o I Eq. 7 led o e ode oed were edgol dgol ooe. Se e vl o ve e vle o d e eell or role w ge Tree role re oe or v w re eled ere. Reer Egeerg d Teolog IJRET Vole Ner Jl-Deeer IEM L e [ ]{ } { } M M M M eol B-le o oor w or reglr or qre e. Te elee w leg d e o d e wre d e ode er. For lo o. Te B-le o or ode o ro Eq. 7 eql e ollowg ler e o eqo Eq. 9 wl e w o e dgol ere d o le o dgol ere re o ereore; er ddree o ve r. T ve o er o d. vego o eg d ee o e ov ISSN 97 ME e deo. Te wo- e orlo 7 8 ll e 9 e or oer ol eer er eor ve orlo

10 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME.. Prole Tere re 5 d o { ; L5} role. Te or e o w 5 row d 5 ol d qre elee Fg.. Te elee de. Te do o o [] []. Te d re oed ro Eq... 5 [.7. e ] ded Fg. lr o or ode rod e d re odered or ldg e ee o odr odo. T o e ree r d ee o reeed odel or olvg ee d o role. 5 Fg: D dro role Prl dervve re reqred w ree o d odr ode or roe. For e o egeerg d e ove rl dervve or odr o re o vlle d old e oeow roed. Te B-le odel w ed or role I Eq. e eod e o eqo reled o e ee o odr odo w e eded Eq L L L L For llo or vle or erl o e elee eer o oder ol ew er o Eq.. Mo o er re ero or e o de e elee

11 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME ee o e re o B-le o. Fg. 7 ow e o o e eevee w regrd o e er o B-le o w ore o deerg. For ele elee w ode 8 9 d e er o reqred B-le o or llo re ro o 7 Fg. 7. T role olved e reeed odel. Fg d 9 ow e orve evor ewee e odel d e rel vle o o or e erl o o elee. e ee ro e gre ere re le relo d greee ewee e odel o d e rel d. Fg: 7 Reqred er o B-le o Fg: 8 Gr o rel d.. Fg: 8 Coor le o rel d

12 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME Fg: 9 Gr o B-le odel Fg: 9 Coor le o B-le odel.. Prole T role relo o e revo oe ore ole w ree o e vro o d. I ele ere re d o{ ; L }. Te d or or e vg row d ol w e do o o [] [ ]. Te d re geered e ollowg eqo π.5 [ e.87 e ] Co 8 o lr odr ode or lg e ee o odr odo re odered. Te rl dervve w ree o d odr o re lled e orwrd d wrd dvded deree orl. Te gr d oor le or Eq. re Fg. d. Te re ow ro e B-le odel Fg. d well. Coro o e gre ow good greee d le relo ewee e rel d d e eroled d. ddle o Fg: Gr o rel d Fg: Coor le o rel d

13 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME Fg: Gr o B-le odel Fg: Coor le o B-le odel.. Prole T ele o o 9 rle d o{ ; L9}. ordg o Fg. e or or qre e w 7 row d 7 ol o d d elee w elee e.. Te d w re gl oler re oed ro Eq.. S [ 8rg / ] o 8 lr o re odered or ldg e ee o odr odo Fg: Newor o d d odr o Te do o d or role [7 ] [7 ]. Slr o e revo role e rl dervve w ree o d e odr o re lled e erl eod dereo. Te reer goverg o e odr o e oed ro e ove dervve. Te reer 7 d 7 or ele e deered ro Eq. 5 d.

14 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME were e 7 8 e. Te wo deol B-le o w led or role or. d l / [ ] Te gr d oor le oed e odel d ro e o re Fg. d. oro ewee ee gre ree good d le relo or rel d d e wo-deol B-le odel Fg: Gr o rel d Fg:. Coor le o rel d B-le odel B-le odel Fg: Gr o B-le odel Fg: Coor le o B-le odel 5

15 Ierol Jorl o dved Reer Egeerg d Teolog IJRET ISSN 97 8Pr ISSN 97 99le Vole Ner Jl-Deeer IEME III. CNCLUSINS ND DISCUSSIN Te erolo eod eell e wo-deol oe ve lo ll re o egeerg ee. Tereore; e develoe eeo d rovee o ee eod re eer. Te reeed odel e o lee d rel ler edgol e o eqo w dgoll do d l olvle. Te reeed odel or erolo o d w reglr d qre elee owerl. lo e eded or o-or e or rglr elee o d. Te l ler e o eqo or oe e re d oded wle o ore 9% o r ere re ero. Te gr oed eod ve o lo o o roere de d ro e elee ee o e o odo o e led B-le o. Tee odo el e dvge d roe o e reeed odel o e vlle eod o wo-deol erolo. REFERENCES Brde R. d Fr J.. Nerl l 9 Ed. Broo-Cole P. Co.Boo. Coll G. W.. II Fdel Nerl Meod d D l ere d le. Der P. 99. Crve d Sre Fg w le Clredo Pre NY. D D.. Nerl d ll Meod or Se d Egeer Ug Me Jo Wle & So I. P. Hooe New Jer. Foel S e Geerl Teor o D Ierolo SEP Kl J. 5. Nerl Meod I Egeerg w MTLB Crdge Uv. PreUK. Loo N Crve g g le eo o dere order Proeedg o e Fr Ierol Me So P Noedl J. d Wrg S. J.. Nerl o d Ed. Srger See Be Med LLC US. Sloo D.. Crve d Sre or oer Gr Srger See Be Med I. US. Se. d S B. 5. Coer ded Egeerg Deg Srger Pler New Del Id. Z M. 9. Tree le le eod or roo d erolo o d Coeorr Egeerg See Vol. No.8 P Z M. 9. vego o B-le d Beer eod or erolo o d Coeorr Egeerg See Vol. No.8 P. -7. Z M.. le -D erolo odel or l o oler d Nrl See Vol. No. Je P. -. M. Ngr N d P. Re Kr Serl ro To Ige Proeo W C B-Sle Ierolo Ierol orl o Elero d Coo Egeerg &Teolog IJECET Vole Ie. 5 - Pled IEME