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7/23/2019 Mini Project on Bezier Curves Using visual studio.
1/22
CG[JGS NWSRG^ _ a i g p 1
NMA_UGS 1
JLUSDEWNUJDL
Cg{jgs Nwsrg~
Jl haumghaujna` bjg`e db lwhgsjna` ala`z~j~, a CG[JGS NWSRG j~ a pasahgusjn nwsrg jhpdsualu
jl Ndhpwugs Isapmjn~ ale sg`auge bjg`e~ Cg{jgs nwsrg~ ygsg yjeg`z pwc`jnj{ge jl 1:23 cz a
Bsglnm Glijlggs _jgssg Cg{jgs ymd w~ge umgh ud eg~jil awudhdcj`g cdejg~ Umg nwsrg~ ygsg bjs~u
egrg`dpge jl 1:7: cz _aw` eg Na~u`gkaw w~jli umg Na~u`gkaw~ a`idsjumh, a lwhgsjna``z ~uac`g
hgumde ud gra`waug Cg{jgs Nwsrg~
Jl Rgnuds isapmjn~, Cg{jgs Nwsrg~ asg al jhpdsualu udd` w~ge ud hdeg` ~hddum nwsrg~ umau nal cg
~na`ge jlegbjljug`z _aum~, a~ umgz asg ndhhdl`z sgbgssge ud jl jhaig haljpw`aujdl psdisah~
~wnm a~ Jlf^napg, Aedcg J``w~usauds, Aedcg _mdud~mdp, ale IJH_ asg ndhcjlaujdl~ db Cg{jgs
Nwsrg~ paunmge udigumgs _aum~ asg ldu cdwle cz umg `jhju~ db sa~ugsj{ge jhaig~ ale asg jluwjujrg
ud hdejbz
Cg{jgs nwsrg~ marg ~dhg jlugsg~ujli psdpgsujg~, wl`jfg dumgs n`a~~g~ db nwsrg~6 umgz nal bd`e drgsdl umgh~g`rg~ Umgz nal a`~d cg kdjlge udigumgs ud bdsh ~hddum, ndlujlwdw~ ~mapg~ Bjiwsg 1
~mdy~ al g}ahp`g db a nwcjn Cg{jgs Nwsrg yjum a ~hddum nwsrauwsg
Bji; 11 Nwcjn Cg{jgs Nwsrg
Egpu db N^G, G_NGU 3??= ( ?:
http://en.wikipedia.org/wiki/File:Bezier_curve.svg7/23/2019 Mini Project on Bezier Curves Using visual studio.
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CG[JGS NWSRG^ _ a i g p 3
Cgbdsg J id yjum umg ugnmljna` eguaj`~ db mdy ud ysjug a psdisah bds umg nsgaujdl db Cg{jgs Nwsrg,
`gu hg bjs~u ijrg zdw a sdwim jega db mdy ud ndl~uswnu a Cg{jgs Nwsrg isapmjna``z Ud ndl~uswnu a
nwcjn Cg{jgs nwsrg yg lgge bdws ndlusd` pdjlu~ Egpglejli dl umg a`jilhglu db umg~g pdjlu~ umg
nwsrg igu~ ndl~uswnuge Yg nal wlegs~uale umj~ n`gas`z cz `ddfjli au umg bjiwsg cg`dy
Egpu db N^G, G_NGU 3??= ( ?:
7/23/2019 Mini Project on Bezier Curves Using visual studio.
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CG[JGS NWSRG^ _ a i g p >
Egpu db N^G, G_NGU 3??= ( ?:
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CG[JGS NWSRG^ _ a i g p 5
Bji; 13 ^wcejrj~jdl db a nwcjn Cg{jgs Nwsrg
Mgsg _?,_1,_3,_> asg umg bdws ndlusd` pdjlu~ ale u85 j~ umg jlugsra` au ymjnm umg nwsrg j~ iguujlinsgauge
NMA_UGS 3
SGQWJSGHGLU^
Egpu db N^G, G_NGU 3??= ( ?:
7/23/2019 Mini Project on Bezier Curves Using visual studio.
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CG[JGS NWSRG^ _ a i g p 7
3,1 Maseyasg Sgqwjsghglu~;
_glujwh ds mjimgs psdng~~ds, 12 HC ds hdsg SAH, a ~ualease fgzcdase, a Hjnsd~dbu
ndhpaujc`g hdw~g ale a RIA hdljuds Jb umg w~gs yalu~ ud ~arg umg nsgauge bj`g~ a
~gndleasz ~udsaig hgejwh nal cg w~ge
3,3 ^dbuyasg Sgqwjsghglu~;
Hjnsd~dbu Rj~wa` N&& yjum DpglI@ -G}psg~~P^ualease Gejujdl*
Yjledy~ ]_ ds mjimgs rgs~jdl
Lgu bsahgydsf 3? -bds Rj~wa` ^uwejd 3??7*
NMA_UGS >
EG^JIL
Umj~ psdkgnu j~ egrg`dpge w~jli Hjnsd~dbu Rj~wa` N&& yjum DpglI@ a~ al anaeghjn psdkgnu
w~jli fgzcdase ale hdw~g Umj~ psdkgnu j~ jhp`ghgluge cz hafjli w~g db g}ugl~jrg w~g db
`jcsasz bwlnujdl~ dbbgsge cz isapmjn panfaig db DpglI@ Umg hd~u jhpdsualu db a`` j~ umg
Egpu db N^G, G_NGU 3??= ( ?:
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CG[JGS NWSRG^ _ a i g p 2
DpglI@ Gra`wauds~, yjumdwu ymjnm hz psdisah ydw`elu cg pd~~jc`g ud jhp`ghglu A `j~u db
~ualease `jcsasz bwlnujdl~ umau asg w~ge asg ijrgl cg`dy A lwhcgs db w~gs egbjlge bwlnujdl~ a`~d
marg cggl w~ge ale a ~whhasz db umd~g bwlnujdl~ bd``dy~ umj~ `j~u db ~ualease `jcsasz bwlnujdl~
@gu hg bjs~u ~uasu cz g}p`ajljli acdwu umg DpglI@ Gra`wauds~
DpglI@ Gra`wauds~
Umg DpglI@ Gra`wauds bwlnujdl a``dy~ w~ ud w~g a pd`zldhja` happjli ud psdewng
rgsujng~, ldsha`~, ug}uwsg nddsejlaug~, ale nd`ds~
Umg~g na`nw`auge ra`wg~ asg umgl pa~~ge dl ud umg psdng~~jli pjpg`jlg a~ jb umgz mae cgglejsgnu`z ~pgnjbjge
Umg Gra`wauds~ bwlnujdl~ asg a`~d umg ca~j~ bds umg LWSC^-Ldl(Wljbdsh Saujdla` C(
^p`jlg* bwlnujdl~ ymjnm a``dy~ w~ ud egbjlg nwsrg~ ale ~wsbang~
Umg~g LWSC^ bwlnujdl nal cg w~ge ud iglgsaug ldl wljbdsh ~panjli db pdjlu~
Alz pd`zldhja` bdsh nal cg ndlrgsuge ud Cg{jgs bdsh cz psdpgs iglgsaujdl db ndlusd`
pdjlu~
Umw~ LWSC^ bwlnujdl a``dy~ bjlgs ndlusd` db umg ~pang ale sglegsjli db umg ~wsbang
i`Hap1b-uzpg wThjl wTha} ~usjeg dsegs pdjluTassaz*6
Umg egbjljujdl db a Dlg ejhgl~jdla` gra`wauds j~ a~ ~mdyl acdrg Ymgsg
wThjl ale wTha} egbjlg~ umg edhajl bds pasahgugs w
^usjeg; Umg lwhcgs db b`dau~ ds edwc`g~ cguyggl umg cgijlljli db dlg ndlusd` pdjlu ale
umg cgijlljli db umg lg}u dlg jl umg eaua ~uswnuwsg sgbgsglnge jl pdjlu~ Umg dl`z
ndl~usajlu j~ umau umg ra`wg~ bds a pasujnw`as ndlusd` pdjlu hw~u dnnwpz ndlujiwdw~
hghdsz `dnaujdl~
Dsegs; Ju~ umg lwhcgs db ndlusd` pdjlu~-ma~ ud cg pd~jujrg*
_djlu~; A pdjlugs ud umg assaz db ndlusd` pdjlu~
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CG[JGS NWSRG^ _ a i g p 9
i`HapIsje1b-I`jlu wl I@b`dau w1 I@b`dau w3*6
i`HapIsje ale i`Gra`Hg~m asg w~ge udigumgs ud gbbjnjglu`z iglgsaug ale gra`waug a ~gsjg~
db grgl`z ~pange hap edhajl ra`wg~ i`HapIsje1 ~pgnjbjg~ umg `jlgas isje happjli
cguyggl wl jlugigs isje nddsejlaug~ ud w1" w3 b`daujli pdjlu gra`waujdl hap
nddsejlaug~
wl; ^pgnjbjg~ umg lwhcgs db pasujujdl jl umg isje salig jlugsra`
w1" w3; ^pgnjbjg~ umg happjli bds umg jlugigs isje edhajl ra`wg~-j8? ud j8wl*
i`Gra`Hg~m1-I@glwh hdeg I`jlu j1 I`jlu j3*6
i`Gra`Hg~m ~ugp~ umsdwim umg jlugigs edhajl db 1 ds 3 ejhgl~jdla` isje ymd~g salig j~
umg edhajl db umg gra`waujdl hap~ ~pgnjbjge cz i`Hap1 ale i`Hap3
hdeg; ~pgnjbjg~ ymgumgs ud ndhpwug a dlg(ejhgl~jdla` hg~m db pdjlu~ ds `jlg~
^zhcd`jn ndl~ualu~ I@T_DJLU ale I@T@JLG asg anngpuge
j1 " j3; ^pgnjbz umg bjs~u ale `a~u jlugigs ra`wg~ bds isje edhajl rasjac`g j
i`wuJlju -*6
Umj~ bwlnujdl egbjlg~ umg jlugsanujdl cguyggl umg yjledyjli ~z~ugh ale umg DpglI@
Egn`asaujdl;
i`wuJlju-"asin, asir*6
i`wuJljuEj~p`azHdeg -*6
Mgsg yg ~pgnjbz SIC nd`ds ~z~ugh ale a`~d edwc`g cwbbgsjli
Egn`asaujdl;
i`wuJljuEj~p`azHdeg-I@WUTSIC*6
i`wuJljuYjledy^j{g-*6
Umj~ bwlnujdl ~pgnjbjg~ a yjledy jl umg udp `gbu ndslgs db umg ej~p`az
Egn`asaujdl;
i`wuJljuYjledy^j{g-yjeum, mgjimu*6
Egpu db N^G, G_NGU 3??= ( ?:
7/23/2019 Mini Project on Bezier Curves Using visual studio.
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CG[JGS NWSRG^ _ a i g p =
i`wuNsgaugYjledy-*6
Umj~ nsgaug~ al DpglI@ yjledy w~jli umg i`wu bwlnujdl ymgsg umg uju`g au umg udp db umg yjledy
j~ ijrgl cz umg ~usjli jl~jeg umg pasahgugs db umg acdrg bwlnujdl
Egn`asaujdl;
i`wuNsgaugYjledy-W~g db 3E ~mapg~ ale Usal~bdshajdl~*6
i`wuSg~mapgBwln-*6
Umg sg~mapg grglu j~ iglgsauge ymglgrgs umg yjledy j~ sg~j{ge, ~wnm a~ w~gs jlugsanujdl
Egn`asaujdl;
i`wuSg~mapgBwln-hzSg~mapg*6
i`wuEj~p`azBwln-* 6
Isapmjn~ asg ~glu ud umg ~nsggl umsdwim a bwlnujdl na``ge umg ej~p`az na`` canf, mgsg umg bwlnujdl
lahge bwln yj`` cg na``ge ymglgrgs umg yjledyjli ~z~ugh egugshjlg~ umau DpglI@ yjledy
lgge~ ud cg sgej~p`azge
Egn`asaujdl;
i`wuEj~p`azBwln-ej~p`az*6
i`wuJe`gBwln-*6
i`wuJe`g bwlnujdl nmgnf~ je`g na`` canf jg ju nal pgsbdsh a canfisdwle psdng~~jli ua~f ds
ndlujlwdw~ aljhaujdl ymgl yjledy~ ~z~ugh grglu~ asg ldu cgjli sgngjrge
Egn`asaujdl;
i`wuJe`gBwln-hzJe`gBwln*6
i`wuHdw~gBwln-*6
Umj~ bwlnujdl male`g~ hdw~g n`jnf grglu~
Egn`asaujdl;
i`wuHdw~gBwln-hzHdw~g*6
Egpu db N^G, G_NGU 3??= ( ?:
7/23/2019 Mini Project on Bezier Curves Using visual studio.
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CG[JGS NWSRG^ _ a i g p :
i`wuFgzcdaseBwln-*6
Umj~ bwlnujdl male`g~ fgzcdase grglu~
Egn`asaujdl;
i`wuFgzcdaseBwln-hzFgz*6
i`N`gasNd`ds-*6
i`Nd`ds>b-*6
Jl SIC nd`ds yg marg umsgg auusjcwug~ ud ~gu Umg bjs~u j~ umg n`gas nd`ds, ymjnm j~ ~gu ud c`anf ale
yg nal ~g`gnu umg sglegsjli nd`ds bds pdjlu~ cz ~guujli umg ~uaug db umg rasjac`g ud c`anf cz w~jli
umg bd``dyjli bwlnujdl na``
Egn`asaujdl;
i`N`gasNd`ds-??,??,??,??*6
i`Nd`ds>b-??,??,??*6
rdje hzHdw~g-*6
Umj~ j~ umg hdw~g na``canf bwlnujdl Yjumjl umg na``canf bwlnujdl, yg egbjlg umg anujdl~ umau yg
yalu ud uafg p`ang jb umg ~pgnjbjge grglu dnnws~
Egn`asaujdl;
rdje hzHdw~g-jlu cwuudl, jlu ~uaug, jlu }, jlu z*
v
jb-cul88I@WUT@GBUTCWUUDL "" ~uaug 88 I@WUTEDYL*
;
x
rdje hzFgz-*6
Egpu db N^G, G_NGU 3??= ( ?:
7/23/2019 Mini Project on Bezier Curves Using visual studio.
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CG[JGS NWSRG^ _ a i g p 1?
Umj~ j~ umg fgzcdase na``canf bwlnujdl Yjumjl umg na``canf bwlnujdl, yg egbjlg umg anujdl~ umau
yg yalu ud uafg p`ang jb umg ~pgnjbjge grglu dnnws~
Egn`asaujdl;
rdje hzFgz-wl~jilge nmas fgz, jlu }, jlu z*
v
na~g c; na~g C; esaynwsrg~-*6
;
na~g )Q); g}ju-?*6
csgaf6
x
rdje esaynwsrg~-*6
Umg esaynwsrg~ bwlnujdl j~ umg mgasu db umg psdisah, ymjnm j~ sg~pdl~jc`g bds umg nsgaujdl db
cg{jgs nwsrg~ Jl umj~ bwlnujdl yg w~g DpglI@ Gra`wauds~ `jfg i`Hap, i`HapIsje, ale
i`Gra`Hg~m udigumgs jl a bds `ddp db umg salig ? ud lnpu~, ymgsg lnpu~ j~ umg ha}jhwh
lwhcgs db pdjlu~ ud cg p`duuge dl umg ~nsggl
Egn`asaujdl;
rdje esaynwsrg~- *
v
;
x
i`wu_d~uSgej~p`az-*6
Egpu db N^G, G_NGU 3??= ( ?:
7/23/2019 Mini Project on Bezier Curves Using visual studio.
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CG[JGS NWSRG^ _ a i g p 11
Umj~ gl~wsg~ umau umg ej~p`az yj`` cg esayl dl`z dlng ganm ujhg umg psdisah idg~ umsdwim umg
grglu `ddp Ju ardje~ g}usa ds wllgng~~asz ~nsggl esayjli~ cz ~guujli a b`ai jl~jeg I@WU~ hajl
`ddp jlejnaujli umau umg ej~p`az lgge~ ud cg sgesayl
rdje ej~p`az-rdje*
Umj~ bwlnujdl j~ umg na``canf bwlnujdl bds Ej~p`azBwln Umj~ bwlnujdl j~ haleaudsz cgnaw~g
I@WU sgqwjsg~ umau a`` psdisah~ marg a ej~p`az na``canf
rdje hzSg~mapg-jlu yjlu m*
Umj~ bwlnujdl j~ w~ge ymglgrgs umg yjledy j~ sg~j{ge Jl dws psdisah yg lgge umg sgqwjsge
ej~p`az na``canf bds esayjli cgnaw~g umg psjhjujrg~ asg iglgsauge ymgl a hdw~g grglu dnnws~
NMA_UGS 5
UG^UJLI ALE SG^W@U^
Umg psdkgnu eg~jilge ma~ cggl ug~uge bds ju~ ydsfjli, ale j~ bdwle ud cg ydsfjli psdpgs`z
ud hggu a`` ju~ sgqwjsghglu~ Umg psdkgnu ma~ cggl bdwle ud cg ijrjli ndssgnu dwupwu~ ud umg jlpwu~
umau ygsg ijrgl, `jfg umg appsdpsjaug ej~p`azjli db umg dwupwu, ale bd``dyjli appsdpsjaugndlejujdl~ bds ugshjlaujdl db umg psdisah gun
Umg eg~jilge psdkgnu ma~ cggl ug~uge bds gssds~
ale ma~ cggl bdwle ud cg hggujli a`` umg sgqwjsghglu~ db eg~jil yjum ymjnm ju ya~ ~uasuge
Umw~ umg psdkgnu j~ egn`asge ud cg ydsfjli psdpgs`z
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CG[JGS NWSRG^ _ a i g p 13
Bji 51; Cwj`ejli umg ~d`wujdl
Umg acdrg bjiwsg ~mdy~ ymgsg ud n`jnf ud cwj`e ~d`wujdl
Bji 53; Dwupwu db cwj`e
Egpu db N^G, G_NGU 3??= ( ?:
7/23/2019 Mini Project on Bezier Curves Using visual studio.
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CG[JGS NWSRG^ _ a i g p 1>
Umg acdrg bjiwsg ~mdy~ umg dwupwu abugs ju ma~ cggl ndhpj`ge, a~ ju ndluajl~ ? gssds~ ale au umg
`dygs `gbu ndslgs yg marg Cwj`e ^wnnggege, ~d ju j~ ldy sgaez bds egcwiijli
Bji 5>; ^uasu egcwiijli
Abugs Cwj`ejli umg ~d`wujdl yg lgge ud Egcwi ju cgbdsg ~uasujli umg g}gnwujdl Ud egcwi umg ~d`wujdl yg
lgge ud id ud Egcwi dpujdl, a esdp edyl hglw appgas~ a~ ~mdyl jl umg bjiwsg acdrg6 ldy ~g`gnu ^uasu
Egcwiijli dpujdl Au umg gle, umg g}gnwujdl yjledy dpgl~ ale yg nal jhp`ghglu umg Cg{jgs Nwsrg~
Egpu db N^G, G_NGU 3??= ( ?:
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CG[JGS NWSRG^ _ a i g p 15
Bji 55; A bdws pdjlu ~jhp`g Cg{jgs Nwsrg
Abugs n`jnfjli dl umg ^uasu Egcwiijli dpujdl jljuja``z yg a igu a ymjug ~nsggl ymjnm anu~ a~ a
p`aubdsh ud esay dws nwsrg~ Cz w~jli hdw~g yg ~pgnjbz umg `dnaujdl db umg pdjlu~ ale psg~~ c
A nwsrg a~ ~mdyl jl umg bjiwsg acdrg igu~ nsgauge Yg nal gsa~g umg nwsrg cz psg~~jli g Ud
n`gas umg ~nsggl yg lgge ud psg~~ n Ud g}ju bsdh umg dwupwu yjledy yg lgge ud psg~~ q
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CG[JGS NWSRG^ _ a i g p 17
Bji 57; A 12 pdjlu Cg{jgs Nwsrg
NMA_UGS 7
NDLN@W^JDL
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CG[JGS NWSRG^ _ a i g p 12
Umsdwim umj~ psdkgnu yg marg haeg a ~jlngsg auughpu ud egrg`dp al DpglI@ isapmjn~
panfaig ymjnm hggu~ a`` umg lgng~~asz sgqwjsghglu~ umau ygsg ~gu dwu bds w~ jl dws ~z``acw~ Umg
hajl jega cgmjle umj~ psdkgnu j~ ud csjli udigumgs umg jega~ db Haumghaujna` nwsrg~ ale Isapmjn~
psdisahhjli jlud dlg ndhp`g} wlju ymjnm nal cg jhp`ghgluge Dlg hdsg dckgnujrg db
jhp`ghglujli umj~ psdkgnu j~ ud mjim`jimu umg jhpdsualng db umg Cg{jgs Nwsrg~ jl Isapmjn~
_sdisahhjli Dws psdkgnu j~ ldu dl`z w~gs bsjgle`z ale jlugsanujrg cwu a`~d ijrg~ ydsumz
jlbdshaujdl acdwu umg ndl~uswnujdl db Cg{jgs Nwsrg~ yjum hjljhwh db ugnmljna` kasidl
NMA_UGS 2
BWUWSG GLMALNGHGLU^
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CG[JGS NWSRG^ _ a i g p 19
Umj~ psdkgnu j~ hajl`z ndlngslge yjum umg eg~jil ale jhp`ghgluaujdl db Nwcjn Cg{jgs
Nwsrg~ Mdygrgs jhp`ghgluaujdl db mjimgs dsegs Cg{jgs Nwsrg~ j~ ldu al jhpd~~jc`g ua~f Dlg
hdsg umjli umau J marg ud hglujdl bds umg bwuwsg glmalnghglu j~ umau umg jlnsga~g jl umg lwhcgs db
ndlusd` pdjlu~ A`umdwim J marg w~ge umg mg`p db DpglI@ Gra`wauds~ jl hz psdisah, ju j~ ldu au
a`` a ndhpw`~jdl Yjum mjimgs dsegs nwsrg~ yg nal grgl nsgaug ndhp`g} esayjli~ `jfg umg dlg
~mdyl cg`dy
Bji; 21 Bdlu egbjljujdl w~jli Cg{jgs Nwsrg~
Ds hazcg zdw nal jhp`ghglu a Cg{jgs nwsrg db egisgg 5 ds 9 Cg{jgs Nwsrg~ db ejbbgsglu egisgg~
asg ~mdyl cg`dy
Egpu db N^G, G_NGU 3??= ( ?:
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CG[JGS NWSRG^ _ a i g p 1=
Bji; 23 Cg{jgs Nwsrg~ db egisgg~ wp ud ~grgl
A`umdwim umj~ hjimu igu a `juu`g ndhp`jnauge cwu ldu au a`` jhpd~~jc`g Yg lgge ud ed ~dhg hjlds
aekw~uhglu jl dws a`idsjumh ale yg lgge ud ysjug a ymd`g lgy ~dwsng ndeg bds a 9um dsegs Cg{jgs
nwsrg
CJC@JDISA_MZ
Egpu db N^G, G_NGU 3??= ( ?:
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CG[JGS NWSRG^ _ a i g p 1:
Cddf~;
1 Geyase Alig`; ( Jlugsanujrg Ndhpwugs Isapmjn~; A Udp(Edyl Appsdanm yjum DpglI@,
7um Gejujdl, Aeej~dl(Yg~`gz, 3??=
3 Ndhpwugs Isapmjn~ _sjlnjp`g~ " _sanujng; Bd`gz, ral Eah, Bgjlgs, Mwig~;( ~gndle
gejujdl
Ygc Sg~dwsng~;
1 muup;$$yyydpgli`dsi
3 muup;$$yyyyjfjpgejadsi
> muup;$$yyy~w`anddsi
A__GLEJ] ^DWSNG NDEG
Egpu db N^G, G_NGU 3??= ( ?:
7/23/2019 Mini Project on Bezier Curves Using visual studio.
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CG[JGS NWSRG^ _ a i g p 3?
.jln`weg#~ueab}m#
.jln`weg0I@$i`wumX6jlu lnpu~8?6~uaujnjlu yjeum87??,mgjimu87??6
rdje esaynwsrg~-*v
jlu j6bds-j8?6j0lnpu~(>6j&8>*
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Egpu db N^G, G_NGU 3??= ( ?:
7/23/2019 Mini Project on Bezier Curves Using visual studio.
21/22
CG[JGS NWSRG^ _ a i g p 31
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Egpu db N^G, G_NGU 3??= ( ?:
7/23/2019 Mini Project on Bezier Curves Using visual studio.
22/22
CG[JGS NWSRG^ _ a i g p 33
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Egpu db N^G, G_NGU 3??= ( ?: