matematika dasar untuk komputer grafik

8/8/2019 Matematika Dasar Untuk Komputer Grafik

1/31


2/31

C~c Lt{ Hctvlg= Alvl(alvl Hctvlg

Hc`l~{icql Hctvlg

^kvgcilc` Hctvlg Dktkvhl`c` Hctvlg

Cvlthktlgc Hctvlg


3/31

Hkv{~cgc` cvvc| qkel |cè ~cdc {h{h`|cfkvlql kikhk`(kikhk` fkv{~c flicèc`

Hctvlg dl qlhfmigc` dkèc` h r `

h r ` 8 mvdm

C 8

23

;61


4/31

Hctvlg 3 r 4 qkvlè dlqkf{t dkèc` s{cdv{~ikctc{ kgtmv

Qkacvc {h{h hctvlg 3 r ` dlqkf{t dkèc`kgtmv fcvlq

Hctvlg ` r 3 dlqkf{t dkèc` kgtmv gmimh


5/31

Dlqkf{t dkèc` hctvlg qkel jlgc hctvlgtkvqkf{t hkhlilgl j{hicb fcvlq dc` gmimh|cè qchc.

Hctvlg `mi cdcicb qkh{c kikhk``|c `mi

Hctvlg ldk`tltcq cdcicb hctvlg qkel |cèqkh{c kikhk``|c `mi gka{cil kikhk`(kikhk`dlcem`ci.


6/31

Hctvlgq F|cè kikhk`(kikhk``|c fkv{~cflicèc` dc~ct dl qgcic dkèc` flicèc` q) |clt{kikhk`(kikhk` hctvlgq Fhcqlè(hcqlèdlgcilgc` dkèc` q. Bcqli`|c dl`|ctcgc` dkèc`qF. Qkfcecl am`tmb) dkèc` hkèe{`cgc`hctvlgq C ~cdc ~kvqchcc` "3.3,) dl qgcic dkèc`

flicèc` ? bcqli`|c cdcicb Dcich evcolgc gmh~{tkv hc`l~{icql qgcic fkvcvtl

hkh~kvfkqcv mf|kg evcolg.

3636??

;4321?

>42?

1>3632

?C


7/31

D{c f{cb hctvlgq Adc` Dhkhlilgl j{hicbfcvlq dc` gmimh |cè qchc) dlqkf{t qkfceclhctvlgq |cè hkhlilgl gkqkq{clc`) dc` dc~ctdlj{hicbgc` qct{ qchc icl`.

^k`j{hicbc` hctvlgq cdcicb ~k`j{hcicbc`kikhk`(kikhk` |cè fkvqkq{clc`) ctc{hk`j{hicbgc` kikhk` gk ljdcvl gkd{chctvlgq.

Kikhk` hctvlgq bcqli ~k`j{hicbc` K8 A ' Dcdcicb klj8 alj' dlj.


8/31

Qkichc hctvlgq dc~ct dl qgcic dc`dlj{hicbgc`) hcgc dc~ct ~{ic dlicg{gc`gmhfl`cql il`kcv tkvbcdc~ hctvlgq tkvqkf{t)qk~kvtl hlqci`|c 6C ( 4F.

Dkol`lql tkvqkf{t hk`{v{`gc` qloct(qloct ~cdchc`l~{icql tlec hctvlgq fkvlg{t l`l. Dlgktcb{lhctvlgq C) F) dc` A |c`e hkhlilgl gkqkq{clc`)hcgc :

C ' F8 F' C7 C ' "F' A, 8 "C ' F,' A7 "o' e,"C ' F,8 o C ' oF' eC ' eF


9/31

^{tcvc` "tvc`q~mqk, dcvl hctvlgq H)dl`|ctcgc` qkfcecl HT) dlicg{gc` dk`ec`hkh~kvt{gcvgc` kikhk`(kikhk` fcvlqhk`jcdl kikhk`(kikhk` gmimh hctvlgq H)

ctc{ kikhk` gk ljhk`jcdl kikhk` gkjldcvlhctvlgq H.

"1)6)(;,T8

;

6

1


10/31

Qkf{cb hctvlgq dlqkf{t qlhktvlq flic~{tcvc``|c qchc dkèc` cqil`|c.

Bc`|c hctvlgq qkel |cè flqc qlhktvlq.

Mikb gcvk`c lt{ hctvlgq Hfkv{g{vc` `r `cdcicb hctvlgq qlhktvlq flic hlj8 hjl{`t{g ldc` jc`tcvc 3 qch~cl dkèc` `.


11/31

^kvgcilc` hctvlgq C dc` Fhk`jcdl CFbc`|ccdc flic gkd{c hctvlgq qcilè amamg) cvtl`|cfc`|cg`|c gmimh hctvlg ~kvtchc) C) qchcdkèc` fc`|cg`|c fcvlq hctvlgq gk d{c) F.

Qkblèec) jlgc C cdcicb hctvlgq 1 r ; dc` Fhctvlgq ; r 6) hcgc CFcdc jcucf`|c) tktc~lFC tldcg


12/31

Qktlc~ q{g{ bcqli gcil A8 CFcdcicb j{hicbbcqli gcil kikhk`(kikhk` fcvlq hctvlgq Cdkèc` kikhk`(kikhk` gmimh hctvlgq F.

Qkacvc ikflb gb{q{q) kikhk` gk ljdcvl hctvlgqbcqli gcil Acdcicb j{hicb bcqli gcil fcvlq gk ldcvl hctvlgq C dkèc` gmimh gk j dcvlhctvlgq F.

Qkblèec bcqli gcil hctvlgq `r hdkèc`hctvlgq hr vcdcicb hctvlgq `r v.


13/31

kikhk` a368 (34) fkvcqci dcvl j{hicb bcqligcil "6)>)?) (1, . "6) 3) 3)2, 8 "6 r 6, ' "> r3, ' "? r 3, ' "(1 r 2, 8 (34

6>33

311;

344;

2

3

3

6

;

1

3

?

.35;>

>432

1?>6


14/31

Fkfkvc~c alvl(alvl dcvl ~kvgcilc` hctvlgqcdcicb : hlqcigc` hctvlgq C) F) dc` Aqcil`eamamg {`t{g ~kvgcilc`) hcgc "CF,A8 C"FA,.

C"F' A, 8 CF' CA.

"C ' F,A8 CA' FA.

"CF,T8 FTCT.


15/31

^kvgcilc` kgtmv qkacvc dmt ~vmd{at "l``kv~vmd{at, fc`|cg dle{`cgc` {`t{ghk`|ctcgc` {g{vc` jcvcg dc` q{d{t.

Hlqci`|c dlgktcb{l d{c f{cb kgtmv

8 dc` u 8

`r

r

:

3

`|

|

:

3


16/31

Dmt ~vmd{at dcvl dc` udl`|ctcgc` dk`ec` u) hk`ebcqligc` r3|3 ' ' r | .

Jcvcg dcvl tltlg "r)|, gk tltlg ~{qct gmmvdl`ct">)>, cdcicb .

Qkacvc {h{h jcvcg dcvl tltlg "r3 ) ) r, gktltlg ~{qct gmmvdl`ct fkvdlhk`ql `cdcicb .

66|r

66

3...

`rr


17/31

Gcic{ cdcicb kgtmv

hcgc jcvcg tkvqkf{t cdcicb ) |cè j{ecdlqkf{t ~c`jcè kgtmv ctc{ yyyy.

Dkèc` dkhlglc` jcvcg dcvl tltlg ^ dc` Scdcicb ~c`jcè qkilqlb kgtmv ^(Sctc{ yy^ (Syy.

`r

r

:

3

vv.


18/31

Dmt ~vmd{at j{ec dc~ct dle{`cgc` {`t{ghk`|ctcgc` q{d{t. Fkqcv`|c q{d{t c`tcvckgtmv dc` ucdcicb

^kvi{ dlgktcb{l ~{ic fcbuc) jlgc kgtmv dc`u cdcicb kgtmv qct{c`) hcgc ~khfcel`|c

tldcg ~kvi{.

yyuyyyyyy

.amq3

vuv


19/31

Jlgc gltc ~{`|c kgtmv qct{c` dc` kgtmv u)dc` u dl~vm|kgqlgc` tkecg i{v{q dk`ec` )dc` bcqli ~vm|kgql`|c { hcgc

yy{yy 8 yyuyy amq

8 yyuyy

8 . uyyuyyyyyy

.

v

uv


20/31

cqcigc` cdcicb kgtmv qct{c`. Qkacvc ekmhktvlq dc~ct dlilbct ~cdc echfcv

fkvlg{t l`l.

Dcvl ql`l gltc hk`dc~ctgc` ~kèkvtlc` fcv{

tk`tcè dmt ~vmd{at |clt{ : dmt ~vmd{atc`tcvc dc` u cdcicb ~c`jcè kgtmv~vm|kgql u tkvbcdc~ ) cqci kgtmv qct{c`.

u

{

v


21/31


22/31

Dlgktcb{l d{c kgtmv tlec dlhk`ql c8 "cr ) c|) cz , dc` f8 "fr ) f| ) fz,.

Avmqq ~vmd{at dcvl gkd{c kgtmv tkvqkf{tdl`|ctcgc` dk`ec` cr fcdcicb

cr f8 "c|fzczf|, l ' "crfzczfr, j ' "crf|c|fr, g

dlhc`c l) j) dc` gcdcicb kgtmv qct{c`

"kgtmv |c`e qki{v{b kikhk``|c cdcicb 3,.


23/31

Gcdcè gcic q{ct{ hctvlgq ~kvi{ dlfcelhk`jcdl fkfkvc~c fimg) dc` qktlc~ fimg dlfkvl`chc ctc{ dlicg{gc` ~kèmicbc` gb{q{q.Qkfcecl am`tmb :

dlhc`c tlc~ fimg tkvqkf{t dl`|ctcgc` dkèc`

41

63

561

432

?>6

HH

HHH

32

>6

3H

4

?

6H 61

1H 5

4H


24/31

Qktlc~ hctvlgq qkel Hhkhlilgl `licl |cèdlqkf{t dktkvhl`c`) |cè dl`|ctcgc` dkèc`yHy.

Dktkvhl`c` hk`|ctcgc` mi{hk dcvl q{ct{

fk`t{g ekmhktvl dc` hkhlilgl lòmvhcql |cèfkvgcltc` dkèc` ~kècv{b tvc`qomvhcqlil`kcv tkvbcdc~ dckvcb ctc{ mi{hk q{ct{mf|kg.

[`t{g hctvlgq H|cè fkv{g{vc` 6 r 6dktkvhl`c` cdcicb qkilqlb dcvl ~kvgcilc` d{cdlcem`ci`|c


25/31

yHy 8 8 h33 h66( h63 h366663

3633

hh

hh


26/31

yHy 8

Dktkvhl`c` dcvl fcelc` |cè ikflb gkalidlqkf{t gmcgtmv. Fcelc` l`l cgc` dle{`cgc`~cdc qcct hkèblt{è l`kvqk hctvlgq.

8 6

432

?>6


27/31

Q{ct{ hctvlgq Hfkv{g{vc` `r `dlqkf{t hctvlgq`m`(qlè{icv flic dktkvhl`c` Htldcg qchcdkèc` >.

Dcich bci l`l hctvlgq Hhkhlilgl l`kvq |cèdlichfcègc` dkèc` H(3 dc` hkhlilgl alvl(alvl

H H(3 8 H(3H 8 L

dlhc`c Lcdcicb hctvlgq ldk`tltcq |cè fkv{g{vc``r `

Alvl icl``|c cdcicb) l`kvq dcvl bcqli gcil d{c

hctvlgq "C F,(3 8 C(3 F(3


28/31

Kikhk`(kikhk` dcvl hctvlgq l`kvq dc~ctdlacvl dk`ec` acvc fkvlg{t l`l. Jlgc C cdcicbl`kvq dcvl H) hcgc clj8

Dlhc`c Hjlcdcicb ~{tcvc` dcvl gmocgtmvhctvlgq H.

yy H

Hjl


29/31


30/31

F{cticb ~vmevch dkèc` hkèe{`cgc` A''{`t{g ~kvgcilc` hctvlg dkèc` mvdm 6r6


31/31

matematika dasar untuk komputer grafik

Documents