0% found this document useful (0 votes)
25 views3 pages

04 2dtransforms

The document discusses 2D transformations useful for computer graphics. Linear transformations like translation, rotation, and scale can be represented by 2x2 matrices, while affine transformations like reflection can be represented by 3x3 matrices acting on homogeneous coordinates. Affine transformations preserve properties important for computer graphics applications.

Uploaded by

jopsrodrigues
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
0% found this document useful (0 votes)
25 views3 pages

04 2dtransforms

The document discusses 2D transformations useful for computer graphics. Linear transformations like translation, rotation, and scale can be represented by 2x2 matrices, while affine transformations like reflection can be represented by 3x3 matrices acting on homogeneous coordinates. Affine transformations preserve properties important for computer graphics applications.

Uploaded by

jopsrodrigues
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 3

,QWURGXFWLRQ

‡ $'WUDQVIRUPLVDXVHIXOPDSSLQJRIWKH'
SODQHRQWRLWVHOI
² +RPHRPRUSKLVP
² 3UHVHUYHVVRPHDPRXQWRIJHRPHWULFLQIRUPDWLRQ
‡ 0DQ\GLIIHUHQWIXQFWLRQVDUHSRVVLEOHXQGHUWKLV
GHILQLWLRQEXWZH OOVHHWKDWVRPHLQSDUWLFXODU
DUHXVHIXOIRUFRPSXWHUJUDSKLFV
'WUDQVIRUPDWLRQV

$SSOLFDWLRQV /LQHDULW\
‡ 6RPHWLPHVLW VHDVLHUWRVSHFLI\DQREMHFWXVLQJ ‡ 2QHLPSRUWDQWFODVVRIWUDQVIRUPVDUHWKHOLQHDU
DWUDQVIRUPWKDQGLUHFWO\ WUDQVIRUPV
‡ ,QVWDQFLQJ ² 7KH\FRUUHVSRQGWRFKDQJHRIEDVLVRUFKDQJHRI
² 7UDQVIRUPVFDQEHDPRUHFRPSDFWUHSUHVHQWDWLRQ FRRUGLQDWHV\VWHPWUDQVIRUPV
WKDQFRSLHVRIDQREMHFW ‡ +RZFDQZHUHSUHVHQWOLQHDUWUDQVIRUPV"
² $WUDQVIRUPHGLQVWDQFHRIDQREMHFWSUHVHUYHV ‡ :KLFKWUDQVIRUPVDUHOLQHDU"
PRUHLQIRUPDWLRQDERXWWKHREMHFWWKDQDFRS\
‡ +LHUDUFKLFDOPRGHOLQJ
² :HFDQJURXSDFROOHFWLRQRIJHRPHWU\XQGHUD
WUDQVIRUPQRGHDQGPDQLSXODWHLWDOODWRQFH
/LQHDU,VQ·W(QRXJK $IILQH*HRPHWU\
‡ :KDWLPSRUWDQWWUDQVIRUPLVQ·WOLQHDU" ‡ 7UHDWLQJWKH(XFOLGHDQSODQHDVDYHFWRUVSDFH
² :K\QRW" LJQRUHVWKHGLVWLQFWLRQEHWZHHQSRLQWVDQG
‡ +RZFDQZHXQLI\DOORIWKHWUDQVIRUPVZH·YH YHFWRUV
GLVFXVVHG" ‡ 7KHDIILQHSODQHLVDVHWRISRLQWVWRJHWKHUZLWKD
VHWRIYHFWRUV
² 1RGLVWLQJXLVKHGRULJLQ
² 7KHGLIIHUHQFHEHWZHHQWZRSRLQWVLVDYHFWRU
² $YHFWRUDGGHGWRDSRLQW\LHOGVDQHZSRLQW
² 9HFWRUVDQGSRLQWVDUHQRWLQWHUFKDQJHDEOH
‡ +RZFDQZHUHSUHVHQWWKHDIILQHSODQH"
‡ +RZFDQZHUHSUHVHQWWUDQVIRUPVLQWKHDIILQH
SODQH"
‡ :KDWJHRPHWULFSURSHUWLHVGRDIILQHWUDQVIRUPV
SUHVHUYH"

3URSHUWLHVRI7UDQVIRUPV ([DPSOHV
‡ &RPSDFWUHSUHVHQWDWLRQ ‡ 5RWDWLRQDERXWDSRLQWRWKHUWKDQWKHRULJLQ
‡ )DVWLPSOHPHQWDWLRQ ‡ 5HIOHFWLRQWKURXJKDOLQHRWKHUWKDQDQD[LV
‡ (DV\WRLQYHUW ‡ 9LHZSRUWWUDQVIRUP
‡ (DV\WRFRPSRVH
6XPPDU\ 5HDGLQJ
‡ $VPDOOQXPEHURI'WUDQVIRUPVDUHHVSHFLDOO\
XVHIXOLQFRPSXWHUJUDSKLFVWUDQVODWLRQURWDWLRQ 7KHUHDGLQJKHUHFRYHUV'DQG'WUDQVIRUPDWLRQV
VFDOHVKHDUUHIOHFWLRQDQGRIFRXUVHLGHQWLW\
‡ 6RPHRIWKHVHWUDQVIRUPVDUHOLQHDUDQGFDQEH
‡ $QJHOFKDSWHU
UHSUHVHQWHGXVLQJD[PDWUL[
‡ )ROH\HWDOFKDSWHUDQG$SSHQGL[$
‡ 6RPHDUHDIILQHDQGFDQEHUHSUHVHQWHGXVLQJD
[PDWUL[DFWLQJRQKRPRJHQHRXVFRRUGLQDWHV ‡ +HDUQ %DNHUFKDSWHU ' FKDSWHU '
‡ $IILQHWUDQVIRUPVKDYHFHUWDLQSURSHUWLHVZKLFK
PDNHWKHPYHU\SUDFWLFDOIRUFRPSXWHUJUDSKLFV

You might also like