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by: Khalil Conroy


Khalil Conroy
University of Central Florida
GPA 3.76


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Class Notes
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This 8 page Class Notes was uploaded by Khalil Conroy on Thursday October 22, 2015. The Class Notes belongs to CAP 5415 at University of Central Florida taught by Staff in Fall. Since its upload, it has received 14 views. For similar materials see /class/227216/cap-5415-university-of-central-florida in System Engineering at University of Central Florida.

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Date Created: 10/22/15
Lecture1 1 Region Properties Mid Term Exam 0 March 8 Thursday 0 Chapters 1 2 amp 3 0 Closed book Geometrical Properties AZZBxy Area x0 y0 iZKZXBWJ iinbay Centroid f X y 7 X F0 A A Moments General Moments mm 2 I xl quxydxdy Discrete M ZZxBxy M ZZyBoc y x0 y0 x0 y0 M ZZxZBOC y M ZZyZBOc y Mfy Z xyBx y x0 y0 x0 y0 x 0 0y Moments Central Moments Translation Invariant gm 2 IIx EPy wax y dx fdy mo1 Centroid x y moo moo Central Moments Hm moo E H Mn 0 le 0 20 Mm w 11 mu H C y An Mm 4972 um m30 3mzof 2W3 ya m21 m20y 2mnf lufzy 112 m12 mozf 2mny 2Llgtty2 ME m03 3m02y 2W3 Moments Humans mm and mm v1 7 20 02 02 7 H20 7 002 112 03 70130 7 32 3 7 002 vi 70130 102 0121 002 Mmenllnnri AlarmIml nm pJJMum lrwnrmnl L95 mm Hull 5 Wm mm 239 am a o a m 5225 a m 6253 a m o n ma 15954 19955 mm 15 an o 22655 23st 2mg 22333 19711 a 21m 20m 25 901 23 no mm a 5 m a w 53 m u m 525 g um um 17 m 2 ex 2a m 3 45 589 343 s u on Hu moments Perimeter amp Compactness 1721mm Thesumafxtsbaxdexpmntsaf hueganApxxelwhc 5 mmmmmm hh at ghbmhnadfmm the backgwundxs called abmdexpxxel Cnmpactness C 1 MIA Orientation of the Region Least second moment Mm z EHv18wdmy xsinerycosemw rmeymSQ pm scus cus ssn Orientation of the Region r 7 x7 xnf 07an xquot rpsm scus yquot pcus ssn Substituting Km m r1 And differentiating xcus ysn Substitute 5 m Km men I Y1xsn rycus p1 Orientation of the Region V2 xsinHiycosH pZ E HrZBxydxdy E xsin 9 7 ycosH pZBxydxdy Substitute r inE and differentiate Wrt to and equate it to zero AJsin effc059 p 0 is the centroid r x xei y yi a x39zBOgy x39dy39 b x39y39Bxydx39dy39 c jjy39zsmwdy39 E asin Z 9 ibsin 9 c059 0 cos2 9 substitute value of E la c7laiccos 2971bsi11 29 2 2 2 Orientation of the Region E la c7laiccos 2971bsi11 29 2 2 2 Differentiating this wrt a Ix213w ydx dy tan29 aic bJ39J39xlBxyd dyl b c y zBWJW dy si1120r 1 b2aicz COSZQ aic 959 yy 7 bz 10 Z a xZBxy7Afz 22 1722 2 xyBxy7AE 622 v213xveAVZ Example 100 1 0000 1 Find area centroid moments compactness perimeter orientation


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