Lecture-11-h - Lecture-11 Region Properties Mid Term Exam...

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1 Lecture-11 Region Properties Mid Term Exam • March 8, Thursday • Closed book
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2 Geometrical Properties ∑∑ = = = m x n y y x B A 0 0 ) , ( A y x yB y A y x xB x m x n y m x n y ∑∑ ∑∑ = = = = = = 0 0 0 0 ) , ( , ) , ( Area Centroid Moments dxdy y x B y x m q p pq ) , ( ∫ ∫ = General Moments ∑∑ ∑∑ = = = = = = m x n y y m x n y x y x yB M y x xB M 0 0 1 0 0 1 ) , ( , ) , ( ∑∑ ∑∑ ∑∑ = = = = = = = = = m x n y xy m x n y y m x n y x y x xyB M y x B y M y x B x M 0 0 2 0 0 2 2 0 0 2 2 ) , ( , ) , ( , ) , ( Discrete
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3 Moments ) ( ) ( ) , ( ) ( ) ( y y d x x d y x B y y x x q p pq - - - - = ∫∫ m Central Moments (Translation Invariant) 00 01 00 10 , m m y m m x = = Centroid Central Moments 3 02 03 03 2 11 02 12 12 2 11 20 21 21 3 20 30 30 2 02 02 11 11 2 20 20 10 01 00 00 2 3 2 2 2 2 2 3 0 0 y y m m y x y m x m m y x x m y m m x x m m y m y x m x m m m m m m m m m m m m m m m m m m m m + - = + - - = + - - = + - = - = - = - = = = =
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4 Moments 2 03 21 2 12 30 4 2 03 12 2 12 30 3
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Lecture-11-h - Lecture-11 Region Properties Mid Term Exam...

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