# Lecture-3 - Lecture-3 Camera Model Homework(Due Exercises...

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1 Lecture-3 Camera Model Homework (Due 1/25/01) Exercises in section 1.11 in “Fundamentals of Computer Vision”. – 1 to 5 – 8 to 9 – 15

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2 Thursday’s class Room 103 CSB Computer Vision Lab • Digitization • Image tools in C – Reading an image – Writing an image – Displaying an image Rotation Around an Arbitrary Axis (Rodriguez’s Formula) ) ) . ( ( ) . ( n n V V n n V V - + = ) ) . ( ( ( sin ) ) . ( ( cos n n V V n n n V V V - × + - = q q C V V V + = ) ( ) cos 1 ( sin V n n V n V V × × - + × + = q q V n n V V n n - = × × ) . ( ) ( n n V V ) . ( = C n n V V n V V ) . )( cos 1 ( sin cos q q q - + × + = n n V V V n n ) . ( ) ( = + × ×
3 Dot and Cross Products z z y y x x z y x z y x n V n V n V n n n V V V n V + + = = ) , , ).( , , ( . ) , , ( ) , , ( ) , , ( x y y x z x x z y z z y z y x z y x z y x z y x n V n V n V n V n V n V n n n V V V k j i n n n V V V n V - - - = = × = × Rotation Around an Arbitrary Axis (Rodriguez’s Formula) - - - = - + + = 0 0 0 ) ( ) ( ) cos 1 ( ) ( sin ) , ( 2 x y x z y z n n n n n n n X n X n X I n R q q q V n R V ) , ( q = ) ( ) cos 1 ( sin V n n V n V V × × - + × + = q q

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4 Rotation Around an Arbitrary Axis (Rodriguez’s Formula)
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Lecture-3 - Lecture-3 Camera Model Homework(Due Exercises...

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