mws_com_inp_txt_lagrange_examples

mws_com_inp_txt_lagrange_examples - Chapter 05.04 Lagrange...

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05.04.1 Chapter 05.04 Lagrange Method of Interpolation – More Examples Computer Engineering Example 1 A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a " 10 " 15 rectangular plate. The centers of the holes in the plate describe the path the arm needs to take, and the hole centers are located on a Cartesian coordinate system (with the origin at the bottom left corner of the plate) given by the specifications in Table 1. Table 1 The coordinates of the holes on the plate. x (in.) y (in.) 2.00 7.2 4.25 7.1 5.25 6.0 7.81 5.0 9.20 3.5 10.60 5.0 Figure 1 Location of the holes on the rectangular plate.
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05.04.2 Chapter 05.04 If the laser is traversing from 2 x to 25 . 4 x in a linear path, what is the value of y at 00 . 4 x using the Lagrangian method and a first order polynomial? Solution For first order Lagrange polynomial interpolation (also called linear interpolation), we choose the value of y as given by 1 0 ) ( ) ( ) ( i i i x y x L x y ) ( ) ( ) ( ) ( 1 1 0 0 x y x L x y x L Figure 2 Linear interpolation. Since we want to find the value of y at 00 . 4 x , using the two points 00 . 2 0 x and 25 . 4 1 x , then  2 . 7 , 00 . 2 0 0 x y x  1 . 7 , 25 . 4 1 1 x y x gives 1 0 0 0 0 ) ( j j j j x x x x x L 1 0 1 x x x x 1 1 0 1 1 ) ( j j j j x x x x x L ( x 0 , y 0 ) ( x 1 , y 1 ) f 1 ( x ) x y
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Lagrange Method of Interpolation-More Examples: Computer Engineering 05.04.3 0 1 0 x x x x Hence ) ( ) ( ) ( 1 0 1 0 0 1 0 1 x y x x x x x y x x x x x y 25 . 4 00 . 2 ), 1 . 7 ( 00 . 2 25 . 4 00 . 2 ) 2 . 7 ( 25 . 4 00 . 2 25 . 4 x x x ) 1 . 7 ( 00 . 2 25 . 4 00 . 2 00 . 4 ) 2 . 7 ( 25 . 4 00 . 2 25 . 4 00 . 4 ) 00 . 4 ( y ) 1 . 7 ( 88889 . 0 ) 2 . 7 ( 11111 . 0 . in 1111 . 7 You can see that 11111 . 0 ) ( 0 x L and 88889 . 0 ) ( 1 x L are like weightages given to the values of y at 00 . 2 0 x and 25 . 4 1 x to calculate the value of y at . 00 . 4 x Example 2 A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a " 10 " 15 rectangular plate. The centers of the holes in the plate describe the path the arm needs to take, and the hole centers are located on a Cartesian coordinate system (with the origin at the bottom left corner of the plate) given by the specifications in Table 2. Table 2
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida - Tampa.

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mws_com_inp_txt_lagrange_examples - Chapter 05.04 Lagrange...

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