mws_com_inp_txt_lagrange_examples

# mws_com_inp_txt_lagrange_examples - Chapter 05.04 Lagrange...

This preview shows pages 1–4. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 9

mws_com_inp_txt_lagrange_examples - Chapter 05.04 Lagrange...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online