mws_com_inp_txt_spline_examples

mws_com_inp_txt_spline_examples - Chapter 05.05 Spline...

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05.05.1 Chapter 05.05 Spline 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 rectangle plate.

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Chapter 05.05 a) If the laser is traversing from 00 . 2 x to 25 . 4 x in a linear path, what is the value of y at 00 . 4 x using linear splines? b) Find the path of the robot if it follows linear splines. c) Find the length of the path traversed by the robot following linear splines. Solution a) Since we want to find the value of y at 00 . 4 x , we need to choose the two data points closest to 00 . 4 x that also bracket 00 . 4 x to evaluate it. The two points are 00 . 2 0 x and 25 . 4 1 x . Then , 00 . 2 0 x 2 . 7 ) ( 0 x y , 25 . 4 1 x 1 . 7 ) ( 1 x y gives ) ( ) ( ) ( ) ( ) ( 0 0 1 0 1 0 x x x x x y x y x y x y ) 00 . 2 ( 00 . 2 25 . 4 2 . 7 1 . 7 2 . 7 x Hence 25 . 4 00 . 2 ), 00 . 2 ( 044444 . 0 2 . 7 ) ( x x x y At , 4 x ) 00 . 2 00 . 4 ( 044444 . 0 2 . 7 ) 00 . 4 ( y . in 1111 . 7 b) We have already obtained the linear spline connecting 00 . 2 x and 25 . 4 x . ), 00 . 2 ( 044444 . 0 2 . 7 ) ( x x y 25 . 4 00 . 2 x (1) The rest of the splines are as follows: ) 25 . 4 ( 25 . 4 25 . 5 1 . 7 0 . 6 1 . 7 ) ( x x y ), 25 . 4 ( 1 . 1 1 . 7 x 25 . 5 25 . 4 x (2) ) 25 . 5 ( 25 . 5 81 . 7 0 . 6 0 . 5 0 . 6 ) ( x x y ), 25 . 5 ( 39063 . 0 0 . 6 x 81 . 7 25 . 5 x (3) ) 81 . 7 ( 81 . 7 20 . 9 0 . 5 5 . 3 0 . 5 ) ( x x y ), 81 . 7 ( 0791 . 1 0 . 5 x 20 . 9 81 . 7 x (4) ) 20 . 9 ( 20 . 9 60 . 10 5 . 3 0 . 5 5 . 3 ) ( x x y ), 20 . 9 ( 0714 . 1 5 . 3 x 60 . 10 20 . 9 x
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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.

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mws_com_inp_txt_spline_examples - Chapter 05.05 Spline...

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