mws_com_inp_txt_ndd_examples

# mws_com_inp_txt_ndd_examples - Chapter 05.03 Newtons...

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05.03.1 Chapter 05.03 Newton’s Divided Difference 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 holes on the rectangular plate.

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05.03.2 Chapter 05.03 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 Newton’s divided difference method of interpolation and a first order polynomial? Solution For linear interpolation, the value of y is given by ) ( ) ( 0 1 0 x x b b x y Since we want to find the value of y at 00 . 4 x , using the two points 00 . 2 x and 25 . 4 x , then , 00 . 2 0 x 2 . 7 ) ( 0 x y , 25 . 4 1 x 1 . 7 ) ( 1 x y gives ) ( 0 0 x y b 2 . 7 0 1 0 1 1 ) ( ) ( x x x y x y b 00 . 2 25 . 4 2 . 7 1 . 7 044444 . 0 Hence ) ( ) ( 0 1 0 x x b b x y ), 00 . 2 ( 044444 . 0 2 . 7 x 25 . 4 00 . 2 x At 00 . 4 x ) 00 . 2 00 . 4 ( 044444 . 0 2 . 7 ) 00 . 4 ( x . in 1111 . 7 If we expand ), 00 . 2 ( 044444 . 0 2 . 7 ) ( x x y 25 . 4 00 . 2 x we get , 044444 . 0 2889 . 7 ) ( x x y 25 . 4 00 . 2 x This is the same expression that was obtained with the direct method. 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.
Newton’s Divided Difference Interpolation-More Examples: Computer Engineering 05.03.3 Table 2 The coordinates of the holes on the plate. x

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mws_com_inp_txt_ndd_examples - Chapter 05.03 Newtons...

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