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Lagrangian Interpolation

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Major: Computer Science. http://numericalmethods.eng.usf.edu. 2. What is Interpolation ? ... A robot arm with a rapid laser scanner is doing a quick quality ... – PowerPoint PPT presentation

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Title: Lagrangian Interpolation


1
Lagrangian Interpolation
  • Computer Engineering Majors
  • Authors Autar Kaw, Jai Paul
  • http//numericalmethods.eng.usf.edu
  • Transforming Numerical Methods Education for STEM
    Undergraduates

2
Lagrange Method of Interpolation
http//numericalmethods.eng.usf.edu
3
What is Interpolation ?

Given (x0,y0), (x1,y1), (xn,yn), find the
value of y at a value of x that is not given.
4
Interpolants
  • Polynomials are the most common choice of
    interpolants because they are easy to
  • Evaluate
  • Differentiate, and
  • Integrate.

5
Lagrangian Interpolation


6
Example
  • A robot arm with a rapid laser scanner is
    doing a quick quality check on holes drilled in a
    rectangular plate. The hole centers in the plate
    that describe the path the arm needs to take are
    given below.
  • If the laser is traversing from x 2 to x
    4.25 in a linear path, find the value of y at x
    4 using the Lagrange method for linear
    interpolation.

Figure 2 Location of holes on the rectangular
plate.
7
Linear Interpolation


8
Linear Interpolation (contd)
9
Quadratic Interpolation
10
Example
  • A robot arm with a rapid laser scanner is
    doing a quick quality check on holes drilled in a
    rectangular plate. The hole centers in the plate
    that describe the path the arm needs to take are
    given below.
  • If the laser is traversing from x 2 to x
    4.25 in a linear path, find the value of y at x
    4 using the Lagrange method for quadratic
    interpolation.

Figure 2 Location of holes on the rectangular
plate.
11
Quadratic Interpolation


12
Quadratic Interpolation (contd)
13
Comparison Table
14
Example
  • A robot arm with a rapid laser scanner is
    doing a quick quality check on holes drilled in a
    rectangular plate. The hole centers in the plate
    that describe the path the arm needs to take are
    given below.
  • If the laser is traversing from x 2 to x
    4.25 in a linear path, find the value of y at x
    4 using a fifth order Lagrange polynomial.

Figure 2 Location of holes on the rectangular
plate.
15
Fifth Order Interpolation




16
Fifth Order Interpolation (contd)
17
Fifth Order Polynomial (contd)
18
Fifth Order Polynomial (contd)
19
Fifth Order Polynomial (contd)
20
Fifth Order Polynomial (contd)
21
Additional Resources
  • For all resources on this topic such as digital
    audiovisual lectures, primers, textbook chapters,
    multiple-choice tests, worksheets in MATLAB,
    MATHEMATICA, MathCad and MAPLE, blogs, related
    physical problems, please visit
  • http//numericalmethods.eng.usf.edu/topics/lagran
    ge_method.html

22
  • THE END
  • http//numericalmethods.eng.usf.edu
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