1 / 27

Understanding Spline Interpolation in Industrial Engineering

Explore spline interpolation methods for industrial engineering majors authored by Autar Kaw and Jai Paul, transforming STEM education with numerical methods. Learn about interpolation using polynomials and splines with examples. Discover linear and quadratic interpolation techniques. Compare solutions and access additional resources on spline methods.

guilford
Download Presentation

Understanding Spline Interpolation in Industrial Engineering

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Spline Interpolation Method Industrial Engineering Majors Authors: Autar Kaw, Jai Paul http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates http://numericalmethods.eng.usf.edu

  2. Spline Method of Interpolationhttp://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. http://numericalmethods.eng.usf.edu

  4. Interpolants Polynomials are the most common choice of interpolants because they are easy to: • Evaluate • Differentiate, and • Integrate. http://numericalmethods.eng.usf.edu

  5. Why Splines ? http://numericalmethods.eng.usf.edu

  6. Why Splines ? Figure : Higher order polynomial interpolation is a bad idea http://numericalmethods.eng.usf.edu

  7. Linear Interpolation http://numericalmethods.eng.usf.edu

  8. Linear Interpolation (contd) http://numericalmethods.eng.usf.edu

  9. 4 3 5 2 6 Y 1 X 7 Example A curve needs to be fit through the given points to fabricate the cam. If the cam follows a straight line profile between x = 1.28 to x = 0.66, what is the value of y at x=1.1 ? Find using linear spline interpolation. http://numericalmethods.eng.usf.edu

  10. Linear Interpolation http://numericalmethods.eng.usf.edu

  11. Linear Interpolation Find the cam profile using linear splines. http://numericalmethods.eng.usf.edu

  12. Linear Interpolation http://numericalmethods.eng.usf.edu

  13. Quadratic Interpolation http://numericalmethods.eng.usf.edu

  14. Quadratic Interpolation (contd) http://numericalmethods.eng.usf.edu

  15. Quadratic Splines (contd) http://numericalmethods.eng.usf.edu

  16. Quadratic Splines (contd) http://numericalmethods.eng.usf.edu

  17. Quadratic Splines (contd) http://numericalmethods.eng.usf.edu

  18. 4 3 5 2 6 Y 1 X 7 Example A curve needs to be fit through the given points to fabricate the cam. If the cam follows a straight line profile between x = 1.28 to x = 0.66, what is the value of y at x=1.1 ? Find using a quadratic spline interpolation. http://numericalmethods.eng.usf.edu

  19. Solution http://numericalmethods.eng.usf.edu

  20. Solution (contd) http://numericalmethods.eng.usf.edu

  21. Solution (contd) http://numericalmethods.eng.usf.edu

  22. Solution (contd) http://numericalmethods.eng.usf.edu

  23. Solution (contd) http://numericalmethods.eng.usf.edu

  24. Solution (contd) http://numericalmethods.eng.usf.edu

  25. Comparison http://numericalmethods.eng.usf.edu

  26. 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/spline_method.html

  27. THE END http://numericalmethods.eng.usf.edu

More Related