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Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
Spline Interpolation
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Spline Interpolation

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Basic spline interpolation

Basic spline interpolation

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Transcript

  • 1. Interpolation Topic: Spline Interpolation Method Major: General
  • 2. What is Interpolation ? Given (x 0 ,y 0 ), (x 1 ,y 1 ), …… (x n ,y n ), find the value of ‘y’ at a value of ‘x’ that is not given.
  • 3. Interpolants
    • Polynomials are the most common choice of interpolants because they are easy to:
      • Evaluate
      • Differentiate, and
      • Integrate .
  • 4. Why Splines ?
  • 5. Why Splines ? Figure : Higher order polynomial interpolation is a bad idea
  • 6. Linear Interpolation
  • 7. Linear Interpolation (contd)
  • 8. Example
    • The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using linear splines.
    Table : Velocity as a function of time Figure : Velocity vs. time data for the rocket example 901.67 30 602.97 22.5 517.35 20 362.78 15 227.04 10 0 0 m/s s v(t) t
  • 9. Linear Interpolation
  • 10. Quadratic Interpolation
  • 11. Quadratic Interpolation (contd)
  • 12. Quadratic Splines (contd)
  • 13. Quadratic Splines (contd)
  • 14. Quadratic Splines (contd)
  • 15. Example
    • The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using quadratic splines.
    Table : Velocity as a function of time Figure : Velocity vs. time data for the rocket example 901.67 30 602.97 22.5 517.35 20 362.78 15 227.04 10 0 0 m/s s v(t) t
  • 16. Solution
  • 17. Solution (contd)
  • 18. Solution (contd)
  • 19. Solution (contd)
  • 20. Solution (contd)
  • 21. Solution (contd)
  • 22. Distance from Velocity Profile
    • Find the distance covered by the rocket from t=11s to
    • t=16s
  • 23. Acceleration from Velocity Profile , Find the acceleration of the rocket at t=16s. The quadratic spline valid at t=16 is given by

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