Basic spline interpolation

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.

4. Why Splines ?

5. Why Splines ? Figure : Higher order polynomial interpolation is a bad idea

6. Linear Interpolation

7. Linear Interpolation (contd)

9. Linear Interpolation

10. Quadratic Interpolation

11. Quadratic Interpolation (contd)

12. Quadratic Splines (contd)

13. Quadratic Splines (contd)

14. Quadratic Splines (contd)

16. Solution

17. Solution (contd)

18. Solution (contd)

19. Solution (contd)

20. Solution (contd)

21. Solution (contd)

23. Acceleration from Velocity Profile , Find the acceleration of the rocket at t=16s. The quadratic spline valid at t=16 is given by