Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

12,313 views

Published on

Basic spline interpolation

No Downloads

Total views

12,313

On SlideShare

0

From Embeds

0

Number of Embeds

46

Shares

0

Downloads

380

Comments

0

Likes

4

No embeds

No notes for slide

- 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 <ul><li>Polynomials are the most common choice of interpolants because they are easy to: </li></ul><ul><ul><li>Evaluate </li></ul></ul><ul><ul><li>Differentiate, and </li></ul></ul><ul><ul><li>Integrate . </li></ul></ul>
- 4. Why Splines ?
- 5. Why Splines ? Figure : Higher order polynomial interpolation is a bad idea
- 6. Linear Interpolation
- 7. Linear Interpolation (contd)
- 8. Example <ul><li>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. </li></ul>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 <ul><li>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. </li></ul>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 <ul><li>Find the distance covered by the rocket from t=11s to </li></ul><ul><li>t=16s </li></ul>
- 23. Acceleration from Velocity Profile , Find the acceleration of the rocket at t=16s. The quadratic spline valid at t=16 is given by

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment