Spline Interpolation and Analysis
Spreadsheet
31 rows x 3 columns
| A | B | C | |
|---|---|---|---|
| 1 | Spline Interpolation | ||
| 2 | Sample Data | ||
| 3 | X Values | Y Values | |
| 4 | 0 | 0 | |
| 5 | 1 | 2.5 | |
| 6 | 2 | 4.2 | |
| 7 | 3 | 5.1 | |
| 8 | 4 | 4.8 | |
| 9 | 5 | 3.2 | |
| 10 | |||
| 11 | Interpolation Point | 2.5 | |
| 12 | |||
| 13 | Cubic Spline Analysis | ||
| 14 | Interpolated Value | 4.766447368 | - |
| 15 | First Derivative | 0.925 | - |
| 16 | Integral (0 to t) | 6.962911184 | - |
| 17 | Integral (1 to 4) | 13.21710526 | - |
| 18 | |||
| 19 | Linear Spline Analysis | ||
| 20 | Interpolated Value | 4.65 | - |
| 21 | First Derivative | 0.9 | - |
| 22 | Integral (0 to t) | 6.8125 | - |
| 23 | Integral (1 to 4) | 12.95 | - |
| 24 | |||
| 25 | Comparison at Multiple Points | ||
| 26 | t | Cubic | Linear |
| 27 | 0.5 | 1.315131579 | 1.25 |
| 28 | 1.5 | 3.454605263 | 3.35 |
| 29 | 2.5 | 4.766447368 | 4.65 |
| 30 | 3.5 | 5.129605263 | 4.95 |
| 31 | 4.5 | 4.102631579 | 4 |
Description
Demonstrate spline interpolation functions for data analysis. Compare cubic and linear spline methods for interpolation, differentiation, and integration.
Spline Types:
- Cubic Spline: Smooth curve passing through all points, continuous first and second derivatives
- Linear Spline: Piecewise linear interpolation, simple but may have discontinuous derivatives
How to use this blueprint
- In Excel, go to the Petroleum Office ribbon tab and click Blueprint Manager
- Search for Spline Interpolation and Analysis
- Click on the blueprint to preview the spreadsheet template
- Click Insert to place it into your worksheet. Modify the input values to match your data.