Interpolation

Gridded and scattered data interpolation, data gridding, piecewise polynomials

Interpolation is a technique for adding new data points within a range of a set of known data points. You can use interpolation to fill-in missing data, smooth existing data, make predictions, and more. Interpolation in MATLAB^® is divided into techniques for data points on a grid and scattered data points.

Several example plots of 1-D and 2-D interpolation

Functions

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1-D and Gridded Interpolation

`interp1`	1-D data interpolation (table lookup)
`interp2`	Interpolation for 2-D gridded data in meshgrid format
`interp3`	Interpolation for 3-D gridded data in meshgrid format
`interpn`	Interpolation for 1-D, 2-D, 3-D, and N-D gridded data in ndgrid format
`griddedInterpolant`	Gridded data interpolation
`pchip`	Piecewise Cubic Hermite Interpolating Polynomial (PCHIP)
`makima`	Modified Akima piecewise cubic Hermite interpolation
`spline`	Cubic spline data interpolation
`ppval`	Evaluate piecewise polynomial
`mkpp`	Make piecewise polynomial
`unmkpp`	Extract piecewise polynomial details
`padecoef`	Padé approximation of time delays
`interpft`	1-D interpolation (FFT method)

Grid Creation

`ndgrid`	Rectangular grid in N-D space
`meshgrid`	2-D and 3-D grids

Scattered Interpolation

`griddata`	Interpolate 2-D or 3-D scattered data
`griddatan`	Interpolate N-D scattered data
`scatteredInterpolant`	Interpolate 2-D or 3-D scattered data

Topics

Gridded and Scattered Sample Data
Introduction to interpolating gridded and scattered data sets.
Interpolating Gridded Data

Interpolation of regularly spaced, axis-aligned data sets.
- Interpolation of Multiple 1-D Value Sets
- Interpolation of 2-D Selections in 3-D Grids
Interpolating Scattered Data

Interpolating scattered data using scatteredInterpolant.
- Extrapolating Scattered Data
- Interpolation Using a Specific Delaunay Triangulation

Featured Examples

Resample Image with Gridded Interpolation

Use griddedInterpolant to resample the pixels in an image. Resampling an image is useful for adjusting the resolution and size, and you also can use it to smooth out the pixels after zooming.

Open Live Script

Normalize Data with Differing Magnitudes

Use normalization to improve scattered data interpolation results with griddata. Normalization can improve the interpolation results in some cases, but in others it can compromise the accuracy of the solution. Whether to use normalization is a judgment made based on the nature of the data being interpolated.

Open Live Script

Teaching Resources

Numerical Methods with Applications

Learn methods for interpolation, numerical integration and derivation, and finite difference methods for differential equations.