### Interpolation/Extrapolation

Interpolation allows you to construct new data points within the range of a discrete set of known data points, while extrapolation extends the range of new data points construction beyond the existing dataset.

In Origin, there are generally three different tools that can be utilized to perform interpolation or extrapolation operations on 2D and 3D data: Interpolation/Extrapolation, Interpolate/Extrapolate Y From X and Trace Interpolation and XYZ Trace Interpolation. All these tools support manual or auto recalculation of results upon changing data or analysis settings and the settings for the interpolation/extrapolation analysis routine can be saved to an analysis theme for later use with similar data.

The customization of interpolated/extrapolated dataset or range is highly flexible, you can either specify the number of interpolation/extrapolation points within given X/XY/XYZ ranges or provide a set of specified X/XY values. The interpolation/extrapolation methods for each scenario is rich and the methods themselves are highly controllable via additional adjustment factors.

We will demonstrate the key features of Origin Interpolation/Extrapolation in the following sections:

1D Interpolation/Extrapolation

In Origin, 1D Interpolation/Extrapolation allows you to interpolate/extrapolate for a specified X range and fixed number of points to be interpolated/extrapolated. The range is determined by X minimum, X maximum and the resolution of interpolated/extrapolated curve is controlled by number of interpolation/extrapolation points. 1D Interpolation/Extrapolation will then generate a set of interpolated/extrapolated data with uniformly-spaced X values using 4 alternative methods.

Besides Linear, Cubic Spline, Cubic B-Spline interpolation methods, Origin also supports Akima Spline interpolation. 1D Interpolation/Extrapolation can also supports Apparent Interpolation so it can interpolate data according to current axis settings:

• 1D Interpolation/Extrapolation Methods:
• 1D Apparent Interpolation:

To visually interpolate/extrapolate multiple curves simultaneously, Origin developed an Interpolate Gadget so that you can freely move and resize the Region of Interest (ROI) object to select interpolation/extrapolation range and apply current analysis to all curves or all layers.

You are allowed to switch between different data plots to quickly see their analyzed results and interpolate X/Y at multiple entered values. You can also choose what to show on top of the ROI box and control the interpolation/extrapolation limits.

• Easily Switch Between Data Plots:
• Quickly Interpolate Y from X:
• Show Information at Gadget Center-Top:
• Interpolate/Extrapolate Limits:

Interpolate/Extrapolate Y From X

Interpolate/Extrapolate Y From X allows you to choose a specified dataset not necesarily uniformly-spaced as the X dataset for interpolation/extrapolation using 4 different methods.

Interpolate/Extrapolate Y From X supports Linear, Cubic Spline, Cubic B-Spline and Akima interpolation methods, in which Cubic Spline and Cubic B-Spline provide additional adjusting settings and interpolation coefficients generation:

2D Interpolation/Extrapolation

2D Interpolation/Extrapolation allows you to interpolate/extrapolate either on a group of existing XYZ data for a given XY dataset or a specified matrix object.

Interpolate Z From XY

Interpolate Z From XY is a powerful feature newly developed in Origin 9.1 SR0, which allows you to specify a set of XY values for interpolation/extrapolation so that it offers additional freedom in 2D interpolation/extrapolation for non-uniformly spaced XY dataset.

In Origin, there are in total 8 interpolation methods available for 2D Interpolation/Extrapolation and most of the methods have extra adjustment factors or settings:

2D Interpolation/Extrapolation On Matrix

2D Interpolation/Extrapolation on Matrix is a powerful and user-friendly feature only availabe in OriginPro, which allows you to specify an uniformly spaced XY dataset for interpolation/extrapolation via choosing the First X/Y and Last X/Y and Number of Cols/Rows for a matrix.

It supports in total five methods for interpolation/extrapolation, and the XY range and number of points for interpolation/extrapolation are highly customizable:

• 2D Interpoaltion/Extrapolation on Matrix Methods:
• Easily Customizable Interpolation/Extrapolation Range and Step Size:

3D Interpolation

In Origin, 3D Interpolation uses a smooth function Q(x,y,z), which is a modification of Shepard's method, to interpolate m scattered data points. 3D Interpolation is a feature only available in OriginPro and can be performed on three dimensional scatter plots (3D XYZ Scatter, 3D XYZ Trajectory) with an additional column as 3D function column.

You can customize the data points for 3D interpolation by specifying X/Y/Z Minimum and Maximum and number of interpolation points in each dimension:

Trace Interpolation and XYZ Trace Interpolation

Trace Interpolation is different from ordinary interpolation since it interpolates the curve based on the index of X coordinate rather than adjacent data points in the X coordinate. When the curve is cyclic or periodic, it is more appropriate to use trace interpolation rather than ordinary interpolation. XYZ Trace Interpolation works the same way as Trace Interpolation but for three dimensional XYZ dataset.

Trace Interpolation

Trace Interpolation is a feature only available in OriginPro, and the graph below is an example to show the difference between ordinary interpolation and trace interpolation on the same periodic curve.

Trace Interpolation tool supports three methods to interpolate the data:

XYZ Trace Interpolation

XYZ Trace Interpolation performs trace interpolation on a given sequence of distinct XYZ triplets data.

XYZ Trace Interpolation tool also supports three methods to interpolate the data: