16.1 Interpolate/Extrapolate


Video Image.png See more related video:Origin VT-0010 Interpolation

Contents

Overview

1DInterpolation.png
Interpolation/extrapolation is a method of estimating and constructing new data points from a discrete set of known data points. This function generates a uniform linearly spaced interpolated curve by one of four methods: Linear, Cubic Spline, Cubic B-Spline, and Akima Spline.

In Origin, the interpolation tool also supports Apparent Interpolation so it can interpolate data according to current axis settings.
1DApparentInterpolation 01.png

To Interpolate/Extrapolate Your Data
  1. Create a new worksheet with input data.
  2. Select Analysis: Mathematics: Interpolate/Extrapolate.... This opens interp1XY dialog box.


The dialog box calls the interp1xy X-Function to perform the interpolate/extrapolate calculation.

Dialog Options

Recalculate

Controls recalculation of analysis results:

  • None
  • Auto
  • Manual

For more information, see: Recalculating Analysis Results

Input

Specifies the XY range to be interpolated.

For help with range controls, see: Specifying Your Input Data

Method

Specify the interpolation/extrapolation method.

  • Linear
    Linear interpolation is a fast method of estimating a data point by constructing a line between two neighboring data points. This method is generally less accurate than more computationally-intensive methods.
  • Cubic Spline
    This method splits the input data into a given number of pieces, and fits each segment with a cubic polynomial. The second derivative of each cubic function is set equal to zero. With these boundary conditions met, an entire function can be constructed in a piece-wise manner.
  • Cubic B-Spline
    This method also splits the input data into pieces, each segment is fitted with discrete Bezier splines.
  • Akima Spline
    This method is based on a piecewise function composed of a set of polynomials. The Akima interpolation is stable to outliers.
Generate X Data by

It supplies two options for generating X Data

  • Number of Points
    Specifies the number of interpolated points.
  • Increment
    Specifies the increment when interpolate by Sampling Interval
X Start

The start X value of interpolated curve.

Note: if want to generate a descending x data, you can X Start>X End.

X end

The end X value of interpolated curve.

An Inverse button Inverse Button.png shows after the Auto checkbox to switch the values of X Start and X End.

Boundary

Boundary condition is only available in Cubic Spline method.

  • Natural
    2nd derivatives are 0 on both ends.
  • Not-A-Knot
    3rd derivatives are continuous on the second and last-second point.
Smoothing Factor

A non-negative parameter that specifies the smoothness of the interpolated curve in Cubic B-Spline interpolation. The factor helps user control the balance between the smoothing and closeness. Larger values will result in smoother curves.

Smoothing is only available in Cubic B-Spline method.

Coefficients

Spline coefficients when using spline or B-spline method.

Apparent Interpolation

Available only when the interpolation is performed on a graph. If selected, interpolation is performed using apparent values when the axes scale type has been changed (from linear to log10, for instance).

Output

Specifies the output XY data range.

Algorithm

For algorithm details, please refer to Interpolate Extrapolate Y from X.

References

For reference details, please refer to Interpolate/Extrapolate Y from X.