CurveExpert Professional 2.7.3 documentation

# Interpolation¶

## Introduction¶

An interpolation, by definition, passes through every data point, and as such, the correlation coefficient will always be 1, and the standard error will always be zero. CurveExpert Professional supports polynomial splines and tension splines. All splines are defined in a piecewise fashion between data points.

Note

The dataset must be sorted (based on the independent variable) in order for any spline interpolation to work. Select Data->Sort from the main menu in order to sort your dataset if necessary. If CurveExpert Professional detects that your dataset is not sorted, it will not allow spline interpolations to be selected.

Note

Currently, CurveExpert Professional supports interpolation for datasets with one independent variable only. For multivariate datasets, all interpolations will be disabled.

## Linear Splines¶

To calculate a linear spline, select Calculate->Linear Spline from the main menu. The linear spline is simply a polynomial spline of order 1. It appears as a “dot-to-dot” connecting each point with a straight line segment. Linear splines only guarantee continuity of the spline at the data points.

## Cubic Splines¶

To calculate a cubic spline, select Calculate->Cubic Spline from the main menu. The cubic spline is simply a polynomial spline of order 3; cubic splines are the most common form of spline. Cubic splines guarantee continuity in the spline, and continuity in the first and second derivatives of the spline at the data points. At the endpoints, the second derivative is set to zero, which is termed a “natural” spline at the endpoints, as the curvature goes to zero.

## Polynomial Splines¶

To calculate a generic polynomial spline, select Calculate->Polynomial Spline from the main menu. A prompt will appear to ask for the degree of the polynomial spline; by way of example, a degree of 1 would be a linear spline, and a degree of 3 would be a cubic spline.

## Tension Splines¶

To calculate a tension spline, select Calculate->Tension Spline from the main menu. A prompt will appear to ask for the amount of tension desired. Tension splines are based on hyperbolic functions, and simulate a cord being stretched with a defined tension (amount of force) between the data points. An extremely high tension approaches a linear spline, and low tensions will appear correspondingly “loose” around the data points, resembling a cubic spline.