6.3. Function interpolation/extrapolation

It is possible to specify the method of interpolation to be used for nonlinear function tables by use of the interpolate attribute of the independentVarPts and independentVarRef elements. This attribute, combined with the extrapolate flag, provides several different ways of realizing the intermediate values of the function when not at one of the specified intersections of independent values.

Possible values for the interpolate attribute are:

discrete

Output uses value associated with nearest breakpoint

floor

Output uses value associated with next (numerically higher) breakpoint

ceiling

Output uses value associated with last (numerically lower) breakpoint

linear (default)

Output is linearly interpolated between breakpoints

quadraticSpline

Output follows a quadratic spline fit through values associated with two nearby breakpoints

cubicSpline

Output follows a cubic spline fit through values associated with three nearby breakpoints

Possible values for the extrapolate attribute are:

neither (default)

Output is held constant at value associated with closest end of breakpoints if the input value is outside the limits of the associated breakpoint set

min

Output follows extrapolated values of function if the input is below the minimum breakpoint value

max

Output follows extrapolated values of function if the input is above maximum breakpoint value

both

Output follows extrapolated values of function if the input is outside the limits of the associated breakpoint set

Implementation of the specific interpolation algorithm is left up to the implementer. One reference is the Wikipedia entry on interpolation [wiki01].

The following implementation notes are suggested:

For discrete interpolation,

The default value for interpolate is linear. The default value for extrapolate is neither.

Figures 4 and 5 below give nine different examples for a 1D table whose independent values are [1, 3, 4, 6, 7.5] with dependent values of [2, 6, 5, 7, 1.5].

Figure 4.  Example of the three discrete enumeration values of interpolate attribute of the independentVarPts and independentVarRef elements for a 1D function table.

Example of the three discrete enumeration values of interpolate attribute of the independentVarPts and independentVarRef elements for a 1D function table.

Figure 5.  Examples of the three higher-order interpolation methods showing the effect of the interpolate attribute of the independentVarPts and independentVarRef elements for a 1D function table.

Examples of the three higher-order interpolation methods showing the effect of the interpolate attribute of the independentVarPts and independentVarRef elements for a 1D function table.

2011-03-25