AKISPL
The AKISPL function returns the iord derivative of the interpolated value of SPLINE/id at X=x and Z=z.
Format
AKISPL (x, z, id)
or
AKISPL (x,0,id [,iord])
or
AKISPL (x,0,id [,iord])
Arguments
x | A real variable that specifies the independent variable value along the x-axis of the AKISPL. |
z | A real variable that specifies the second independent variable value along the z-axis of the surface being interpolated. Specify z = 0 if the SPLINE statement defines only one curve. |
id | An integer variable that specifies the identifier of a SPLINE statement that you define in the Adams Solver dataset. |
iord | An integer variable that specifies the order of the derivative to be taken at the interpolated point. iord may not be specified when interpolating on a surface (for example, when  ).Default: 0 Range: 0 < iord < 2 |
Extended Definition
The AKISPL function uses the Akima method of interpolation to create a spline function across a set of data points. The data points to be interpolated are defined by a SPLINE statement in the Adams Solver dataset. The SPLINE that you define in the dataset may represent a curve (x-y points) or a surface (x-y-z points). Interpolation in the y direction is cubic, and interpolation in the z direction is linear. To interpolate the values specified in a curve, set z = 0.
iord specifies the order of the derivative and may be used only when interpolating a curve (that is, when z = 0).
AKISPL is very fast, since it uses local methods. It always produces good results for the value of the function being approximated. AKISPL returns good estimates for the first derivative of the approximated function when the data points are evenly spaced. In instances where the data points are unevenly spaced, the estimate of the first derivative may be in error. In all cases, the second derivative of the function being approximated is unreliable.
For more information on the Akima method of interpolation, see the references listed in Additional Publications.
Tip: | If you want to force a particular region of a spline function to be linear, you should know that four consecutive points on a straight line will yield a linear section in the region between the central two points, and, similarly, four consecutive points on a straight line at the end of a spline will yield a linear fit from the second point onward. |
Examples
SFORCE/1, I=409, J=109, TRANSLATION
, FUNCTION=AKISPL(TIME, 0, 1, 1)
, FUNCTION=AKISPL(TIME, 0, 1, 1)
This SFORCE statement defines a translational force that acts between Markers 409 and 109. The SPLINE statement provides the discrete data used to generate the interpolation function using the Akima spline. Since this SPLINE statement defines only one curve, the value of z is defined to be 0. AKISPL returns the first derivative of the spline at the interpolated point since iord = 1.
See other Interpolation available.