L_UMTP_2DInterpolation

This function block is used for sequential 2D interpolation on a rectangular surface. It is a generalization of FB L_UMTP_BilinearInterpolation to the interpolation vectors for x and y and the selection of the interpolation type for the coordinate directions x and z: piecewise linear and cubic spline with Hermite or natural boundary conditions.

Calculation procedure in FB:

First interpolation in x-direction to determine a grid point vector. The calculation for computation time optimization is only performed with lrx change or aFALSEäTRUE edge at input xEnable.
Second interpolation in y-direction to determine the result lrz.

If lrx or lry are outside the minimum or maximum values of alrX or alrY, the input values are limited. This means that no extrapolation will be applied.

alrX and alrY must be strictly monotonically increasing.

If the basic data of the interpolation (number of interpolation points, values in alrX, alrY or alrZ or eInterpTypeX/Y) are changed, a FALSEäTRUE edge is again required at input xEnable.

The function block can also be used to perform a 1D interpolation. Therefore, the number di-NumOfYValues should be set to one.

Function: 2D-Interpolation

		L_UMTP_2DInterpolation
BOOL	—	xEnable	xValid	—	BOOL
ARRAY [*] OF LREAL	—	alrX	xError	—	BOOL
DINT	—	diNumOfXValues	eErrorID	—	L_IE1P_Error
L_UMTP_InterpolationType	—	eInterpTypeX	lrz	—	LREAL
ARRAY [*] OF LREAL	—	alrY
DINT	—	diNumOfYValues
L_UMTP_InterpolationType	—	eInterpTypeY
ARRAY [,] OF LREAL	—	alrZ
LREAL	—	lrx
LREAL	—	lry

Inputs

Name Data type	Information/possible settings
xEnable BOOL	TRUE	Perform interpolation
FALSEäTRUE	If values in alrX, alrY, alrZ or the number of interpolation points to be used or the type of interpolation for x or y are changed a positive edge at the xEnable input is required.
alrX ARRAY [*] OF LREAL	Support points in x-direction 1-based variable length vector with max. 10 entries. alrX must be strictly monotonically increasing. Equidistance is not required.
diNumOfXValues DINT	Optional: Number of values from alrX and rows in alrZ to be evaluated for interpolation
eInterpTypeX L_UMTP_InterpolationType	Type of interpolation in x-direction
alrY ARRAY [*] OF LREAL	Support points in y-direction 1-based variable length vector with max. 10 entries. alrX must be strictly monotonically increasing. Equidistance is not required.
diNumOfYValues DINT	Optional: Number of values from alrY and rows in alrZ to be evaluated for interpolation
eInterpTypeY L_UMTP_InterpolationType	Type of interpolation in y-direction
alrZ ARRAY [,] OF LREAL	Values at the interpolation points z = z(x,y) 2D matrix with variable dimension, max. 10 × 10 entries. The dimensions of alrX, alrY and alrZ must match.
lrx LREAL	x-coordinate to be evaluated
lry LREAL	y-coordinate to be evaluated

Name

Data type

Information/possible settings

xEnable

BOOL

TRUE

Perform interpolation

FALSEäTRUE

If values in alrX, alrY, alrZ or the number of interpolation points to be used or the type of interpolation for x or y are changed a positive edge at the xEnable input is required.

alrX

ARRAY [*] OF LREAL

Support points in x-direction

1-based variable length vector with max. 10 entries.

alrX must be strictly monotonically increasing. Equidistance is not required.

diNumOfXValues

DINT

Optional: Number of values from alrX and rows in alrZ to be evaluated for interpolation

eInterpTypeX

L_UMTP_InterpolationType

Type of interpolation in x-direction

alrY

ARRAY [*] OF LREAL

Support points in y-direction

1-based variable length vector with max. 10 entries.

alrX must be strictly monotonically increasing. Equidistance is not required.

diNumOfYValues

DINT

Optional: Number of values from alrY and rows in alrZ to be evaluated for interpolation

eInterpTypeY

L_UMTP_InterpolationType

Type of interpolation in y-direction

alrZ

ARRAY [*,*] OF LREAL

Values at the interpolation points z = z(x,y)

2D matrix with variable dimension, max. 10 × 10 entries. The dimensions of alrX, alrY and alrZ must match.

lrx

LREAL

x-coordinate to be evaluated

lry

LREAL

y-coordinate to be evaluated

Outputs

Name Data type	Information/possible settings
xValid BOOL	Input values are plausible and calculation of lrz successful
xError BOOL	An error has occurred
eErrorID L_IE1P_Fehler	Detailed error information
lrz LREAL	Interpolated value lrz = lrz(lrx,lry), based on the interpolation points alrX, alrY and alrZ

Application example

(* Declaration *)

alrX : ARRAY[1..10] OF LREAL;

alrY : ARRAY[1..10] OF LREAL;

alrZ : ARRAY[1..10,1..10] OF LREAL;

fb2DInterp1 : L_UMTP_2DInterpolation;

lry : LREAL;

(* Implementation *)

// support points for interpolation – x direction

alrX[1] := 0.0;

alrX[2] := 1.0;

// support points for interpolation – y direction

alrY[1] := -4.0;

alrY[2] := -2.0;

alrY[3] := 2.0;

alrY[4] := 4.0;

alrY[5] := 6.0;

alrY[6] := 10.0;

// support points for interpolation – z values

alrZ[1,1] := 11.0; alrZ[2,1] := 15.0;

alrZ[1,2] := 8.0; alrZ[2,2] := 13.0;

alrZ[1,3] := 8.0; alrZ[2,3] := 11.0;

alrZ[1,4] := 3.0; alrZ[2,4] := 7.0;

alrZ[1,5] := 5.0; alrZ[2,5] := 8.0;

alrZ[1,6] := 5.0; alrZ[2,6] := 9.0;

// call fb

fb2DInterp1(xEnable := TRUE,

alrX := alrX,

diNbrOfXValues := 1, // 1D interpolation

eInterpTypeX := L_UMTP_InterpolationType.Linear,

alrY := alrY,

diNbrOfYValues := 6, // use first 6 values of alrY

   eInterpTypeY      := L_UMTP_InterpolationType.Linear,
                           // CubicSplineNatural
                          // CubicSplineHermite

alrZ := alrZ,

lrx := 0.3,

lry := lry);

The following graphic shows the interpolation results by comparing the available interpolation types.

Comparison of the different interpolation types (in y-direction) for the above code example for different lry values at lrx := 0.3;