# PS Scattered Lookup Table (3D)

Approximate three-dimensional function using scattered data lookup

Since R2023a

Libraries:
Simscape / Foundation Library / Physical Signals / Lookup Tables

## Description

The PS Scattered Lookup Table (3D) block computes an approximation to some function `f=f(x1,x2,x3)` given the coordinates of a scattered set of input data points in a 3D space and function values at each of these data points. The three inputs and the output are physical signals. The inputs specify the coordinates of a query point along the three directions. The output is the computed function value corresponding to the input query point.

The block computes an output value by using Delaunay triangulation to interpolate the query input value against an unstructured, or scattered, set of data points. You define the lookup table by specifying the Data points coordinate 1 parameter (vector of data point coordinates along the first direction), the Data points coordinate 2 parameter (vector of coordinates of the same data points along the second direction), the Data points coordinate 3 parameter (vector of coordinates of the same data points along the third direction), and the Data points function value (vector of function values corresponding to each of these data points). All four vectors must be of the same size.

## Ports

### Input

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The query input value along the first direction, specified as a scalar or as an N-D array.

The query input value along the second direction, specified as a scalar or as an N-D array. The signal size must match the signal size along the first direction.

The query input value along the third direction, specified as a scalar or as an N-D array. The signal size must match the signal size along the first direction.

### Output

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Output function value, based on applying the scattered lookup method to the two input values. The output signal size matches the input signal size along the first direction. The output signal unit is determined by the unit of the Data points function value parameter.

## Parameters

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Data set of input values along the first direction, specified as a one-dimensional array. Specify at least four values.

Parameter unit must be commensurate with the unit of the input signal at port x1. By default, the unit is `1` (unitless). You can select a different unit from the drop-down list or type the desired unit name, such as `rpm`, or a valid expression, such as `rad/s`. For more information and a list of unit abbreviations, see How to Specify Units in Block Dialogs and Unit Definitions.

Data set of input values along the second direction, specified as a one-dimensional array of the same size as Data points coordinate 1.

Parameter unit must be commensurate with the unit of the input signal at port x2. By default, the unit is `1` (unitless). You can select a different unit from the drop-down list or type the desired unit name, such as `rpm`, or a valid expression, such as `rad/s`. For more information and a list of unit abbreviations, see How to Specify Units in Block Dialogs and Unit Definitions.

Data set of input values along the third direction, specified as a one-dimensional array of the same size as Data points coordinate 1.

Parameter unit must be commensurate with the unit of the input signal at port x3. By default, the unit is `1` (unitless). You can select a different unit from the drop-down list or type the desired unit name, such as `rpm`, or a valid expression, such as `rad/s`. For more information and a list of unit abbreviations, see How to Specify Units in Block Dialogs and Unit Definitions.

Data set of function values for the lookup, specified as a one-dimensional array of the same size asData points coordinate 1.

Parameter unit determines the unit of the output signal at port f. By default, the unit is `1` (unitless). You can select a different unit from the drop-down list or type the desired unit name, such as `rpm`, or a valid expression, such as `rad/s`. For more information and a list of unit abbreviations, see How to Specify Units in Block Dialogs and Unit Definitions.

Select the approximation method for calculating the output value when the input value is outside the convex hull of the data set:

• `Linear` — Linear extrapolation based on boundary gradients.

• `Nearest` — Nearest neighbor extrapolation. This method evaluates to the value of the nearest neighbor on the boundary.

## Version History

Introduced in R2023a