Math

LookupTable2D Block

2-D lookup table with bilinear interpolation. Maps two input values (x, y) to an output value using breakpoints and table data.

Open LookupTable2D in BlockWerk →

# 2-D Lookup Table Block

Description

The 2-D Lookup Table block maps two input values (x, y) to an output value using bilinear interpolation within a predefined grid of data points. It is commonly used for complex nonlinear relationships that depend on two variables, such as motor efficiency maps, aerodynamic drag coefficients, or complex sensor calibrations.

Mathematical Model

Output z = f(x, y) based on:

1. Finding the bounding box: x_i <= x < x_{i+1} and y_j <= y < y_{j+1} 2. Using bilinear interpolation to calculate z within that rectangle using the 4 corner values from the tableData.

Parameters

X Breakpoints (xBreakpoints)

A space-separated list of strictly monotonically increasing values representing the x-axis grid coordinates. Example: 0 1 2 3

Y Breakpoints (yBreakpoints)

A space-separated list of strictly monotonically increasing values representing the y-axis grid coordinates. Example: 0 10 20

Table Data (tableData)

A space-separated list of output values (z). The data must be provided in row-major order (iterating through all x columns for the first y row, then the second y row, etc.). The total number of elements must equal length(xBreakpoints) * length(yBreakpoints).

Extrapolation

Behavior when inputs fall outside the defined breakpoint ranges:

Linear: Extrapolates the surface gradient linearly beyond the edges.
Clip: Limits the output to the value at the nearest boundary of the table.

Examples

Efficiency Map

Mapping speed (x) and torque (y) to determine motor efficiency (z).

Remarks

Both xBreakpoints and yBreakpoints must be strictly increasing.
Providing mismatched dimensions between breakpoints and tableData will result in configuration errors or NaN outputs.
Interpolation within the table bounds is always bilinear.