Fitting a 2D Surface

This tutorial demonstrates how to use the 2D surface fitting mode to fit a model to data defined over a 2D grid. This is useful when your measurements depend simultaneously on two variables, and the response surface can be described by a global model of the form $z = f(x, y)$.

Step 1 – Load the data

Use File > Load Data and select:

examples/data/surface_fit_tuto.csv

This dataset includes:

  • X: the first independent variable
  • Y: the second independent variable
  • Z: the observed value at each (X, Y) point

After loading, the application automatically switches to 2D mode, and the Fit Strategy selector appears in the control dock.

Select the strategy:

Fit surface (Z = f(X, Y))

Step 2 – Define the formula

We use a 2D Gaussian surface combined with an interaction term:

z = A * exp(-((x - B)**2 + (y - C)**2) / (2 * D**2)) + E * x * y

This model contains five parameters:

  • A: amplitude of the Gaussian peak
  • B: center position along X
  • C: center position along Y
  • D: width of the Gaussian
  • E: interaction term that introduces a cross-dependence between X and Y

This formula is global: it is fitted to all points simultaneously.

Step 3 – Run the fit

Click Fit in the fit control dock. The application will:

  • Fit all data points using the selected method (default: lmfit)
  • Display the raw data and fitted surface in a3D view with crosses for data and a surface for the fit

You can also switch to alternative methods:

  • odr for orthogonal error regression
  • emcee for Bayesian sampling

For emcee, it’s often recommended to first run a classical fit to initialize the parameters.

2D surface fit

Notes

This 2D surface fitting mode assumes that all variables x, y, and z are numeric and that the formula defines a continuous surface. Avoid sharp discontinuities or piecewise expressions when using this strategy.