<p>Scanning probe microscopy (SPM) is a powerful technique for mapping nanoscale surface properties through tip–sample interactions. Thermal scanning-probe lithography (tSPL) is an advanced SPM variant that uses a silicon tip on a heated cantilever to sculpt and measure the topography of polymer films with nanometer precision. The surfaces produced by tSPL—smooth topographic landscapes—allow mathematically defined contours to be fabricated on the nanoscale, enabling sophisticated functionalities for photonic, electronic, chemical and biological technologies. Evaluating the physical effects of a landscape requires fitting arbitrary mathematical functions to SPM datasets; however, this capability does not exist in standard analysis programs. Here, we provide an open-source software package (FunFit) to fit analytical functions to SPM data and develop a fabrication and characterization protocol based on this analysis. We demonstrate the benefit of this approach by patterning periodic and quasi-periodic landscapes in a polymer resist with tSPL, which we transfer to hexagonal boron nitride (hBN) flakes with high fidelity via reactive ion etching. The topographic landscapes in polymers and hBN are measured with tSPL and atomic force microscopy, respectively. Within the FunFit program, the datasets are corrected for artifacts, fit with analytical functions and compared, providing critical feedback on the fabrication procedure. This approach can improve analysis, reproducibility and process development for a broad range of SPM experiments. The protocol can be performed within a working day by a trained graduate student or researcher, where fabrication and characterization take a few hours, and software analysis takes a few minutes.</p>