# Two 3D Fractal-Based Approaches for Topographical Characterization: Richardson Patchwork versus Sdr

## TL;DR

This paper compares two fractal-based methods for analyzing surface topography, finding they yield similar results despite different approaches.

## Contribution

The study identifies a relevant scale for each method that captures the effect of grit blasting parameters on surface area.

## Key findings

- The relative area calculated by both Richardson Patchwork and Sdr methods is similar across different surface complexities.
- A tiling of 7657.64 µm² is relevant for the Patchwork method, while a 124.6 µm cut-off is relevant for the Sdr method.
- The fractal-like characteristics of grit-blasted surfaces enable multiscale analysis of relative area.

## Abstract

Various methods exist for multiscale characterization of surface topographies, each offering unique insights and applications. The study focuses on fractal-based approaches, distinguishing themselves by leveraging fractals to analyze surface complexity. Specifically, the Richardson Patchwork method, used in the ASME B46.1 and ISO 25178 standards, is compared to the Sdr parameter derived from ISO 25178-2, with a low-pass Gaussian filter for multiscale characterization. The comparison is performed from the relative area calculated on topographies of TA6V samples grit blasted with different pressures and blasting materials (media). The surfaces obtained by grit blasting have fractal-like characteristics over the scales studied, enabling the analysis of area development at multiple levels based on pressure and media. The relative area is similar for both methods, regardless of the complexity of the topographies. The relevance scale for each calculation method that significantly represents the effect of grit blasting pressure on the increased value of the relative area is a tiling of 7657.64 µm² of triangle area for the Patchwork method and a 124.6 µm cut-off for the low-pass Gaussian filter of the Sdr method. These results could facilitate a standard, friendly, new fractal method for multiscale characterization of the relative area.