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Topography involves measuring and mapping land elevations, natural features, and artificial structures to create accurate representations of the terrain. Topographic surveying relies on traditional and modern methods, each with distinct advantages and limitations.Traditional Surveying Methods:Transit stadia surveys and plane table surveys were widely used traditional surveying methods. These techniques relied on instruments like theodolites and stadia rods for measuring distances and angles,...
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Topographic maps represent the Earth's surface features using contour lines, which connect points of equal elevation to create a two-dimensional representation of three-dimensional terrain. Creating a topographic map requires a systematic approach.Begin by plotting a scaled grid and marking intersections corresponding to the survey's elevation data points. Assign elevation values at these intersections to build the base map. Next, determine contour levels using a consistent contour interval,...
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Two 3D Fractal-Based Approaches for Topographical Characterization: Richardson Patchwork versus Sdr.

François Berkmans1,2,3, Julie Lemesle4,5, Robin Guibert1

  • 1CNRS, UMR 8201-LAMIH-Laboratoire d'Automatique de Mécanique et d'Informatique Industrielles et Humaines, University Polytechnique Hauts-de-France, F-59313 Valenciennes, France.

Materials (Basel, Switzerland)
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PubMed
Summary
This summary is machine-generated.

This study compares fractal-based surface topography analysis methods, Richardson Patchwork and Sdr parameter, finding similar relative area results. These findings may lead to a new standard fractal method for multiscale characterization.

Keywords:
Sdr parameterfractal-based analysismultiscale analysissurface topography

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Area of Science:

  • Surface Metrology
  • Fractal Analysis
  • Materials Science

Background:

  • Multiscale characterization of surface topography is crucial for understanding material properties.
  • Fractal-based approaches offer unique insights into surface complexity.
  • Existing standards like ISO 25178 provide methods for surface analysis.

Purpose of the Study:

  • To compare the Richardson Patchwork method with the Sdr parameter for multiscale surface topography characterization.
  • To analyze the relative area of grit-blasted TA6V samples using fractal-based methods.
  • To determine the relevance scale for each method in representing grit blasting effects.

Main Methods:

  • Fractal-based analysis using the Richardson Patchwork method (ASME B46.1, ISO 25178).
  • Comparison with the Sdr parameter using a low-pass Gaussian filter (ISO 25178-2).
  • Calculation of relative area on TA6V samples subjected to varying grit blasting pressures and media.

Main Results:

  • Grit-blasted surfaces exhibit fractal-like characteristics over the studied scales.
  • Both methods yielded similar relative area values, irrespective of surface complexity.
  • Relevant scales identified: 7657.64 µm² for Patchwork and 124.6 µm cut-off for Sdr.

Conclusions:

  • The Richardson Patchwork and Sdr methods provide comparable relative area measurements for fractal surfaces.
  • Specific relevance scales were determined for each method to capture grit blasting effects.
  • Results support the development of a standardized, user-friendly fractal method for multiscale relative area characterization.