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Polygon Size Estimator

The Polygon Size Estimator is an interactive tool designed to estimate the edge length of an equilateral triangular polygons in photogrammetry meshes.
Given the total number of polygons and surface area, it determines the theoretical edge length for uniform triangular elements.

tip

No mesh has a perfectly even distribution of ideal equilateral traingles. We know that.
Real-world meshes may have varying polygon sizes and shapes.
That's why this is an estimator and not a calculator.
It's meant to give the user a theoretical value, which sometimes is better than nothing.

The Tool​

Polygon Size Estimator

Mesh Parameters

Total number of triangular polygons in the mesh
Total surface area of the mesh in square meters

Results

Polygon Edge Length
0.000 m
Area per Polygon
0.00 mm²
Polygon Density
0 polygons/m²

About this Estimator tool​

This calculator determines the ideal edge length for equilateral triangular polygons in a photogrammetry mesh.
It assumes uniform polygon distribution and equal-area triangles across the surface.

  • Mesh quality assessment for photogrammetry reconstructions
  • Planning optimal polygon density for 3D models
  • Comparing mesh resolution across different capture methods
  • Estimating geometric detail level in reconstructed surfaces

How to Use the Estimator tool​

Step 1: Enter Mesh Parameters​

Number of Polygons: Enter the total count of triangular polygons in your mesh. This information is typically available in your 3D modeling software or photogrammetry processing reports.

Surface Area (m²): Input the total surface area of your mesh in square meters. This can be calculated by your photogrammetry software or measured from the reconstructed model.

Step 2: Review Results​

The tool provides three key metrics:

  • Ideal Edge Length: The theoretical edge length for perfectly uniform equilateral triangles
  • Area per Polygon: The average surface area covered by each polygon
  • Polygon Density: The number of polygons per square meter of surface

Understanding the Results​

Ideal Edge Length​

This represents the edge length that each triangular polygon would have if:

  • All polygons were perfect equilateral triangles
  • All polygons had equal area
  • Polygons were uniformly distributed across the surface

Practical Applications:

  • Mesh Quality Assessment: Compare against your actual mesh to evaluate uniformity
  • Resolution Planning: Determine target polygon counts for desired detail levels
  • Comparative Analysis: Compare mesh quality across different capture methods

Area per Polygon​

This metric shows how much surface area each polygon represents on average. Smaller values indicate higher mesh resolution and finer detail capture.

Use Cases:

  • Detail Level Estimation: Smaller polygon areas capture finer surface details
  • Processing Requirements: Higher polygon density requires more computational resources
  • Quality Benchmarking: Compare against industry standards for your application

Polygon Density​

Expressed as polygons per square meter, this metric indicates the mesh resolution density.

Applications:

  • Capture Planning: Determine required image overlap and resolution for target density
  • Performance Optimization: Balance detail level with processing and rendering performance
  • Quality Standards: Ensure mesh meets project requirements for geometric accuracy

Practical Examples​

Example 1: Building Facade​

  • Surface Area: 100 m² (10m × 10m wall)
  • Polygons: 500,000
  • Result: ~0.67mm edge length, high detail suitable for architectural documentation

Example 2: Archaeological Artifact​

  • Surface Area: 0.01 m² (10cm × 10cm object)
  • Polygons: 50,000
  • Result: ~0.021mm edge length, extremely high detail for scientific analysis

Example 3: Landscape Survey​

  • Surface Area: 10,000 m² (100m × 100m area)
  • Polygons: 1,000,000
  • Result: ~3.8mm edge length, suitable for topographic mapping

Tips for Using the Estimator tool​

Mesh Quality Assessment​

  • Compare calculated vs. actual: Use this as a baseline to evaluate mesh uniformity
  • Identify problem areas: Large deviations may indicate reconstruction issues
  • Quality control: Ensure consistent polygon density across your model

Planning Photogrammetry Captures​

  • Target resolution: Work backwards from desired edge length to plan polygon count
  • Resource allocation: Balance detail requirements with processing capabilities
  • Capture strategy: Higher polygon density requires more images and overlap

Optimization Guidelines​

  • Performance vs. Quality: Higher polygon density improves detail but increases file size
  • Application-specific: Choose appropriate density for your end use (visualization, analysis, archival)
  • Processing limits: Consider hardware capabilities when planning mesh density

Technical Notes​

Mathematical Foundation​

The calculation uses the standard formula for equilateral triangle area:

Area = (√3/4) × edge²

Solving for edge length:

edge = √((4 × Area) / √3)

Assumptions and Limitations​

  • Uniform Distribution: Assumes polygons are evenly distributed across the surface
  • Equilateral Triangles: Real meshes may have varying triangle shapes and sizes
  • Flat Surface Approximation: Complex geometries may have different effective surface areas
  • Ideal Conditions: Actual photogrammetry results depend on image quality, overlap, and processing parameters

Best Practices​

  • Use this tool as a theoretical baseline for mesh planning and assessment
  • Combine with actual mesh analysis tools for comprehensive quality evaluation
  • Consider surface complexity when interpreting results for non-planar geometries
  • Account for processing software variations in polygon generation algorithms
  • Photogrammetry Calculator: Calculate ground sampling distance and camera parameters
  • Mesh Analysis Software: Tools like MeshLab, CloudCompare for detailed mesh inspection
  • Photogrammetry Software: Agisoft Metashape, RealityCapture, OpenDroneMap for mesh generation
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