Calculate Geometric Attributes of Spatial Polygons

Calculate geometric attributes of spatial polygons including area, perimeter, compactness, elongation, orientation (bearing), fractal dimension, and various shape indices. The package relies heavily on 'terra' methods and vector data objects < https://github.com/rspatial/terra>.

geomattR

Overview

Honestly, I use developing this package as a way to learn about spatial indices by decomposing their formulas and explaining to myself how they work while writing the documentation.

geomattR provides a comprehensive toolkit for calculating geometric and morphometric attributes of spatial polygons. It computes area, perimeter, compactness, elongation, orientation, fractal dimension, and various shape indices.

This package is particularly useful for: - Geospatial analysts analyzing shape and size of geographic features - Urban planners characterizing building and neighborhood geometry - Environmental scientists studying habitat patch metrics - Remote sensing practitioners extracting morphological features from vector data - Landscape ecologists quantifying landscape structure - Political scientists examining electoral district shapes - Epidemiologists analyzing spatial spread patterns

Core spatial calculations use the terra package for efficient spatial data handling and geodesic measurement support, while geosphere is used for bearing estimation when a metric requires geographic coordinates. Distance- and area-based metrics are computed, and shape indices are derived from those quantities.

Installation

Install from GitHub:

# Install devtools if needed
# install.packages("devtools")
devtools::install_github("gortegasolis/geomattR")

Quick Start

library(geomattR)
library(terra)

# Create a sample polygon (WGS84 - geographic CRS)
coords <- cbind(c(0, 0, 1, 1, 0), c(0, 1, 1, 0, 0))
polygon <- vect(coords, type = "polygon", crs = "EPSG:4326")

# Calculate all geometric attributes (uses geodesic measurements automatically)
result <- calculate_geometric_attributes(polygon)

# View results
print(result)

# Calculate only specific metrics
result_subset <- calculate_geometric_attributes(
  polygon,
  metrics = c("area", "perimeter", "compactness", "bearing")
)

Features

Available Metrics

Size Metrics

• area: Total area in square meters.
• perimeter: Total perimeter length in meters.
• hole_area: Total area of interior holes in square meters.
• hole_area_pct: Percentage of the gross polygon area (including holes) occupied by holes: $HA% = \frac{\text{hole_area}}{\text{area} + \text{hole_area}} \times 100$.

Shape Metrics

• compactness: Polsby-Popper compactness, a circularity index that compares polygon area to the area of a circle with the same perimeter: $C = \frac{4\pi A}{P^2}$. Values closer to 1 indicate more compact (circle-like) shapes.
• reock: Reock compactness, defined as polygon area relative to the area of its minimum enclosing circle: $R = \frac{A}{A_{MEC}}$. Values closer to 1 indicate that the polygon fills its enclosing circle more efficiently.
• elongation_rectangle: Elongation index from the minimum bounding rectangle of the convex hull. In the current implementation, it is computed as the mean of the two largest side lengths divided by the mean of the two shortest side lengths: $E = \frac{\text{mean}(\text{long sides})}{\text{mean}(\text{short sides})}$.
• shape_index: Dimensionless irregularity index comparing polygon perimeter to the perimeter of a circle with the same area: $SI = \frac{P}{2\sqrt{\pi A}}$. A value of 1 corresponds to a perfect circle; larger values indicate increasing irregularity.
• circularity_ratio: Circularity index based on area and maximum hull distance: $CR = \frac{4A}{\pi L_{\max}^2}$.
• fractaldimension: Perimeter-area scaling index of boundary complexity following the FRAGSTATS convention: $D = \frac{2\ln(0.25P)}{\ln(A)}$. Approaches 1 for simple (square-like) shapes and 2 for highly convoluted boundaries.

Orientation Metrics

• bearing: Axial orientation of the maximum length line, measured as the geographic bearing from the southernmost to the northernmost point, in decimal degrees ($-90^{\circ}$ to $90^{\circ}$). Because the line is always oriented south-to-north, it describes the orientation of an axis, not a travel direction: $-90^{\circ}$/ $90^{\circ}$ is east-west, $0^{\circ}$ is north-south.
• northerness: Cosine of bearing: $N = \cos(\text{bearing} \times \frac{\pi}{180})$ (ranges from 0 to 1; 1 = north-south axis, 0 = east-west axis).
• ew_length: Average east-west extent in meters: $EW = \frac{d(NW, NE) + d(SW, SE)}{2}$.
• ns_length: Average north-south extent in meters: $NS = \frac{d(SW, NW) + d(SE, NE)}{2}$.
• maxlength: Maximum distance across the convex hull: $L_{\max} = \max_{p_i, p_j} d(p_i, p_j)$.

Geometry Metrics

• num_holes: Number of interior holes (rings).
• num_polygons: Number of separate polygon parts (multi-part count).
• decimallongitude: Centroid longitude in decimal degrees.
• decimallatitude: Centroid latitude in decimal degrees.
• sinuosity: Perimeter-to-diameter proxy (perimeter divided by maximum hull distance): $S = \frac{P}{L_{\max}}$.

Geodesic Calculations

geomattR prioritizes geodesic calculations by default (method = "geo"), which makes the metrics suitable for continental or global scale studies. haversine and cosine are also supported as faster (but less precise) great-circle approximations. All three methods are lon/lat great-circle methods; if the input has a projected CRS, terra::distance() ignores method and computes Cartesian distances instead. For methods that need geographic coordinates, the package will transform the geometry to WGS84 internally and then restore the output geometry to the original CRS when applicable.

Area, perimeter, extent, maximum distance, and bearing are computed according to the selected method. Derived shape indices (for example compactness, sinuosity, and fractaldimension) are calculated from those base quantities. For details on the methods geo, haversine and cosine, please refer to the documentation of the terra package.

Documentation

Full documentation is available in R:

?calculate_geometric_attributes
?get_distant_points
?calc_elongation

Related Packages

• terra: Foundational spatial data handling (required)
• geosphere: Geodetic bearing calculations (required)
• sf: Alternative vector format support
• NLMR: Neutral landscape models with shape metrics
• landscapemetrics: Comprehensive landscape ecology metrics

Citation

If you use geomattR in your research, please cite also terra and geosphere:

citation("geomattR")

License

MIT License - see LICENSE file for details

Contributing

Contributions are welcome! Please open an issue or submit a pull request on GitHub.

Author

Gabriel Ortega-Solís ([email protected]) ORCID: 0000-0002-0516-5694

Acknowledgment

This package began as a side project during my time as a technician on BEAST – BiodivErsity dynamics Across a continuum of Space, Time, and their scales, led by Petr Keil, and was therefore partially funded by the European Union (ERC, BEAST, grant no. 101044740). Views and opinions expressed are those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency; neither the European Union nor the granting authority can be held responsible for them.

Discussions with P. Keil on spatial and geometric problems inspired the package. G. Ortega-Solís developed all core functions; Claude Code was used to double-check the code and to help write unit tests.