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Related Concept Videos

Areas Within Irregular Boundaries01:26

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Calculating areas within irregular boundaries, such as along rivers or curved roads, is crucial in various fields, including surveying, engineering, and environmental management. Surveyors often begin by creating a traverse, a connected series of straight lines approximating the area's boundary. The coordinates of each traverse point are essential for calculating the enclosed area. The double meridian distance formula is a widely used technique for this purpose. This method utilizes the...
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Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific...
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Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
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Updated: May 5, 2026

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Clusters in irregular areas and lattices.

William F Wieczorek1, Alan M Delmerico, Peter A Rogerson

  • 1Center for Health and Social Research, State University of New York College at Buffalo, CLAS A203 Buffalo, NY, USA.

Wiley Interdisciplinary Reviews. Computational Statistics
|November 28, 2013
PubMed
Summary

Polygon shape and size significantly impact spatial analysis results, affecting visualization and clustering statistics. The choice of areal units, whether irregular census boundaries or regular lattices, depends on specific analytical needs.

Keywords:
cluster analysisgeographic information systemsgeostatisticsneighborhoods

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Area of Science:

  • Spatial analysis
  • Geographic information systems
  • Spatial statistics

Background:

  • Geographic areas with count or rate data are common in various fields.
  • Political or census boundaries are frequently used for spatial analyses due to data availability.
  • Polygon shape can influence spatial statistical properties like clustering.

Purpose of the Study:

  • To examine the impact of polygon shape and size on spatial data visualization and statistical properties.
  • To compare the effects of regular lattices (hexagons, squares) versus irregular census areas (zip codes, tracts).

Main Methods:

  • Utilized point data (alcohol outlets) geocoded and allocated to regular lattices and census areas.
  • Set lattice unit numbers to approximate census area counts.
  • Employed spatial clustering statistics and visualization to assess polygon shape impact.

Main Results:

  • Observed substantial similarities and notable differences in results across various polygon shapes and sizes.
  • Demonstrated that irregular census polygons may capture characteristics missed by large regular lattices.
  • Found that polygon shape and size influence spatial clustering and visualization.

Conclusions:

  • The selection of areal unit size and shape is critical and depends on the specific spatial analysis context.
  • Irregular census boundaries may offer advantages in reflecting underlying characteristics.
  • Further research on combining irregular polygons and regular lattices is recommended.