مقایسهٔ روش‌ها

	Compactness Index	Urban Sprawl Measurement
حوزه	Urban Studies	Urban Studies
خانواده	Process / pipeline	Process / pipeline
سال پیدایش	2010	2014
پدیدآور	Geographic shape-analysis tradition (Richardson, Cole; codified by Angel, Parent & Civco)	Reid Ewing & Shima Hamidi (building on Galster et al.)
نوع	Geometric/morphological index of how compact a settlement footprint is	Composite index combining multiple dimensions of urban form into a sprawl/compactness score
منبع بنیادین	Angel, S., Parent, J., & Civco, D. L. (2010). Ten compactness properties of circles: Measuring shape in geography. The Canadian Geographer, 54(4), 441–461.	Ewing, R., & Hamidi, S. (2015). Compactness versus sprawl: A review of recent evidence from the United States. Journal of Planning Literature, 30(4), 413–432.
نام‌های دیگر	Shape Compactness Measure, Polsby-Popper Index, Richardson Compactness, Perimeter-Area Compactness	Sprawl Index, Compactness Index of Sprawl, Ewing Sprawl Index, Composite Sprawl Measure
مرتبط	4	4
خلاصه	A compactness index measures how compact the shape of a settlement, district, or built-up area is, almost always by comparing it to the circle — the most compact shape enclosing a given area. Classic indices such as the Polsby–Popper or Richardson ratio compare a polygon's area to its perimeter, while more elaborate measures compare interpoint distances or fitted circles, all returning a value of one for a perfect circle and falling toward zero as the shape becomes elongated, indented, or fragmented. Angel, Parent and Civco systematized these into a coherent family by showing that the circle is optimal on ten distinct geometric properties, clarifying which index answers which question.	Urban sprawl measurement quantifies how compact or sprawling a metropolitan region is by combining several distinct dimensions of urban form into a single composite index. The dominant approach, developed by Reid Ewing, Shima Hamidi and colleagues, captures four factors — development density, land-use mix, activity centering, and street-network connectivity — and folds standardized indicators of each into one score, calibrated so the average region equals 100 and higher values mean greater compactness. Because sprawl is multidimensional, no single variable such as density adequately describes it, which is why the composite-index strategy has become the standard for comparing regions and linking form to outcomes.