手法を比較

	Figure-Ground Analysis	Compactness Index
分野	Urban Studies	Urban Studies
系統	Process / pipeline	Process / pipeline
提唱年	1986	2010
提唱者	Giambattista Nolli (Nolli map, 1748); Roger Trancik (figure-ground theory)	Geographic shape-analysis tradition (Richardson, Cole; codified by Angel, Parent & Civco)
種類	Pipeline for mapping and measuring built mass versus open space in urban fabric	Geometric/morphological index of how compact a settlement footprint is
原典	Trancik, R. (1986). Finding Lost Space: Theories of Urban Design. Wiley. ISBN: 9780471289562	Angel, S., Parent, J., & Civco, D. L. (2010). Ten compactness properties of circles: Measuring shape in geography. The Canadian Geographer, 54(4), 441–461.
別名	Solid-Void Analysis, Nolli Map Analysis, Poché Mapping, Built-Mass and Open-Space Analysis	Shape Compactness Measure, Polsby-Popper Index, Richardson Compactness, Perimeter-Area Compactness
関連	4	4
概要	Figure-ground analysis is an urban-design technique that maps a city as a pattern of solids and voids — buildings rendered as black figure against the white ground of streets, squares, and open space (or vice versa) — to reveal the structure, density, and spatial quality of the urban fabric. Descended from Giambattista Nolli's 1748 map of Rome, it makes legible the relationship between built mass and open space that ordinary plans obscure. Roger Trancik's 1986 Finding Lost Space established it as a core method of contemporary urban-design theory, arguing that good cities are defined as much by the shape of their voids as by their buildings.	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.