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Compactness measure - Wikipedia

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Compactness measure is a numerical quantity representing the degree to which a shape is compact. The circle and the sphere are the most compact planar and solid shapes, respectively. Various compactness measures are used. However, these measures have the following in common: A common compactness measure is the isoperimetric quotient, the ratio of the area of the shape to the area of a circle (the most compact shape) having the same perimeter. In the plane, this is equivalent to the Polsby–Popper test. Alternatively, the shape's area could be compared to that of its bounding circle,[1][2][3] its convex hull,[1][4] or its minimum bounding box.[4] Similarly, a comparison can be made between the perimeter of the shape and that of its convex hull,[4] its bounding circle,[1] or a circle having the same area.[3] Other tests involve determining how much area overlaps with a circle of the same area[2] or a reflection of the shape itself.[1] Compactness measures can be defined for three-dimensio

Compactness measure - Wikipedia Jump to content From Wikipedia, the free encyclopedia Measure of the degree to which a geometric shape is compact Not to be confused with the topological notion of compact space . Compactness measure is a numerical quantity representing the degree to which a shape is compact . The circle and the sphere are the most compact planar and solid shapes, respectively. Properties [ edit ] Various compactness measures are used. However, these measures have the following in common: They are applicable to all geometric shapes. They are independent of scale and orientation.

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