heightused

Heightused is a metric used to quantify the vertical extent occupied by a set of elements within a coordinate system. It is applied in fields such as geographic information systems, architectural modeling, and computer graphics to describe how much of the vertical space is utilized by features, objects, or data points.

Definition and calculation: For a defined subset S of objects, each with a vertical coordinate y, heightused(S) is the difference between the maximum and minimum vertical coordinates among the subset: heightused(S) = max{y | (x, y, z) ∈ S} − min{y | (x, y, z) ∈ S}. In practice, heightused may be expressed in absolute units (for example meters) or as a normalized proportion by a reference height H, with heightused_norm = heightused(S)/H. Some workflows exclude extreme outliers or apply a height threshold to focus on a specific vertical band.

Applications: In GIS and remote sensing, heightused helps assess the vertical distribution of features, such as canopy height or building heights. In 3D modeling and game development, it informs camera placement, level design, and collision detection. In robotics and sensor networks, heightused can indicate vertical coverage or the extent of a sensor’s field. In data visualization, it can guide scale selection and aspect-ratio decisions.

Limitations: The value is relative to the chosen subset and coordinate system; it is sensitive to outliers and requires clear definitions of the vertical axis and reference height. Without a defined domain, heightused alone may be ambiguous.

See also: bounding box, heightfield, vertical extent.