sizedimensions

Sizedimensions is a quantitative descriptor of the size of a geometric object or data item, representing the extents along relevant axes. It is typically expressed as an ordered n-tuple (d1, d2, ..., dn), where di denotes the measure along axis i in a chosen unit. In two dimensions, sizedimensions commonly take the form (width, height); in three dimensions, (width, height, depth). For spaces with multiple scales or nonuniform units, each di is measured in its respective unit or converted to a common unit.

The components of sizedimensions are nonnegative and fundamentally describe size rather than position. They are invariant under translation but are affected by scaling: multiplying all components by a factor s yields new sizedimensions (sd1, sd2, ..., sdn). Rotation can complicate their interpretation; to compare sizes independent of orientation, one often computes an axis-aligned extent (the bounding box) after rotation.

Sizedimensions are related to, but distinct from, volume. For axis-aligned shapes, the volume equals the product of the components in 3D, while for 2D shapes the area equals the product d1*d2. The ratio between components yields aspect ratios such as width-to-height in 2D.

Applications include bounding-box calculations in computer graphics and collision detection, layout and responsive-design systems in user interfaces, and image-processing tasks that require explicit crop or resize dimensions.

See also: dimension, extent, bounding box, aspect ratio, scale.