Design Nomenclature / Form & Geometry

Volume

Also called capacity, cubic content, enclosed volume

The measure of the space a closed surface encloses, computed from a mesh by the divergence theorem — summing the signed tetrahedra from the origin to each triangle. It requires a watertight, consistently oriented surface: an open or partly flipped mesh returns a number, and the number is meaningless. Also used loosely for the enclosed region itself.

A faceted cylinder in isometric wireframe with the origin marked below it, one triangle of its surface joined to that origin by three lines to form a tetrahedron shaded positive, and a triangle on the far side joined the same way to form a tetrahedron drawn dashed and signed negative because its normal points away — the two summing to the enclosed volume.

In practice

In a design review 'volume' usually means the region — 'break up the volume' — not cubic millimetres. In print prep and costing it means the number, and a single flipped normal is enough to corrupt it.

Not to be confused with

How this term connects

ManifoldMassNormalSectionVoidWatertightVolume
Related Confused with