volumescaling

Volume scaling is the procedure of resizing a three-dimensional region or dataset by a scale factor. It is used in fields such as computer graphics, computational geometry, and scientific visualization to adjust the size of an object or volume, either isotropically (same factor in all directions) or anisotropically (different factors along axes).

Mathematically, isotropic scaling about the origin maps each point x to s x. The volume, which is the measure in three dimensions, changes by a factor s^3. Anisotropic scaling with factors (s_x, s_y, s_z) maps x to (s_x x, s_y y, s_z z) and changes volume by the product s_x s_y s_z.

Applications include resampling medical imaging volumes (adjusting voxel size), adjusting coordinate frames in 3D models, and performing box-volume changes in molecular dynamics under constant pressure. In rendering, volume scaling may be used to fit scenes to a viewport or to simulate different scales.

Practical considerations include the choice of interpolation during resampling (nearest-neighbor, trilinear, higher-order), which affects quality; preserving aspect ratios; units and physical meaning of coordinates; potential distortion for nonuniform scaling; and numerical stability in simulations when used with converted densities or masses.

See also: scaling, resampling, affine transformation, isotropic scaling, anisotropic scaling.