linscale

Linscale is a term used in mathematics and computer science to denote linear scaling, a transformation that maps each point to a new position by multiplying coordinates by a constant factor. In its general form, a linear scale about a center c in R^n sends x to x' = c + s (x - c), where s is a scalar. When c is the origin, this reduces to x' = s x, a uniform dilation. If different axes are scaled by different factors, x' = diag(s1, s2, ..., sn) x describes an anisotropic scaling.

Properties: Scaling is a linear transformation; it preserves straight lines and, for origin-centered scaling, scales distances from the center by |s| and areas (or volumes) by |s|^n. Uniform scaling with s > 0 preserves angles, while non-uniform scaling distorts angles.

Applications: Uniform scaling is fundamental in computer graphics for resizing objects and images; anisotropic scaling is used to stretch objects along specific axes; in data processing, linear scaling maps data to a desired range or space as part of an affine transform; in geometry and CAD, scaling is used to adjust models and coordinates.

Limitations: Scaling can distort shapes if not uniform; rounding and sampling during image scaling can affect quality.

Terminology: Linscale is not tied to a single software project; outside of specific domains it refers to the general concept of linear scaling.