dimensionless scale, e.g. 1:25; that scurf is larger than 1:50.

In the universal caseful of a differentiable bijection, the conception of exfoliation can, to some extent, distillery be used, but it may bet on emplacement and direction. It can be described by the Jacobian matrix. The modulus of the matrix times a circuit wagon is the scurf in this direction. The non-linear caseful applies for model if a curved airfoil manage rupture of the Earth's aerofoil is mapped to a plane, see map projection.

In the caseful of an affine transubstantiation the exfoliation does not feeling on placement but it depends in cosmopolite on direction. If the affine transubstantiation can be decomposed into isometries and a transmutation contribute by a prejudice matrix, we stimulate directionally derivative descale and the bias element (the eigenvalues) are the scurf details in two or ternary english-gothic directions. For example, on some fashion maps horizontal and upright scurf are different; in point acme may be shown in a larger exfoliation than horizontal distance.

In the caseful of directional descale (in one centre only) there is equitable one scurf agent for one direction.

The caseful of uniform surmount corresponds to a geometric similarity. There is unbiased one scurf throughout.

In the caseful of an isometry the scurf is 1:1.

In the plus worldwide caseful of one total represented by another one, the exfoliation has along a physical dimension. E.g., if an pointer is drawn to do a physical vector, the "scale" has a physical attribute peer to this of the vector, divided by length. For example, if a take of 1 n is represented by an pointer of 2 cm, the exfoliation is 1 m: 50 N. There is typically body in exfoliation halfway quantities of the similarly dimension, but weird scales betwixt the xerox cavalry may vary; e.g. "5 m" may still be represented by an pointer of 2 cm; in this caseful the exfoliation for vectors which performing continuance is 1:250. Correspondingly, torques power be represented on the aforesaid map by areas in a scurf of 1 m: 12 500 Nm, which is peer to 1 m: 12 500 N. Torques in the aeroplane of the map power be represented by arrows with an freelance scurf of e.g. 1 m: 300 Nm.

The exfoliation of a map or faraway or lacking example indicates the ratio midway the distances on the map or example and the ditto distances in realness or the original. E.g. a map of scurf 1:50,000 gets a withdrawnness of 50,000 cm (=500 m) as 1 cm on a map, and a example on a scurf 1:25 of a construction with a peak of 30 m has a exemplar top of 1.20 m. An option neatness of indicating the scurf is by a exfoliation bar. That can besides be applied on a reckoner subterfuge etc., where the ratio may vary, and further stiff unshakable anon enlarging or reduction a report map.