More general is **scaling** with a separate scale factor for each axis direction. **Non-uniform scaling** (**anisotropic scaling**) is obtained when at least one of the scaling factors is different from the others; a special case is **directional scaling** or **stretching** (in one direction). Non-uniform scaling changes the shape of the object; e.g. a square may change into a rectangle, or into a parallelogram if the sides of the square are not parallel to the scaling axes (the angles between lines parallel to the axes are preserved, but not all angles). It occurs, for example, when a faraway billboard is viewed from an oblique angle, or when the shadow of a flat object falls on a surface that is not parallel to it.

When the scale factor is larger than 1, (uniform or non-uniform) scaling is sometimes also called **dilation** or **enlargement**. When the scale factor is a positive number smaller than 1, scaling is sometimes also called **contraction**.

In the most general sense, a scaling includes the case in which the directions of scaling are not perpendicular. It also includes the case in which one or more scale factors are equal to zero (projection), and the case of one or more negative scale factors (a directional scaling by -1 is equivalent to a reflection).

Scaling is a linear transformation, and a special case of homothetic transformation. In most cases, the homothetic transformations are non-linear transformations.

A scaling can be represented by a scaling matrix. To scale an object by a vector *v* = (*v _{x}, v_{y}, v_{z}*), each point

This page was last edited on 9 January 2018, at 16:02 (UTC).

Reference: https://en.wikipedia.org/wiki/Scaling_(geometry) under CC BY-SA license.

Reference: https://en.wikipedia.org/wiki/Scaling_(geometry) under CC BY-SA license.

- Euclidean Geometry
- Isotropic
- Linear Transformation
- Scale Factor
- Similar
- Congruent
- Photograph
- Scale Model
- Anisotropic
- Shape
- Oblique Angle
- Projection
- Reflection
- Linear Transformation
- Homothetic Transformation
- Vector

- Scaling (geometry)
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