ScalingTransform

ScalingTransform[{sx,sy,…}]

gives a TransformationFunction that represents scaling by a factor si along each coordinate axis from the origin.

ScalingTransform[{sx,sy,…},p]

gives scaling centered at the point p.

ScalingTransform[s,v]

gives scaling by a factor s along the direction of the vector v.

ScalingTransform[s,v,p]

gives scaling along the direction of v, centered at the point p.

Details

Examples

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Basic Examples  (2)

Scaling along the coordinate axes:

Scaling along the vector {1,1} by a factor s:

Vectors in the scaling direction get scaled by a factor s:

Scope  (4)

Scaling along the coordinate axes about the point {px,py}:

Scaling along the vector {1,1} about the point {px,py} by a factor s:

Transformation applied to a 2D shape:

Transformation applied to a 3D shape:

Applications  (2)

A projection can be viewed as a special case of scaling:

Scaling a circle in different directions:

Properties & Relations  (3)

The inverse of ScalingTransform[s,v] is given by ScalingTransform[1/s,v]:

The inverse of ScalingTransform[{s1,…,sn}] is given by ScalingTransform[{1/s1,…,1/sn}]:

When the directions along which scalings are applied are orthogonal, transforms commute:

In this case the order in which transformations are applied does not matter:

Possible Issues  (1)

The order in which scaling transformations are applied is significant:

The difference between applying the transforms in different order:

Neat Examples  (1)

Scale a 3D object about a point p:

Scale along the axis:

Scale along the axis:

Scale along the axis:

Wolfram Research (2007), ScalingTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/ScalingTransform.html.

Text

Wolfram Research (2007), ScalingTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/ScalingTransform.html.

CMS

Wolfram Language. 2007. "ScalingTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ScalingTransform.html.

APA

Wolfram Language. (2007). ScalingTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ScalingTransform.html

BibTeX

@misc{reference.wolfram_2024_scalingtransform, author="Wolfram Research", title="{ScalingTransform}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ScalingTransform.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_scalingtransform, organization={Wolfram Research}, title={ScalingTransform}, year={2007}, url={https://reference.wolfram.com/language/ref/ScalingTransform.html}, note=[Accessed: 22-December-2024 ]}