BUILT-IN MATHEMATICA SYMBOL

ScalingTransform

gives a TransformationFunction that represents scaling by a factor

along each coordinate axis from the origin.

ScalingTransform

gives scaling centered at the point p.

ScalingTransform

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

ScalingTransform

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

MORE INFORMATION

ScalingTransform gives a TransformationFunction that can be applied to vectors.

EXAMPLES

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Basic Examples (2)

Scaling along the coordinate axes:

Scaling along the vector

by a factor s:

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

Scaling along the coordinate axes:

In[1]:=

Out[1]=

Scaling along the vector

by a factor s:

In[1]:=

Out[1]=

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

In[2]:=

Out[2]=

Scope (4)

Scaling along the coordinate axes about the point

:

Scaling along the vector

about the point

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

is given by ScalingTransform

:

The inverse of ScalingTransform

is given by ScalingTransform

:

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: