What is orientation or shear transform collectively termed?

In summary, orientation or shear transform collectively is known as affine transformation. The purpose of an affine transformation is to preserve the parallelism of lines and the ratio of lengths along the x and y-axis. An affine transformation differs from other transformations in that it does not necessarily preserve angles and shapes, but rather preserves parallel lines. Affine transformations are commonly used in computer graphics, image processing, and computer vision to resize, rotate, and distort images. And yes, all affine transformations are linear, but not all linear transformations are affine as affine transformations also include translation.
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What is an orientation (i.e., set of Euler rotations) or shear transform collectively termed? It seems that these transforms, along with the scale transform are known as "linear" transforms, as described in the Venn diagram on page 2:

https://www.cs.tau.ac.il/~dcor/Graphics/cg-slides/trans3d.pdf

It seems that an orientation or shear transform does not scale the volume, unlike a scale transform, which obviously does. I wonder if there is some classification that these 2 transforms are part of that but that excludes scale. Perhaps isochoric?
 
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  • #2
Yes isochoric means volume preserving.
 

1. What is orientation or shear transform collectively termed?

Orientation or shear transform collectively is known as affine transformation.

2. What is the purpose of an affine transformation?

The purpose of an affine transformation is to preserve the parallelism of lines and the ratio of lengths along the x and y-axis.

3. How is an affine transformation different from other transformations?

An affine transformation differs from other transformations in that it does not necessarily preserve angles and shapes, but rather preserves parallel lines.

4. What are some common applications of affine transformations?

Affine transformations are commonly used in computer graphics, image processing, and computer vision to resize, rotate, and distort images.

5. Are all affine transformations linear?

Yes, all affine transformations are linear, but not all linear transformations are affine. This is because affine transformations also include translation, while linear transformations do not.

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