On wikipedia I read that similarity transformation is a subgroup of affine transformation. But I didn't get the difference.
Can someone explain it in easy words for beginners of the topic?
2026-03-30 11:35:23.1774870523
difference between similarity and affine transformation
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In very simple words,
An affine transformation can be thought of as the composition of two operations: (1) First apply a linear transformation, (2) Then, apply a translation
Essentially, an affine transformation is like a linear transformation but now you can also "shift" or translate the origin. (Recall that in an linear transformation, the origin is sent to the origin)
This means that an affine transformation will still transform lines to lines and parallel lines to parallel lines. But in general, angles may not be preserved (just like a linear transformation).
A similarity transform is a special kind of affine transformation that preserves "shape". You can think of this as some combination of (1) Translation, (2) Rotation, (3) Uniform Scaling (all dimensions are scaled the same way), and (4) Reflection
Preserving shape means that a similarity transform also preserves angles