# Differences in forms of transformations.

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1) Vector * Transformation => 2nd Vector
2) Transformation * Transformation => 2nd Transformation
3) Transformation + Transformation => 2nd Transformation
4) Vector * (Transformation * Transformation) => 2nd Vector
5) Vector * (Transformation + Transformation) => 2nd Vector

a) What is the difference between 2) + 3)?
b) What is the difference between 4) + 5)?

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a) What is the difference between 2) + 3)?
b) What is the difference between 4) + 5)?

Well, one is an addition, the other a multiplication. In 3d math multiplications of transformations are more common, because when you have a homogeneous matrix (most likely your transformation), then the multiplication is like executing the transformation in a sequence.

Extended example:
Take the coffee cup in front of you, you are the center. Now move it away from you (first: translation), then rotate it around youself (second: rotation), and eventually move it closer to yourself (third: translation). This can be described as three transformation matrices:
translation_1
rotation
translation_2

The final trnasformation is
final_transformation = translation_2 * rotation * translation_1

That is the final position and orientation of your coffee cup Edited by Ashaman73

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That means addition of transformation is actually increasing the level of "change"
Multiplication is combining the "change"

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To concatenate (append together) transforms, you multiply the matrices together.

Adding two transformation matrices together has no meaning -- the results aren't useful. So, I've never seen (3) and (5) used in a game. Edited by Hodgman

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As far as I know, a rotation matrix consists of different components sin(theta) cos(theta) at different positions affecting different things.
So I also think addition is superflourous.

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