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)?
Differences in forms of transformations.
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
That means addition of transformation is actually increasing the level of "change"
Multiplication is combining the "change"
Multiplication is combining the "change"
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.
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.
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