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the gr8 debate
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>>617542
Here's a good quiz for you brainlet: why do we need 4 dimensional matrices to manage transformation in three dimensions? The answer is mathematically obvious, but then it's /3/ we're talking about.
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>>617578
The 4th column is there to express a translation, the 4th row is added because the algorithm that inverts matrices needs it as scratch space. It's not exactly a 4 dimensional matrices and it's not "mathematically obvious".
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>>617578
>conflates the size of a matrix with its dimension

lmao why are you even trying to talk about stuff you have no understanding of?
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>>617594
Half wrong. I wouldn't have expected anything else from a brainlet.

It is mathematically obvious. Matrices are, by definition, linear maps that preserve the point of origin. 3 dimensional matrices can represent any linear transformation in 3d space that keeps the origin, i.e rotation (around the origin), shearing, scaling. Translations do not keep the origin. By definition a 3 dimensional matrix can't represent a translation in 3d space.

Any non-brainlet mathematician would have given that trivial answer. But I guess you're an ``artist'', you poor soul.

The matrices used in computer graphics are four dimensional. It's not a 'fourth row' or 'not exactly 4 dimensional matrices' or any number of such deranged thing. Those matrices are four dimensional. The fourth dimension is used to keep the translation parameters by a mathematical trick that is called homogeneous coordinates. Check it out.
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>>617603
>Matrices are, by definition, linear maps that preserve the point of origin
You mean:
Matrices are, by definition, a vector space.
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>>617603
Dude. Bring you low quality troll to Wikipedia's math related pages where it belongs.
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>>617603
not him but aren't affine transformations used in computer graphics to describe linear transformations without an origin? those do use the fourth row caveat he was referring to, correct?
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>>617603
>mathematically obvious
>mathematical trick
You suck.
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WHICH IS BETTER TO USE LADS
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>>617603
check it out, it's babby's first math class in uni :^)
come back here when you know why translations need to be expressed as matrices in 3D calc.




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