the gr8 debate

>>617542Here'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.

>>617578The 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".

>>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?

>>617594Half 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.

>>617603>Matrices are, by definition, linear maps that preserve the point of originYou mean:Matrices are, by definition, a vector space.

>>617603Dude. Bring you low quality troll to Wikipedia's math related pages where it belongs.

>>617603not 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?

>>617603>mathematically obvious>mathematical trickYou suck.

WHICH IS BETTER TO USE LADS

>>617603check 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.