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May 30th, 2009, 09:49 AM   #1
Joined: May 2009

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simple high level uses of quaternions and matrices

Hi everyone,

I'm looking for a high level explanation of quaternions and matrices in the context of transforming 3d points without complex definitions and theory

I just asked a friend about this and I figured I'd ask it here too. I'm in computer graphics and animation. Recently I have tried to do some research in matrix math and quaternions. The problem is that most of the information I can find tells about the complex equations behind these mathematical concepts. I've found many books and websites on the subject, but most of them are too complicated with low level knowledge on the inner workings of math theory. They basically teach you how to create a 3d game engine and 3d software, but don't clearly show to me what to do with the knowledge in the context of USING 3d software.

Since the computer software already has these capabilities, to add, subtract, multiply, execute trigonometric functions, on any kind of data, I don't really need to know the complex math behind it at the moment.

I understand some of the equations, but I am still at a loss of exactly how to use them to achieve the 3d transformations I need to do.

What I've failed to find is a reference that gives good, simple, real world applications of when to combine, multiply, etc. matrices and quaternions to achieve various 3d transformations and rotations.

The information that I actually need is really extremely simple, such as statements like this:

"If you have a 3d vector position, multiply it by a 4 X 4 matrix to transform and rotate it. Multiply it by the same inverse matrix to rotate and transform it back to the original position" ( I think this one is correct)

"subtract the pivot point, Multiply a 3d point position by a quaternion in order to rotate it, and add the pivot point"
or it could even be written like:
((P - pivot) * quat)+pivot

"to interpolate between two quaternions (slerp), just add them together, then add them to a 3d point position and dot product the pivot point" (I know this is wrong, I just made it up, but I'm looking for this kind of info) returns a lot of info, some of which I understand, and I basically understand what a quaternion and matrix is and how to create them in my 3d package.

These examples are probably wrong by the way, just examples of the type of information I need, without the complex equations and math theory.

Thanks everyone!
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