PDA

View Full Version : Quaternions: 2 different definitions????



mauricio_di_mauro
08-29-2009, 09:39 AM
Hey Guys,

I am trying to understand quaternions.
I am using a book called: "Mathematics for Computer Graphics" and the NEHE-Tutorial.
Nehe_Quaternion (http://nehe.gamedev.net/data/lessons/lesson.asp?lesson=Quaternion_Camera_Class)
But after looking closely i have seen that they have 2 different Quaternion definitions.
The + changes to -, when the position of two coefficients is changed.
It would make sense, if this were two imaginary digits but s is real.

Can i assume that it is the same?

But i dont understand why the unsign is changing, when i multiplicate an imaginary with a real digit.

I thought that the multiplication of two imaginary digits is not commutative.

Is it the same with imaginary digits and real ones?

Thanks



BOOK | NEHE | Difference |
------------------------------------------------------------
M11 = 1 - 2(yy + zz) | 1 - 2(yy + zz) |
M12 = 2(xy - sz) | 2(xy + zs) | X
M13 = 2(xz + sy) | 2(xz - ys) | X
M14 = 0 | 0 |
------------------------------------------------------------
M21 = 2(xy + sz) | 2(xy - zs) | X
M22 = 1 - 2(xx + zz) | 1 - 2(xx + zz) |
M23 = 2(yz - sx) | 2(zy + xs ) | X
M24 = 0 | 0 |
------------------------------------------------------------
M31 = 2(xz - sy) | 2(xz + ys) | X
M32 = 2(yz + sx) | 2(yz - xs) | X
M33 = 1 - 2(xx + yy) | 1 - 2( xx + yy ) |
M34 = 0 | 0 |
------------------------------------------------------------
M41 = 0 | |
M42 = 0 | |
M43 = 0 | |
M44 = 1 | |
------------------------------------------------------------

MarkS
08-29-2009, 12:02 PM
Math is not my strong point, but I want to say that since it is not commutative, flipping the variable changes the sign.

The question is, does each method give you the same result?

Alfonse Reinheart
08-29-2009, 02:38 PM
Your "Mathematics for Computer Graphics" and the NeHe tutorial both use different conventions. Since it's a math book, odds are your math book uses column-major conventions. Whereas NeHe, since it's a tutorial for using graphics hardware, uses row-major conventions (since that's what most graphics hardware uses).

Invert the matrix from your book, and you'll find it matches with the tutorial.