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http://meatfighter.com/juggler/
I like his descriptions of why cross products and dot products and stuff
work the way they do.
--
Darren New, San Diego CA, USA (PST)
Linux: Now bringing the quality and usability of
open source desktop apps to your personal electronics.
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Darren New <dne### [at] san rrcom> wrote:
> http://meatfighter.com/juggler/
>
> I like his descriptions of why cross products and dot products and stuff
> work the way they do.
>
Very interesting--I like his graphical/geometrical approach.
He also talks about 'quaternions.' I'm not a mathematician, but this isn't the
first time I've seen that subject mentioned. Several months ago, I read a
fascinating mathematics book called MATHEMATICS: THE LOSS OF CERTAINTY by Morris
Kline (published in 1980.) It's really a book-length essay, a kind of
philosophical discussion about the basic 'illogic' of some of modern
mathematics. The book has practically no hard 'math' equations at all (so I
actually read it cover-to-cover!) He talks about quaternions (and the earlier
calculus) as being a kind of 'breaking point' between the pure logic of previous
maths, and more modern constructs. Definitely worth a read.
Ken
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"Kenneth" <kdw### [at] earthlinknet> wrote in message
news:web.4bdee551b47a5f4dae92d9930@news.povray.org...
> He also talks about 'quaternions.' I'm not a mathematician, but this
> isn't the
> first time I've seen that subject mentioned. Several months ago, I read a
> fascinating mathematics book called MATHEMATICS: THE LOSS OF CERTAINTY by
> Morris
> Kline (published in 1980.) It's really a book-length essay, a kind of
> philosophical discussion about the basic 'illogic' of some of modern
> mathematics. The book has practically no hard 'math' equations at all (so
> I
> actually read it cover-to-cover!) He talks about quaternions (and the
> earlier
> calculus) as being a kind of 'breaking point' between the pure logic of
> previous
> maths, and more modern constructs. Definitely worth a read.
>
> Ken
>
It seems as though the application of quaternions has come-and-gone over the
years.
This Wiki link explains things quite well.
http://en.wikipedia.org/wiki/Quaternion
For an actual use of quaternions, check this URL - used to create Julia
fractals in three dimensions. This website hasn't been updated in some time
(2002)... still interesting none-the-less.
http://www.physcip.uni-stuttgart.de/phy11733/quat_e.html
Laurent
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Laurent wrote:
> It seems as though the application of quaternions has come-and-gone over the
> years.
In the video game programming book I'm reading, the author says something
along the lines that quaternions are(*) a rotation about an arbitrary
vector. They're nothing magical. They're just a vector and a float,
representing a rotation around a specific axis. That said, the math behind
the quaternions are magical.
(*) Of course, he's speaking of quaternions as implemented in the software
library he's describing. I don't know how general this usage is.
--
Darren New, San Diego CA, USA (PST)
Linux: Now bringing the quality and usability of
open source desktop apps to your personal electronics.
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> (*) Of course, he's speaking of quaternions as implemented in the software
> library he's describing. I don't know how general this usage is.
They are used a lot in 3D animation for two main reasons. One is that if
you are realistically simulating forces on 3D bodies then it makes the
rotation maths very simple, and avoids all the problems you get with using
Euler angles or matrices. The other is that it is much simpler to
interpolate between two quaternions (than two rotation matrices or two sets
of Euler angles) so that you get a correct and valid rotation at each point
(eg rotating a camera or interpolating key frames).
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Darren New <dne### [at] sanrrcom> wrote:
> (*) Of course, he's speaking of quaternions as implemented in the software
> library he's describing. I don't know how general this usage is.
>
From what I remember, only unit quaternions (those one unit long) are used for
these kinds of 3D rotations. I had to avoid those libraries when looking for
code to implement operations valid for any quaternion.
Also, according to the POV-Ray source, "This module implements Quaternion
algebra julia fractals."
povray-3.7.0.beta.35a/source/backend/math/quatern.cpp
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