|
 |
I've fixed quaternions.inc so that you shouldn't get the warnings any
more. And I've made changes thanks to Tor Oval Kristenen's suggestions.
I realise that the include was meant almost exclusively for script
writers , so I added a sample macro for a regular object modifier. More
could be made like this taking advantage of quaternions.
RotSimulXYZ(Angles) // In Degrees!
It will rotate an object along the three axes XYZ using Euler angles
simultaneously (all at the same time). So it's like a rotate but it
doesn't suffer from Gimbal Lock.
ex.:
object ( Basketball
RotSimulXYZ(<90,0,90>)
}
I still prefer Radians, myself, since Radians apply direclty to the
radius of an object and how much it should rotate, but I made it degrees
here to remain consistent with regular Povray transforms.
Post a reply to this message
Attachments:
Download 'quaternions.inc.txt' (7 KB)
|
|
|
|
Alain,
Thanks for this inc. Not only should it prove useful in itself, but I'll be
talking about quaternions (briefly) in my multivariable Calculus class, and
I'll share this with my students (if you don't mind) as a good
demonstration of some of their uses. Sir William Rowan Hamilton would be
proud.
BTW, Hamilton provides me with my favorite quote I use in college algebra
(the uniquely American way of terming what should be remedial algebra --
worse yet, the prerequisite for "college" algebra at this school is called
"higher algebra;" higher than what, I'm not sure.)
Hamilton, from his "Theory of Conjugate Functions" (1837):
"[I]t requires no particular scepticism to doubt, or even to disbelieve, the
doctrine of Negatives and Imaginaries, when set forth (as it has commonly
been) with principles like these: that a greater magnitude may be
subtracted from a less, and that the remainder is less than nothing; that
two negative numbers, or numbers denoting magnitudes each less than
nothing, may be multiplied, the one by the other, and that the product will
be a positive number, or a number denoting a magnitude greater than
nothing; and that although the square of a number, or the product obtained
by multiplying that number by itself, is therefore always positive, whether
the number be positive or negative, yet that numbers, called Imaginary, can
be found or conceived or determined, and operated on by all the rules of
positive and negative numbers, as if they were subject to those rules,
although they have negative squares, and mut therefore be supposed to be
themselves neither positive or negative, nor yet null numbers, so that the
magnitudes which they are supposed to denote can neither be greater than
nothing, nor less than nothing, nor even equal to nothing. It must be hard
to found a science on such grounds as these."
Dave Matthews
Post a reply to this message
|
|
|
|
As has been pointed out by Tor Olav Kristensen, line 176 of quaternons.inc
should read:
<AT*Q.x,AT*Q.y,AT*Q.z,0.5*ln(Qsc(Q))>
("log" should actually be "ln".)
This is located in the Qln() macro, and was used by the interpolation
macros only. I'll wait before posting an update until I've tested
everything more thouroughly and/or brought more enhancements.
Post a reply to this message
|
|
|
|
Another note: someone mentionned to me that an orientation they were
incrementing might not be working.
It's important to keep in mind that (quoted from my Calculus book, which,
by the way, only barely mentions quaternions): "quaternions do not obey the
commutative law (that is, A * B != B * A); this was the first algebra in
which such behavior was studied."
So the order of multiplication is important.
Basically, if you have an orientation qO and you want to increment it with
the orientation qI, you will want to multiply them like this:
#declare q0 = QMultiply(qI,qO);
That will work, the other way around might yield unexpected results.
Post a reply to this message
|
|
mnwest