Trying to understand rotation

Can anybody suggest a good resource to help me understand rotations in their various notations, when one would want to use each, and how the transformations work? The wiki just isn't giving me enough to go on, as it assumes some math I never had. I'd be willing to pick up a textbook if someone can recommend one that's usable without a professor.

Quaternions (the rotations used by SL) are quite a tricky area, especially because it's only a special type that is used to represent rotations. Your best bet is usually to look at games-programming related texts, since they explain what you need to know to use them, rather than all the ridiculously complicated background maths.

Here's an article on GamaSutra. I haven't read the whole thing, but they usually have good stuff:

http://www.gamasutra.com/view/feature/3278/rotating_objects_using_quaternions.php

Do not try to understand how quaternions work! learn what rules apply to them!

Nobody can picture what they are like human beings can't imagine a space with more than 3 dimensions. That fact does not prevent mathematicians from making math for spaces with much more than 3 dimensions

Are you refering to http://wiki.secondlife.com/wiki/Rotation? If not, take a look. It's pretty straightforward.

I agree with Rolig -- the SL wiki article on rotations is pretty accessible, even for a non-mathematician like me.

In addition, I was given some extremely helpful guidance on the subject in this thread /54/90/295032/1.html and I frequently find myself referring to Void Singer's cheat sheet at http://wiki.secondlife.com/wiki/User:Void_Singer/Rotations

I think one of the most useful things ever written on the subject was by Francis Chung at /54/3b/50692/1.html#post540396

Blast, you can't put images in this forum?

http://images.icanhascheezburger.com/completestore/2009/3/27/128826641247812908.jpg

Nothing but ferrets, I guess.

I always have to post links to flickr. The forums' image capabilites are flaky, to put it mildly.

testing..............

[img]http://images.icanhascheezburger.com/completestore/2009/3/27/128826641247812908.jpg[\img]


Nope. Looks like ferrets are SOL.

back \ not forward /

The Wikipedia articles are also pretty decent, though there's a lot you can probably skip.

http://en.wikipedia.org/wiki/Quaternion
http://en.wikipedia.org/wiki/Quaternion#Quaternions_and_the_geometry_of_R3

http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation
http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation#Parameterizing_the_space_of_rotations_with_quaternions

Um, no, never backslash. Ever.

This particular forum has disabled inline images.

The pictures of the ferret appear for me, but then I'm using BBCode in Text.

Yep mine are working for me in both Opera and Firefox

except mine are working and yours aren't

Yours aren't working. You're being fooled by your browser extension - and your browser extension is buggy. "\" is not legal syntax, and must not be accepted. Mine is explicitly a link, not an image, using the "?" trick. If I didn't have the "?" it would work fine for you, but not for people who are using standard browsers without hacks... and that's what matters to me.

Except that it IS working with Strife's bbcode script in BOTH Google Chrome and Firefox.

If it is working then that does not mean that it is not working.........................................

The forums have needed the bbcode hack for quite a while now to work properly. Impossible to get code to show properly any other way so I do not strive to get my posts to work for people stuck using IExplorer.

A discussion of the forum's img posting condition is off topic and in the wrong forum.

Regarding


I understand the English but don't get all the formula part.

The formula part would be clearer (to me, that is) on three lines, because those are three separate things that looked to me at first like one big thing that didn't make any sense.

It starts out "1/r"; what does the reciprocal of r mean? If you rotate something by R, does 1/R rotate it back?

I wish there built in relative rotation commands in LSL, I find them convenient and easy to understand. "llSpinXdegrees(45), llSpinYdegrees(15), something like that.

Yeah.. according to the wiki,

You're just repeating what I said. It's not working with a normal browser with no extensions. It's only working with Strife's hack.

I don't use it. The code shows up correctly in the edit pane when I quote it.

And?

Also it definitely is not in the wrong forum. Notice that there have been no further updates even in the office meetings of a forum update? This is all we have and it looks like all we are ever going to have and it is less and less functional everyday. Just a couple of months ago you could attach images and docs to the scripting forum although you couldn't in RA for a long time................

Quaternions are a deeply disturbing, almost frightening concept.

There: a pointless observation but nonetheless back on topic.

I guess the two biggest rotation formulas to commit to memory are:

//rotate an object on it's z axis 90 from whatever rotation it is at
llSetRot(llGetRot() * llEuler2Rot(<0, 0, 90 * DEG_TO_RAD >));

//and add a rotation to a vector. In this case rez an object so that it is in front of the av, no 
matter what direction they are facing:
llRezObject("obj_name", llGetPos() + (<0,0,1> * llGetRot()), ZERO_VECTOR, ZERO_ROTATION, rez_chan);

EDIT: removed for clarity, see later post.

Eh? Not sure what you mean by that. "Dividing" by a rotation does, in fact, give you the inverse transformation. If you take a vector or rotation, "multiply" it by a rotation R, then "divide" it by the same rotation R, you'll get your original vector/rotation. If you want to get the inverse rotation to R without immediately applying it to some value, you can take 'ZERO_ROTATION/R'. That's the equivalent of reversing either the angle OR axis direction of the rotation, and you can get the same thing by reversing the sign of the 's' component as you did. To be a little more correct, you'd actually reverse the sign of all the other components and leave 's' unchanged, but in practice reversing just 's' works too in LSL. That is because the LSL "multiplication" by a quaternion actually performs two multipllcations; one by the quaternion itself and one by its conjugate. so multiplying the quaternion by -1 just results in multiplying the whole result by -1*-1 = +1.

EDIT: removed for clarity, see later post.