[Tutorial] OPL Rotation with Quaternions

[_Varis_]

If you don't feel like math, use my tool. :P

http://devcrate.com/repository/.Tool...sions/QGen.exe

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See the lower half of my post for how to rotate objects by multiple amounts on multiple axes with one quaternion expression!


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Preface

This guide is aimed primarily at those who already understand the mathematical concepts at work here. Using this software involves rudimentary knowledge of trigonometry. If you don't know what this is, just stop reading here and go learn that.

As TheDeathArt has said, don't try to use software that is smarter than you.

* * *

Background

Kal (along with most software that involves the positioning of objects in a 3D coordinate system) utilizes quaternions to determine rotations of objects in the client; traditional Euler rotations using three angles are too ambiguous to be of any use to a computer.

A quaternion is a set of four values (W X Y Z) that are used in to specify a rotation in 3D space. To specify a particular rotation one needs to determine the axis about which the rotation is being made and the angle by which the object is to be rotated.

* * *

The OPL Editor

The interface of TheDeathArt's OPL Editor consists of:

-The filepath to the object (figure this one out for yourself)
-The vertical position of the object in the client (self-explanatory)
-Four fields labeled W, X, Y, and Z (the quaternion components)
-The scale of the object (again, self-explanatory)

To fill out the filepath, vertical position, and scale, all one needs is a very basic knowledge of Kal. The actual rotation of the object requires some thinking, and in some cases involving rotation in multiple directions, complex multiplication of quaternions (this is slightly more difficult than single rotations, they just take more time). I'll be dealing with that in a later guide; although most rotations dealt with in the Kal client are single quaternions, such as those used for rotating buildings and other objects along the Z axis only.

Each quaternion, as I mentioned before, has four components: W, X, Y, and Z. W determines the angle by which you will be rotating the object. W is cos( θ / 2 ). X, Y, and Z define the axis around which the object will be rotated. They reference a point on the unit sphere (for those of you who have not taken trigonometry, this is just the unit circle in three dimensions). A line segment is drawn from the origin to this point, and that becomes the axis around which the rotation occurs. X, Y, and Z are all multiplied by sin( θ / 2 ).

Thus:

W = cos( θ / 2 )
X = X*sin( θ / 2 )
Y = Y*sin( θ / 2 )
Z = Z*sin( θ / 2 )

So a rotation of 30 degrees about the z axis (0 0 1) would be:

W = cos( 15

[MentaL]

[GrAfIc]

it doesnt work -.-
Tested it , objects transforms into anoying lines who appear/disapear all the time...

[GrAfIc]

nvm , it does work
apperantly it doesnt takes . as comma.

tx for the guide :)

[Proven]

I dont know whether this is allowed to ask but how to rotate a object about two axis?

for example 90

[Grimm-D]

sin90 goes for z axis
sin45 for x

[Gallardo1]

in your case: θ = 90

[_Varis_]

Rotating on one axis, then doing a separate rotation on another axis can get kind of annoying. The way in which this is done is multiplying the actual quaternions together.

I have a half-done guide on this on my HD somewhere; I'll finish it.

[Proven]

That would be very nice. Thanks for your help.

[Boarderkoen]

_Varis_ help me out here. I'm having trouble calculating the Quaternions value for an object with multi- axis rotation.

In example:
10 degrees on the X Axel
45 degrees on the Y Axel
180 degrees on the Z Axel

How is this suppose to be calculated?
X=Sin(10/2);
Y=Sin(45/2);
Z=Sin(180/2);
W=??????

[_Varis_]

I've got a writeup of how to do that done. I'll post it tomorrow.

[CptKenpachi]

so im guessing the W is the 4th dimension?

[_Varis_]

No. The i, j, and k are the fourth dimension. They are the imaginary coefficients. All of the unit vectors that can be made with a quaternion fall on a hypersphere. A hypersphere is a four-dimensional figure that we cannot really truly represent in our three-dimensional world. The imaginary parts of the quaternion make up the fourth dimension.

I did not mention these imaginary numbers because in our case, we can prettymuch ignore them when using quaternions to rotate objects in Kal.

[_Varis_]

Added part two.

Boarderkoen, that should answer your question.

[Boarderkoen]

thanks _Varis_ !!

You just made my day.I've been trieing to understand Quaternions for some time. You just made it simple. Thanks

Gz reb3lzrr

//Edit I made an application that caculates the quaternion very easily ( Idk why the numbers a slightly off _Varis_'s numbers in the GUIDE). I'll release if ppl are intrested

[Flohle]

//Edit I made an application that caculates the quaternion very easily ( Idk why the numbers a slightly off _Varis_'s numbers in the GUIDE). I'll release if ppl are intrested

I think it's usefull :) and maybe it's faster, too.

:kisss:interested:kisss:but not for money xD :2gunsfiring_v1:

[CptKenpachi]

awww man, definately would like this lil tool, spending 10 minutes changing coordinate values for a object all the time, loging in and loging out lots and lots and lots lol.

definately helpful tool,

GJ koen

[Boarderkoen]

I think it's usefull :) and maybe it's faster, too.

:kisss:interested:kisss:but not for money xD :2gunsfiring_v1:

awww man, definately would like this lil tool, spending 10 minutes changing coordinate values for a object all the time, loging in and loging out lots and lots and lots lol.

definately helpful tool,

GJ koen

It's definatly faster,, expesialy when calculating multi-axel rotations.

Ofcourse I'll releases it for free, it only took me a half an hour. And because I see ppl are intrested in it. It will be here on RZ somewhere tomorrow ;)

Gz reb3lzrr

[_Varis_]

Yay, I'm obsolete. This guide took me hours to research, and you wrote your program in 30 minutes. Least I was useful enough to have a programmer make a tool. ^^ /begs for credit

I made an excel sheet that does what your program does yesterday. Guess I won't be needing to upload it now. :D

Glad I was able to help you out.

I will say this though... before you release it, change the , to . in the quaternion output. It may lead people to put it into the editor, which based on what Grafic said, messes things up.

[zig]

where can i get the program?

[Dopestar]

like said it should be on here today, if not he will release it soon

[zig]

k thanks dope

[zig]

Boarderkoen please give us this tool.
thanks :D

[CptKenpachi]

stfu leech.

go play outside or summin until he puts it up.

[Boarderkoen]

Well, a little delay:

http://forum.ragezone.com/showthread...60#post4062260 their you go

[zig]

ty man realy helped me :D