Is there a simple definition for Euler in scripting?

[Faubio Alter]

http://en.wikipedia.org/wiki/Euler's_formula

What is it? What does it do? How can you use it in a scripts?

[Clyde Lindman]

Simple? Maybe to someone who has a masters in mathematics. Euler rotation is expressed as the usual x,y,and z plus a 4th element I do not understand, even after researching it, even after talking to mathematicians about it. So in LSL we convert it back and forth using llEuler2Rot and llRot2Euler. I've given up trying to understand it. I just use it and it works

[Faubio Alter]

Thanks for the reply.

[DR Dahlgren]

Actually that is incorrect. A euler rotation is a vector , <x,y,z> expressed in radians. Quaternions are a 4 number vector , x,y,z and s. Here is the wiki info on Euler -

Euler vector

Another way to represent a 3D angle is using three numbers, <X, Y, Z>, which represent the amount which the object is rotated around each axis. This is used in the Edit window, for example, and is generally easy for people to visualize. It is easy to adjust the Rotation <x, y, z> numbers in the Edit window and see how the object behaves. Note that in the Edit window, the numbers are in degrees, that is, a right angle is 90.

In LSL, these three angles are expressed in radians instead of degrees, that is, a right angle is PI/2. (A radian is sort of a very fat degree.) Note that these three numbers are a vector type and not a rotation type, though it can represent the same information. This is called the Euler representation of a 3D angle. In LSL the rotation around z is done first, then around y, and finally around x.

 

Basically you are describing the final position by saying, if I rotate this object on its Z axis a certain amount, then on its Y axis a certain amount and then finally on its X axis a certain amount, it will end up at the desired position. This is not the same result you would get by simply rotating each axis in a random order by the same amount. Try it in world and maybe it will make more sense.

There are some good conversion functions for changing rotation (quarternion) to euler and euler to degress that can make scripiting rotations easier.

The full wiki info on rotation can be found here:

http://wiki.secondlife.com/wiki/Rotation

[Identity Euler]

You may find useful these webpages: http://www.slbuilding.com/Rotations.html http://lslwiki.net/lslwiki/wakka.php?wakka=llRot2Euler

[Faubio Alter]

Do you folks agree with this statement? The Euler is the combined out come of all three X, Y, and Z rotations? The Euler being the sum of the X, Y, and Z rotations?

[Sophia Debevec]

See this page for  Euler ANGLES rather than the one you mentioned in your original post as it seems much of your confusion may stem from reading about another area of Euler's research:  http://en.wikipedia.org/wiki/Euler_angles

[Faubio Alter]

Source:

http://en.wikipedia.org/wiki/Euler_angles

This is equivalent to saying that a rotation matrix can be decomposed as a product of three elemental rotations.

definition 1

http://www.thefreedictionary.com/decomposed

[Faubio Alter]

I think this comes closest to the simple answer:

if I rotate this object on its Z axis a certain amount, then on its Y axis a certain amount and then finally on its X axis a certain amount, it will end up at the desired position.

You get the Kudos

[Faubio Alter]

I've been wondering about this for months so I thought I'd ask, so 4-5 technical pages later. One visit to a scripting group that provided no answers, I find out that X rotation + Y rotation + Z rotation = Euler. Amazing.!

Next time I'll ask a difficult question.

[DR Dahlgren]

ROFL - since you like rotations, why not start on quaternions?

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

 

:-)

[Faubio Alter]

Hey, these guys say there simpler.

Unit quaternions provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock

Doc you trying to mess with us.