Am 01.03.2013 22:42, schrieb Alain:

>> Am 01.03.2013 04:14, schrieb Alain:

>>>
>>> In my math classes when looking at geometry, we only used the
>>> left-handed coordinate and rotation system. Also, Y was always UP and Z
>>> forward, NEVER relative to the paper's surface.
>>>
>>> It was the same in my physics courses.
>>
>> What? For us it was /always/ right-handed, for both maths and physics. I
>> can't believe it's different across the world in such disciplines.
>>
>> ... unless of course you use a different scheme to assign axes to the
>> fingers. We used thumb=X, index=Y, and middle=Z.
>
> Using the right hand, it require you to twist your arm to have the thumb
> point toward +X, then the index point to +Z
>
> In my courses, with the left hand, it was: thumb = +Y, index= +Z,
> middle= +X with the index pointing forward and the thumb up.
> Very easy to hold, and you can still have a pen in your right hand...

That's a left-handed system indeed, but I doubt it's the standard used 
in professional mathematics and physics. (Then again, in professional 
mathematics the handedness of the world is just abstracted away anyway. 
That leaves physics though.)


> Maybe just a coincidence, but it's the same thing that is used to get
> the direction of the force exerced on a conductor in a magnetic field.
> The index is in the direction of the current (positive), the thumb in
> the direction of the magnetic field (north pole), and the middle finger
> in the direction of the force.

If you swap any of the two components, you can do the same stunt with 
the right hand.

But here are two stunts you can't do left-handed:

Make a "thumbs-up" sign with your right hand. Point your thumb in the 
direction of current in a wire. The fingers will curl in the direction 
of the magnetic field around the wire.

Make a "thumbs-up" sign with your right hand. Hold your hand so that the 
fingers curl in the direction of current flowing in a coil. The thumb 
will point in the direction of the magnetic field inside the coil.


> For the rotations, you point the thumb toward the + side of an axis, and
> the fingers curl in the direction of the positive rotation.

That's true in both left- and right-handed coordinate systems, simply 
due to the way positive rotation is defined. (In other words, in a 
left-handed coordinate system positive rotation is defined just the 
other way round as in a right-handed one.)


> That's why, for me, ther was no learning curve to use the POV-Ray
> coordinate system. It's exactly the same I always used in school.

It might be a UK-schools special, which would explain why POV-Ray uses 
it. (Then again, you are not from the UK, are you?)


>> If you put a proper math-style 2D coordinate system (X axis right, Y
>> axis "top") onto paper, and then add +Z as height above ground, that's a
>> left-handed system to me.
>>
> That's exactly how architecs work. And that's right handed.

Doing the gymnastics again, yes - it is indeed.

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