Kaveh <kav### [at] delete_thisfocalimagecom> wrote:
> I find it easier just to use the curled fingers method, not the index
> and third fingers. To get the sense of the z axis, I position the left
> hand such that the four fingers curl from the x to the y axis. Then the
> thumb shows the direction of the z axis.

  That description was very unclear. I did not visualize at all which
direction the thumb is pointing at...

-- 
#macro M(A,N,D,L)plane{-z,-9pigment{mandel L*9translate N color_map{[0rgb x]
[1rgb 9]}scale<D,D*3D>*1e3}rotate y*A*8}#end M(-3<1.206434.28623>70,7)M(
-1<.7438.1795>1,20)M(1<.77595.13699>30,20)M(3<.75923.07145>80,99)// - Warp -

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On 18 Nov 2002 15:34:03 -0500
Warp <war### [at] tagpovrayorg> wrote:

>   (If you didn't know, you can easily visualize which direction does
> a positive angle rotate an object by pointing your thumb (of the left
> hand if you are using the left-handed coordinates) towards the positive
> axis around which you are rotating and bend your fingers.)

  I use only this rule for all my "visualizations" when I'm writing scenes, and I
agree with you: when you have the right hand already on the numeric pad, the
lef-handed system is very useful. Not joking!

--
Jaime Vives Piqueres
http://www.ignorancia.org

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Warp <war### [at] tagpovrayorg> wrote:

> Kaveh <kav### [at] delete_thisfocalimagecom> wrote:
> > I find it easier just to use the curled fingers method, not the index
> > and third fingers. To get the sense of the z axis, I position the left
> > hand such that the four fingers curl from the x to the y axis. Then the
> > thumb shows the direction of the z axis.
> 
>   That description was very unclear. I did not visualize at all which
> direction the thumb is pointing at...

It was not clear, I agree. I will put it another way. Put your left hand
in the 'aerobics' position, with fingers curled. Now, point your thumb
in the +z direction. Now if you were to rotate the x axis to coincide
with the y, it your fingers are giving the correct direction.

In a right handed system, sometimes a screw is used. If the screw has
its tip in the +z direction, turning the screw from x to y pushes the
screw in the z direction. But this is of course opposite to the
left-handed system.

All easier to see of course than to describe. 

I just find it easier to have something real like a screw, than to
remember a mnemonic.

-- 
Kaveh

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Jaime Vives Piqueres <jai### [at] ignoranciaorg> wrote:

> On 18 Nov 2002 15:34:03 -0500 Warp <war### [at] tagpovrayorg> wrote:
> 
> >   (If you didn't know, you can easily visualize which direction does a
> > positive angle rotate an object by pointing your thumb (of the left hand
> > if you are using the left-handed coordinates) towards the positive axis
> > around which you are rotating and bend your fingers.)
> 
>   I use only this rule for all my "visualizations" when I'm writing
> scenes, and I agree with you: when you have the right hand already on the
> numeric pad, the lef-handed system is very useful. Not joking!

I think the reason I brought this up in the first place was that when
studying physics, I found it easiest to imagine a normal wood screw,
turning from x to y axis. In a right handed system, the screw moves in
the +z direction. Now I have to use my hand, as there are no left-handed
screws!

-- Kaveh

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Kaveh wrote:

> Now I have to use my hand, as there are no left-handed
> screws!


There is such thing as 'left-handed screws', but you do not see them 
very often. Most of the time, there is a 'right-handed screw' at the 
other end, thus a turn of the screw either separate or bring closer the 
parts with the bolts (symmetrically!).
Typical application: pairs of compass for technical drawing.

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Let me try (A degree in physics must be useful somewhere)

For a LEFT handed Coord. sys.

1)  Place the 4 fingers of you LEFT hand so they point in the +X direction.
In the default configuration of POVRay this is heading off the Right side of
your moniter.

2)  "Curl" your fingers so they move from +X to +Y.  Again Default POVRay:
"curl" from right to top of your moniter

3) Your thumb now points in the direction of the +Z axis.  In the example
above "into" the screen.



"Kaveh" <kav### [at] delete_thisfocalimagecom> wrote in message
news:1flwt0q.1eoksy3ek3y68N%kaveh@delete_this.focalimage.com...
> Warp <war### [at] tagpovrayorg> wrote:
>
> > Kaveh <kav### [at] delete_thisfocalimagecom> wrote:
> > > I find it easier just to use the curled fingers method, not the index
> > > and third fingers. To get the sense of the z axis, I position the left
> > > hand such that the four fingers curl from the x to the y axis. Then
the
> > > thumb shows the direction of the z axis.
> >
> >   That description was very unclear. I did not visualize at all which
> > direction the thumb is pointing at...
>
> It was not clear, I agree. I will put it another way. Put your left hand
> in the 'aerobics' position, with fingers curled. Now, point your thumb
> in the +z direction. Now if you were to rotate the x axis to coincide
> with the y, it your fingers are giving the correct direction.
>
> In a right handed system, sometimes a screw is used. If the screw has
> its tip in the +z direction, turning the screw from x to y pushes the
> screw in the z direction. But this is of course opposite to the
> left-handed system.
>
> All easier to see of course than to describe.
>
> I just find it easier to have something real like a screw, than to
> remember a mnemonic.
>
> --
> Kaveh

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jfmiller <jfm### [at] hotmailcom> wrote:

> Let me try (A degree in physics must be useful somewhere)
> 
> For a LEFT handed Coord. sys.
> 
> 1)  Place the 4 fingers of you LEFT hand so they point in the +X direction.
> In the default configuration of POVRay this is heading off the Right side of
> your moniter.
> 
> 2)  "Curl" your fingers so they move from +X to +Y.  Again Default POVRay:
> "curl" from right to top of your moniter
> 
> 3) Your thumb now points in the direction of the +Z axis.  In the example
> above "into" the screen.

Correct. Thank you for the clarification. :-)

Having thought about it, for me at least, a right-handed system would be
easier to use. I remember I never liked mnemonics. The 3-finger system
is really a mnemonic, whereas using the screw analogy (at least in my
simple mind) seems to have some physical basis to it.

Also, all vector calculus I learned was right-handed. If I remember
rightly, the vector A x B, gives a vector C whose direction is given by
using the right handed rule or screw rule, going from A to B. 

In physics, When a current goes through a wire, you get a magnetic
field, going around it in a right handed way, although I think this is
just a matter of convention.

So, in short, everything I have come across has used the right-handed
screw analogy, except POVray. As I am not comfortable with a left-handed
screw, I now have to use my left hand.

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Kaveh <kav### [at] delete_thisfocalimagecom> wrote:

> As I am not comfortable with a left-handed
> screw, I now have to use my left hand.

Oh boy. I *knew* I would get myself into trouble at last. :-(

Just a little anecdote I remember, in our physics class. A friend had
terrible trouble using the right hand finger rule. He said it always
came out the wrong way. When I asked him to demonstrate it to me, he was
holding his index and third fingers in the wrong directions, with the
third pointing fingers forwards, the index bent!

-- 
Kaveh

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jfmiller <jfm### [at] hotmailcom> wrote:
> 1)  Place the 4 fingers of you LEFT hand so they point in the +X direction.
> In the default configuration of POVRay this is heading off the Right side of
> your moniter.

> 2)  "Curl" your fingers so they move from +X to +Y.  Again Default POVRay:
> "curl" from right to top of your moniter

> 3) Your thumb now points in the direction of the +Z axis.  In the example
> above "into" the screen.

  And someone thinks this is easier than simply pointing your thumb to
+X, index finger to +Y and middle finger to +Z?

-- 
#macro M(A,N,D,L)plane{-z,-9pigment{mandel L*9translate N color_map{[0rgb x]
[1rgb 9]}scale<D,D*3D>*1e3}rotate y*A*8}#end M(-3<1.206434.28623>70,7)M(
-1<.7438.1795>1,20)M(1<.77595.13699>30,20)M(3<.75923.07145>80,99)// - Warp -

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>   And someone thinks this is easier than simply pointing your thumb to
> +X, index finger to +Y and middle finger to +Z?

No not really, It's all a matter of what you've learned.  By using the
"curl" method it is then easier to introduce the consept of rotation as
"curling" ones finger in the direction of rotation and having the thumb pint
along the correct axis.  It also helps in sphereical Coords to remember
which way theta rotates.  But really it's just a matter of preference.

JFMILLER

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