On Wed, 05 Jul 2000 21:20:20 -0500, David Fontaine wrote...
> Jamie Davison wrote:
> 
> > <grin>
> >
> > Oh, and I figured it out using a pencil, paper and calculator, and the
> > rotations I came out with were <45.0,0.0,35.26439>.  This was using
> > nothing more complicated than basic trigonometry and Pythagoras' theorem.
> 
> <grin>
> *cough cough*
> I will not tolerate imperfection! Rotate <45,0,asin(1/sqrt(3))> ;-)

Nope, I came to it through Rotate <45.0, 0.0, atan(1/sqrt(2))>  :)

Or you could have used Rotate <45.0, 0.0, acos(sqrt(2)/sqrt(3))  But 
that's just silly.

They all give you the same result, so who cares <grin>

Using the (admittedly crap) windows calculator, the following came out of 
the two simpler methods:

asin(1/sqrt(3)) = 35.2643896827546543153770003300188
atan(1/sqrt(2)) = 35.2643896827546543153770003300188

Is that perfect enough?  Or do you require anally retentive levels of 
precision?  ;)

Bye for now,
     Jamie.

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On Thu, 6 Jul 2000 21:32:47 +1200, Ian Witham wrote...
> > Oh, and I figured it out using a pencil, paper and calculator, and the
> > rotations I came out with were <45.0,0.0,35.26439>.  This was using
> > nothing more complicated than basic trigonometry and Pythagoras' theorem.
> 
> 
> okay okay.. as so many of you have pointed out it isn't all that tricky
> after all <hangs his head in shame> :-(

It wasn't too easy either...  I took me a sheet of paper and a fair 
amount of cursing before I remembered enough of my maths to figure it 
out.  It's just too easy to sound glib and self satisfied when you've got 
the answer sitting in front of you while you compose the posting to the 
NG :)

Having a copy of Moray to display and verify the transformations didn't 
hurt either <grin>

Oh, and I did a quick scene with 3200 cubes rotated at .1 degree 
intervals, but got bored waiting for it to render :)

Bye for now,
     Jamie.

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David Fontaine wrote in message <3964C951.BCF19E94@faricy.net>...
>Wait, wait, I have a *really* hard one! What would it look like if you took
a
>regular octahedron, aligned opposite points on the y-axis, and spun it?
Only
>kidding, of course... (not to self--shut up)


Or how about a regular hexahedron?  :-)

Mark

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Of course, it really should be written as asin(sqrt(3)/3)...

Jamie Davison wrote:

> Nope, I came to it through Rotate <45.0, 0.0, atan(1/sqrt(2))>  :)
>
> Or you could have used Rotate <45.0, 0.0, acos(sqrt(2)/sqrt(3))  But
> that's just silly.
>
> They all give you the same result, so who cares <grin>
>
> Using the (admittedly crap) windows calculator, the following came out of
> the two simpler methods:
>
> asin(1/sqrt(3)) = 35.2643896827546543153770003300188
> atan(1/sqrt(2)) = 35.2643896827546543153770003300188
>
> Is that perfect enough?  Or do you require anally retentive levels of
> precision?  ;)

--
David Fontaine     <dav### [at] faricynet>     ICQ 55354965
Please visit my website: http://www.faricy.net/~davidf/

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Mark Wagner wrote:

> David Fontaine wrote in message <3964C951.BCF19E94@faricy.net>...
> >Wait, wait, I have a *really* hard one! What would it look like if you took
> a
> >regular octahedron, aligned opposite points on the y-axis, and spun it?
> Only
> >kidding, of course... (not to self--shut up)
>
> Or how about a regular hexahedron?  :-)
>
> Mark

Oops, should be NOTE to self (missed the 'e')
Did you know that any four non-consecutive points on a cube define a regular
tetrahedron? :) Of course, there's only two ways to do that on a cube.

--
David Fontaine     <dav### [at] faricynet>     ICQ 55354965
Please visit my website: http://www.faricy.net/~davidf/

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On Fri, 07 Jul 2000 13:36:02 -0500, David Fontaine wrote...
> Of course, it really should be written as asin(sqrt(3)/3)...

Why?  It all comes out the same in the end, so use the syntax you like 
and can understand.

Or am I missing something here?  Admittedly, my mathematics goes up to 
about halfway through 'A' Level, when we hit the more complex end of 
calculus and statisitcs, whereupon my brain fell over, so I could easily 
be missing something.

Bye for now,
     Jamie.

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On Fri, 7 Jul 2000 22:51:16 +0100, jam### [at] dh70qdu-netcom (Jamie
Davison) wrote:

>On Fri, 07 Jul 2000 13:36:02 -0500, David Fontaine wrote...
>> Of course, it really should be written as asin(sqrt(3)/3)...
>
>Why?  It all comes out the same in the end, so use the syntax you like 
>and can understand.

Well, 1/sqrt(3) = sqrt(3)/3
It's just that the latter is the rationalized, more acceptable form of
it.


Peter Popov ICQ : 15002700
Personal e-mail : pet### [at] usanet
TAG      e-mail : pet### [at] tagpovrayorg

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On Fri, 07 Jul 2000 07:14:47 +0300, Peter Popov wrote...
> >> Of course, it really should be written as asin(sqrt(3)/3)...
> >
> >Why?  It all comes out the same in the end, so use the syntax you like 
> >and can understand.
> 
> Well, 1/sqrt(3) = sqrt(3)/3
> It's just that the latter is the rationalized, more acceptable form of
> it.

OK, so I *was* missing something :)

I think I'll stick to the incorrect syntax myself, as if nothing else, it 
helps me remember where in the calculations I got the value from. (if you 
could see the average page of scribbling and trigonometry, you'd 
understand why I need help remembering such things <grin>)

Bye for now,
     Jamie.

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