Stuart Meerkat wrote:

> I have a gear creation include file that i'm trying to make do bevel
> gears, the trouble is that when ever i make the points for a conic_sweep
> prism, they seem to be scaled to be slightly bigger(1.1?) in x/z... this
> trouble doesn't exist when i'm making a linear_sweep of the exact same
> values... is there some settings or an error that isn't documented? or
> does anyone have the scale factor?
>
> If there is alot of interest in this code, i might release it... but i'm
> not sure yet...
>
> also... has anybody made a rope include file that can make a sertain
> length of rope between two points that are not level?
> I have all the math, but can't seem to solve it...
> (anybody know how to solve n=sinh(z)/z for z?)
>
>      the Loial Raven, Matthew Peters

Oh... i'm using a friends computer, so don't e-mail to the above address
my address is  Loi### [at] yahoocom

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Stuart Meerkat wrote:

> also... has anybody made a rope include file that can make a sertain
> length of rope between two points that are not level?
> I have all the math, but can't seem to solve it...
> (anybody know how to solve n=sinh(z)/z for z?)
> 
>      the Loial Raven, Matthew Peters

I believe there is a rope example that come with Chris Colefax's spline
include file which boasts the ability to make hanging/dropping chains,
ropes, etc.

http://www.geocities.com/SiliconValley/Lakes/1434/

-- 
Ken Tyler

mailto://tylereng@pacbell.net

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I think that it doesn't have the length variable, instead it has a variable
called a... you need to solve a whole bunch of stuff to get that though...


Ken wrote:

> Stuart Meerkat wrote:
>
> > also... has anybody made a rope include file that can make a sertain
> > length of rope between two points that are not level?
> > I have all the math, but can't seem to solve it...
> > (anybody know how to solve n=sinh(z)/z for z?)
> >
> >      the Loial Raven, Matthew Peters
>
> I believe there is a rope example that come with Chris Colefax's spline
> include file which boasts the ability to make hanging/dropping chains,
> ropes, etc.
>
> http://www.geocities.com/SiliconValley/Lakes/1434/
>
> --
> Ken Tyler
>
> mailto://tylereng@pacbell.net

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Matthew Peters wrote:
> 
> I have a gear creation include file that i'm trying to make do bevel
> gears, the trouble is that when ever i make the points for a conic_sweep
> prism, they seem to be scaled to be slightly bigger(1.1?) in x/z... this
> trouble doesn't exist when i'm making a linear_sweep of the exact same
> values... is there some settings or an error that isn't documented? or
> does anyone have the scale factor?
> 
> If there is alot of interest in this code, i might release it... but i'm
> not sure yet...
> 
> also... has anybody made a rope include file that can make a sertain
> length of rope between two points that are not level?
> I have all the math, but can't seem to solve it...
> (anybody know how to solve n=sinh(z)/z for z?)

What size are your gears?  I've just run a quick test using circular
points with a radius of around 1 unit, and both the linear and conic
sweeps are equal sizes in all dimensions.  However, problems with very
small object co-ordinates have been reported in the past...

As for the hanging cable question, I have to admit I've also been unable
to discover the answer (analytically, at least).  Therefore, at the
moment I can see two possible solutions: using approximation to find the
necessary 'droop factor' to give a desired catenary-segment length
(within a certain tolerance) or simulating the cable as a series of
linked springs.

The first option is probably quite feasible under POV-Ray 3.1 - I've
just created macros to reparameterize cubic splines by arc-length
(allowing constant length along the spline path regardless of shape),
and the sampling/interpolation performance seems to be quite acceptable
(and far faster than would have been possible under POV-Ray 3.0).

The second option (similar to the spring simulations described so
excellently by Hugo Elias) would also allow simulating cables with only
one end fixed (swinging pony-tails, etc.), variable masses along the
cable (eg. a necklace with a heavy pendant), and more.

I hope to be testing both methods soon, so that I can release a properly
updated version of my Link include file.  Some have suggested including
this as a feature of the POV-Ray Spline System I am working on at the
moment (so splines could have gravity forces applied to them), and it
might even be an idea to get both methods up and running...

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Just been having a look at your problem, of shin(z)/z=n, lets re-arrange
this to:
shin(z)=nz.

I'm assuming n is an integer, in which case I'm pretty sure therre will
be 2 roots. One will be pretty small <1, for n being reasonably high. 
In which case we can use the Taylor series expansion.  The other root we
won't be able to use the series, as it is non-convergent.  the problem
is, unless n is really small, we'll have to carry a lot of the tS to get
a reasonable answer, if n > 100 it should be OK (and we'd just need the
first 3 terms), but otherwise we'll have to solve the TS numerically,
I'd recommend bisection as I'm not sure Newton will work (but I always
use bisection - don't like the idea of a series which might not converge
- I'd prefer to guarantee it works and use a little more processor).  If
you have no idea about what I'm talking about, just email and I'll
explain further.

The Taylor Series is by the way :
  shin(z)/z= 1 + z^2/3! + z^4/5! ..... z^n/(n+1)!


So if we take the first four terms and then sub into the quadratic
formulae, we should get the answer for Z^2, root that and we would get
an answer, which for n>100 would be about 10^-5 accurate.  This is all
very roughly estimated, BTW.

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here is the test that shows the error... please could someone help, i've
already renamed all my variables and tried almost every aproach i can think
of... well, there was one thing left that i think might cause it... but i
have no clue of why sine and cosine would be redefined only when in
conic_sweep prisms... hmm...

well, here it is...

hope this works... ah well, have fun all :)
    the Loial Raven

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Attachments:
Download 'test.pov.txt' (10 KB)

oh ya, my addy is still different... should be fixed now...

Stuart Meerkat wrote:

> here is the test that shows the error... please could someone help, i've
> already renamed all my variables and tried almost every aproach i can think
> of... well, there was one thing left that i think might cause it... but i
> have no clue of why sine and cosine would be redefined only when in
> conic_sweep prisms... hmm...
>
> well, here it is...
>
> hope this works... ah well, have fun all :)
>     the Loial Raven
>
>   ------------------------------------------------------------------------
>
>                   Name: test.pov
>    test.pov       Type: POV-Ray scene file
(application/x-unknown-content-type-POV-Ray.Scene)
>               Encoding: base64

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Matthew Peters wrote:
> 
> here is the test that shows the error... please could someone help, i've
> already renamed all my variables and tried almost every aproach i can think
> of... well, there was one thing left that i think might cause it... but i
> have no clue of why sine and cosine would be redefined only when in
> conic_sweep prisms... hmm...

It took a while to 'decode' your code, but I think your problem is a lot
simpler than you think - the height of your prism (fake_th) is greater
than 1, therefore the conic_sweep extends out beyond the linear sweep. 
If you replace the fake_th with 1, you'll get prisms of exactly the same
dimensions.  If you want to create bevelled gears, it might be easiest
to create the top bevel prism from -1 to (-1 + bevel_height), and then
translate it up (+y) to sit on top of your linear prism.  The bottom
bevel could be the same object scaled by <1, -1, 1> or created at (1 -
bevel height) to 1, and translated down (-y).

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AHA!!! conic sweep prisms are drawn on the y*1 plane and then extruded past
there!!!... that's all my problems, so... if i am right, then i can just scale
the conic prism to the right length...

Let me go check... hehehe...
Thanks for all the help :)

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OK, i think it's fixed... if anyone is interested in this include... er... i
guess i'll give it out... hehehe... just e-mail me :) it should be done in a
few days or less (:

Thanks once again :)
    the Loial Raven

P.S. the catanery still lies... anyone got a clue about how to solve that?

Stuart Meerkat wrote:

> I have a gear creation include file that i'm trying to make do bevel
> gears, the trouble is that when ever i make the points for a conic_sweep
> prism, they seem to be scaled to be slightly bigger(1.1?) in x/z... this
> trouble doesn't exist when i'm making a linear_sweep of the exact same
> values... is there some settings or an error that isn't documented? or
> does anyone have the scale factor?
>
> If there is alot of interest in this code, i might release it... but i'm
> not sure yet...
>
> also... has anybody made a rope include file that can make a sertain
> length of rope between two points that are not level?
> I have all the math, but can't seem to solve it...
> (anybody know how to solve n=sinh(z)/z for z?)
>
>      the Loial Raven, Matthew Peters

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