Why can't I get a working superellipse?

See code below and image below.  It looks like I'm losing two quadrants
of the s-e. Note that when the n2 is changed to 1.0 I get a nice sphere.

I then read in a web page for CS from U of Western Australia:
http://www.cs.uwa.edu.au/undergraduate/units/600.105/Lab6.html

> Note for this representation to work `exponentiation' must be defined
as
>      p                   p
>    x   =  sign(x) |x|
>
> Where the sign function returns +1 for +ve x, 0 for 0 x, and -1 for
-ve x.
> This allows exponentiation to `work' for  arbitrary x and p.
>

I tried coding this into my parametric using the abs() function, BUT
mega said I had too many parameters.....

I remember asking about exactly how povray did the exponents ages ago,
and perhaps here we have a concrete problem. Any pointers?

/////------------------------------------
#declare n1=1;
#declare n2=0.99;

parametric {
                function
               (cos(u)^n1)*(cos(v)^n2),
               ((cos(u)^n1))*(sin(v)^n2),
                ((sin(u))^n1)
                <-pi*1,-2*pi>, <pi*1,pi*2>
                <-20,-20,-20>, <20,20,20>
                accuracy 0.001
                precompute 15, [x,y, z]
                pigment{SeaGreen*0.8}
                finish{ambient 0.3}
                 }

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Attachments:
Download 'superelllipse.jpg' (3 KB)

Preview of image 'superelllipse.jpg'

"Greg M. Johnson" wrote:
> 
> Why can't I get a working superellipse?
> 
> See code below and image below.  It looks like I'm losing two quadrants
> of the s-e. Note that when the n2 is changed to 1.0 I get a nice sphere.
> 
> I then read in a web page for CS from U of Western Australia:
> http://www.cs.uwa.edu.au/undergraduate/units/600.105/Lab6.html
> 
> > Note for this representation to work `exponentiation' must be defined 
> as
> >      p                   p
> >    x   =  sign(x) |x|
> >
> > Where the sign function returns +1 for +ve x, 0 for 0 x, and -1 for
> -ve x.
> > This allows exponentiation to `work' for  arbitrary x and p.
> >
> 
> I tried coding this into my parametric using the abs() function, BUT
> mega said I had too many parameters.....

See code below.


> I remember asking about exactly how povray did the exponents ages ago,
> and perhaps here we have a concrete problem. Any pointers?


Maybe it is done like this ?

x^n = exp(n*ln(x))

If so, then ln(x) may not be defined for x <= 0


I'm too tired to write more, so I'm going to sleep now.


Regardzzzzz,

Tor Olav
-- 
mailto:tor### [at] hotmailcom
http://www.crosswinds.net/~tok/tokrays.html


// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7

#version unofficial MegaPov 0.5;

#include "colors.inc"

global_settings { ambient_light color White*2 }

// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7

#declare n1 = 0.2;
#declare n2 = 0.2;

parametric {
  function
     abs(cos(u))^n1*if(cos(u), 1, -1)*abs(cos(v))^n2*if(cos(v), 1, -1),
     abs(cos(u))^n1*if(cos(u), 1, -1)*abs(sin(v))^n2*if(sin(v), 1, -1),
     abs(sin(u))^n1*if(sin(u), 1, -1)
     <-pi, -pi>, <pi, pi>
     <-1.1, -1.1, -1.1>, <1.1, 1.1, 1.1>
  accuracy 0.001
  precompute 15, [x, y, z]
  pigment { color White }
}

// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7

background { color Blue/2 }

light_source { <-3, 1, -1>*10 color White*2 }

camera {
  location <1, 1, -2>*1.5
  look_at <0, 0, 0>
}

// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7

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In article <3A53D643.959D0047@online.no>, Tor Olav Kristensen 
<tor### [at] onlineno> wrote:

> Maybe it is done like this ?
> 
> x^n = exp(n*ln(x))

Uh, I think "x^n = pow(x, n)" is more likely...

-- 
Christopher James Huff
Personal: chr### [at] maccom, http://homepage.mac.com/chrishuff/
TAG: chr### [at] tagpovrayorg, http://tag.povray.org/

<><

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Chris Huff wrote:

> Uh, I think "x^n = pow(x, n)" is more likely...

And is that undefined for  negative x and noninteger n?  That would
explain my missing quadrants on my superellipsoid. Will try Tor's code,
but have you any examples of working s-e's, too?

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In article <3A548297.54B63D54@my-dejanews.com>, 
gre### [at] my-dejanewscom wrote:

> > Uh, I think "x^n = pow(x, n)" is more likely...
> 
> And is that undefined for  negative x and noninteger n? 

It is defined as "x raised to the power of n", and works fine with 
negative x and fractional values of n.


> That would explain my missing quadrants on my superellipsoid. Will 
> try Tor's code, but have you any examples of working s-e's, too?

Not for parametrics...I never messed with them very much. I think your 
problem is more of a problem with the parametric shape than the function 
evaluation. For isosurfaces, I usually use something like:
function {Radius - sqrt(x^c1 + y^c2 + z^c3)}

Which isn't the same as the superellipsoid primitive, but works.

-- 
Christopher James Huff
Personal: chr### [at] maccom, http://homepage.mac.com/chrishuff/
TAG: chr### [at] tagpovrayorg, http://tag.povray.org/

<><

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Chris Huff wrote:

> It is defined as "x raised to the power of n", and works fine with
> negative x and fractional values of n.
>
> > That would explain my missing quadrants on my superellipsoid. Will
> > try Tor's code, but have you any examples of working s-e's, too?
>
> Not for parametrics...I never messed with them very much. I think your
> problem is more of a problem with the parametric shape than the function
> evaluation. For isosurfaces, I usually use something like:
> function {Radius - sqrt(x^c1 + y^c2 + z^c3)}
>
> Which isn't the same as the superellipsoid primitive, but works.

Thanks, but just to make sure you understand that predicament.

When I set up parametric equations for a superellipsoid and set my e,n, as
<1,1> I got a perfect sphere. When I set them as <0.99, 1.0>, I got
something which was very close to a sphere where it existed but was missing
in 2 quadrants. So you see I wasn't trying to set up a sphere (hence your
suggestion for the sphere equation?) but was showing how the parametric
bombs out strangely in certain cases; my question is whether the parametric
cannot handle x^n with negative x and noninteger n.

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On Thu, 04 Jan 2001 09:03:03 -0500, Greg M. Johnson wrote:
>Chris Huff wrote:
>
>> Uh, I think "x^n = pow(x, n)" is more likely...
>
>And is that undefined for  negative x and noninteger n? 

It is undefined for negative x and nonintegral _values_ of n.
pow(-3.14, 2.0) is well defined (apart from rounding effects). 

	hp

-- 
   _  | Peter J. Holzer    | Just because nobody in off-topic was
|_|_) | Sysadmin WSR       | particularly creative with their flames
| |   | hjp### [at] wsracat      | doesn't make them not flames
__/   | http://www.hjp.at/ |	-- Ron Parker in povray.general

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"Greg M. Johnson" wrote:
> 
> Chris Huff wrote:
> 
> > Uh, I think "x^n = pow(x, n)" is more likely...
> 
> And is that undefined for  negative x and noninteger n?

My HP-48 says this:

-2.5^1.2 = -2.42932519862 - i*1.76500807116

(I.e.: That the result is a complex number.)


And in "The C Library Reference Guide" 
http://www.xs4all.nl/~pvl/c/

I found this page:

http://www.xs4all.nl/~pvl/c/2.7.html#pow

(It describes briefly the functions in C's math.h)

It says this about the range of pow()

x cannot be negative if y is a fractional value.
x cannot be zero if y is less than or equal to zero. 


And then I found this page:

http://www.informatik.uni-hamburg.de/RZ/software/gnu/libraries/libc_13.html#SEC255

that also mentions the range for the arguments of pow()
(in glibc GNU C library)

Index page here:
http://www.informatik.uni-hamburg.de/RZ/software/gnu/libraries/libc_toc.html



But I don't know how correct the above pages are 
and if POV uses C's pow function.


Regards,

Tor Olav
-- 
mailto:tor### [at] hotmailcom
http://www.crosswinds.net/~tok/tokrays.html

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Chris Huff wrote:
> 
> In article <3A53D643.959D0047@online.no>, Tor Olav Kristensen
> <tor### [at] onlineno> wrote:
> 
> > Maybe it is done like this ?
> >
> > x^n = exp(n*ln(x))
> 
> Uh, I think "x^n = pow(x, n)" is more likely...

Yes, but do you know how this is actually computed ?


Regards,

Tor Olav
-- 
mailto:tor### [at] hotmailcom
http://www.crosswinds.net/~tok/tokrays.html

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In article <3A551CB5.7A4B4E1F@online.no>, Tor Olav Kristensen 
<tor### [at] onlineno> wrote:

> > Uh, I think "x^n = pow(x, n)" is more likely...
> 
> Yes, but do you know how this is actually computed ?

With the standard C "pow(x, n)" function, I assume...

-- 
Christopher James Huff
Personal: chr### [at] maccom, http://homepage.mac.com/chrishuff/
TAG: chr### [at] tagpovrayorg, http://tag.povray.org/

<><

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