Ron Parker <ron### [at] povrayorg> wrote in message
news:3885c3c6@news.povray.org...
> On Wed, 19 Jan 2000 11:55:15 +0100, Sigmund Kyrre Aas wrote:
> >Has anybody thought of adding spherical or toroidal coordinate systems
> >to the isosurface patch?
> >Just an idea.
>
> Spherical coordinates are already added, sort of.  As far as I know there
> aren't any usable toroidal coordinate systems, because every point in
> space could be defined in two or more unique ways in such a system.

There are, thought they are odd.

    x =  sinh v cos phi /(cosh v -cos u)
    y =  sinh v sin phi /(cosh v -cos u)
    z =  sin u /(cosh v -cos u)

    The v = const. curves are nested tori filling all of space except for a
circle and its axis of symmetry.  u=const. are the spheres containing that
circle; and phi is the longitude, with phi=const. being halfplanes emanating
from the axis. The coordinate surfaces at any point are all orthogonal.

    Source: Schaum's math tables.

    Why anybody would want them for raytracing I don't know, but I'm sure
somebody will <grin>.

    -Robert Dawson

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I was just playing around in Maple, and made some shapes there I'd like
to use in pov. f.x:

plot3d((1.2)^x * sin(y),x=-8..Pi,y=0..Pi,coords=spherical);
(snail's house)

plot3d(y,x=0..3*Pi,y=0..3*Pi,coords=toroidal,scaling=constrained);
(ufo)

I can post images in p.b.i if you are interested.

I've found several conversion functions in my "Matematische
Formelsamlung" by Rottmann, fx for torus:
x=l*cos(phi)*sinh(ksi)/(cosh(ksi)-cos(eta))
y=l*sinh(ksi)/(cosh(ksi)-cos(eta))
z=l*sin(eta)/(cosh(ksi)-cos(eta))
I'm not sure what l is, and certainly not how to do the #declare
function {thing}.

As for the built in functions, you can only pass numbers to those, not
functions. I don't see how I can use them here.

sig.

Chris Huff wrote:
> 
> If I understand what you mean, these already exist in the form of the
> built in functions(like "R", "TH", "PH", and whatever you can make with
> the trig functions like atan()). And you can construct your own
> functions to do whatever you want, just declare them.
> #declare WeirdCoordinateA = function {blahblah}
> #declare WeirdCoordinateB = function {blahblah}
> #declare WeirdCoordinateC = function {blahblah}
> 
> Then just use these functions as returning the coordinate values for
> your function.
> 
> --
> Chris Huff
> e-mail: chr### [at] yahoocom
> Web page: http://chrishuff.dhs.org/

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Do you mean like being able to rotate functions? Such as: (x^8+y^8+z^8
rotate y*45)

If so, that would be too cool. Such a thing would be a huge help.

Sigmund Kyrre Aas wrote:

> Has anybody thought of adding spherical or toroidal coordinate systems
> to the isosurface patch?
> Just an idea.
>
> sig.

--
Samuel Benge

E-Mail: STB### [at] aolcom

Visit the still unfinished isosurface tutorial:
http://members.aol.com/stbenge

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Sigmund Kyrre Aas wrote:
> Has anybody thought of adding spherical or toroidal coordinate systems
> to the isosurface patch?
> Just an idea.

Funny you should mention that, I thought about suggesting that feature
almost at the same time as your post...

:-)

Philippe

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No, I don't mean that (see post from yesterday), and I don't quite see
the urge for such a feature. Wouldn't this do the trick?:
isosurface {
   function {}
   rotate y*45
}

ps Just visited your isotutorial, and it looks very promising! 

sig.


SamuelT. wrote:
> 
> Do you mean like being able to rotate functions? Such as: (x^8+y^8+z^8
> rotate y*45)
> 
> If so, that would be too cool. Such a thing would be a huge help.
> 
> Sigmund Kyrre Aas wrote:
> 
> > Has anybody thought of adding spherical or toroidal coordinate systems
> > to the isosurface patch?
> > Just an idea.
> >
> > sig.
> 
> --
> Samuel Benge
> 
> E-Mail: STB### [at] aolcom
> 
> Visit the still unfinished isosurface tutorial:
> http://members.aol.com/stbenge

-- 
Sigmund Kyrre Aas 
Trondheim, Norway

Post a reply to this message

>No, I don't mean that (see post from yesterday), and I don't quite see
>the urge for such a feature. Wouldn't this do the trick?:
>isosurface {
>   function {}
>   rotate y*45
>}

Not if you plan to compose it with another function.  What we need is to
let vrotate() be allowable in isosurface functions, but that'd require us
to allow vectors.

-- 
These are my opinions.  I do NOT speak for the POV-Team.
The superpatch: http://www2.fwi.com/~parkerr/superpatch/
My other stuff: http://www2.fwi.com/~parkerr/traces.html

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SamuelT. <STB### [at] aolcom> wrote in message
news:38868E41.19938684@aol.com...
> Do you mean like being able to rotate functions? Such as: (x^8+y^8+z^8
> rotate y*45)
>

Being able to do general coordinate transformations would be a
very nice feature, but I think would require function{} accepting
vector-valued functions as additional parameters ( and the
attendant applying of the transforms)

For simple things like rotation about y you can get by with stuff like:

#declare F=function(x^8+y^8+z^8}
#declare A=pi/4;
#declare FRotated=function{cos(A)*x+sin(A)*z,  y, -sin(A)*x+cos(A)*z}

That is, applying a matrix rotation 'by hand' to the coordinates.
Of course this is not a very satisfactory solution since composing
rotations gets very ugly very quickly.

Post a reply to this message

david sharp wrote:
> Being able to do general coordinate transformations would be a
> very nice feature, but I think would require function{} accepting

I agree too that. Could be an interesting addition to matrix{}.

I'm posting images in p.b.i, since I'm not sure if you know what I'm
after.

.sig

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/*
Quick & dirty & UNTESTED cylindrical & polar coordinates function

copied from a math book,
blindly adapted for left-handed coordinate system
& thorougly UNTESTED (not even for parse errors)
(Philippe Debar phi### [at] hotmailcom )

*/

// Cylindrical coordinates

#declare CylRadius=function{sqrt(x^2+z^2)}
// use y for height


// Polar coordinates
#declare PolarRadius=function{sqrt(x^2+y^2+z^2)}
#declare PolarHorizontalAngle=function{atan2(z,x)}
#declare PolarVerticalAngle=function{atan2(CylRadius(x,y,z),y)}


// I hope it'll work

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I finally tried your functions, and they worked quite fine. Trouble is I
get a frayed surface near the y-axis, so I doubt I can use this for my
snail. Increasing accuracy doesn't work either.
Thanks, anyway. Bet I can use this for something else!

sig.

//Maple command:
//plot3d((1.2)^x * sin(y),x=-8..Pi,y=0..Pi,coords=spherical);

// spherical coords by Philippe Debar phi### [at] hotmailcom
#declare CylRadius=function{sqrt(x^2+z^2)}
#declare  Z = function{sqrt(x^2+y^2+z^2)}
#declare  X = function{atan2(z,x)}
#declare  Y = function{atan2(CylRadius(x,y,z),y)}

isosurface { 
    function { 
        (1.2)^X * sin(Y)-Z
    }
    accuracy .01
    max_trace 1
    threshold 0
    clipped_by {sphere {0,10}}
    pigment { rgb 1 } finish { specular .5 }
    rotate 0*y
}

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