What makes you say that? ;-)
Although I have gained quite a bit of useful trig using POV, so maybe I
should add a tutorial to my website...

Sander wrote:

> Am I right in assuming you are writing a book on mathematics, David? :-P

--
___     ______________________________________________________
 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
 |_/avid |ontaine               http://www.faricy.net/~davidf/

"Sitting on a cornflake, waiting for the van to come" -Beatles

Post a reply to this message

Thanks! Just what I needed.
In case you were wondering, I was looking at the icosahedral stellations and
read that all the lines dividing the plane are the intersections with the
planes of the other faces on the icosahedron... Now it should only take me
five years to work out all the trig...

--
___     ______________________________________________________
 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
 |_/avid |ontaine               http://www.faricy.net/~davidf/

"Sitting on a cornflake, waiting for the van to come" -Beatles

Post a reply to this message

I follow the answers to your math questions eagerly: I learn a thing or 2,
too!
Keep on asking them...
--
Regards,
Sander


David Fontaine <dav### [at] faricynet> schreef in berichtnieuws
38AEFF3C.C3FF00E4@faricy.net...
> What makes you say that? ;-)
> Although I have gained quite a bit of useful trig using POV, so maybe I
> should add a tutorial to my website...
>

Post a reply to this message

Serge LAROCQUE <sgl### [at] hotmailcom> wrote:
: Now, the cross-product ( I hope this will be displayed properly)
:                             i        j        k
: N = PQxQR =     -3    1        -2     = (-1,9,6)
:                             3    -3        5

  I seriously suggest you to use a monospaced font.

-- 
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):5;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/

Post a reply to this message

Serge LAROCQUE wrote:

> > In case you were wondering, I was looking at the icosahedral stellations and
> > read that all the lines dividing the plane are the intersections with the
> > planes of the other faces on the icosahedron... Now it should only take me
> > five years to work out all the trig...

Calculate all the points of the icosahedron (with one face being parallel to x-z
plane) and store them in p1-p12 on the TI-89. Shortcut: calculate two points,
rotate them 120 and 240 around y to get the other points on that hemisphere, and
reflect those about the origin to get the other hemisphere.
Now here comes my fancy user-defined function (psuedo-code here):

 Input pa,pb,pc
 v1=pa-pb   v2=pc-pb
 <coefficients>c={v1 cross v2[1], v1 cross v2[2], v1 cross v2[3], (v1 cross v2)
dot pa}
 // Ax+By+Cz=D and y=<dist. from origin to center of any face> fd
 // therefore z=-(A/C)x+(D-B(fd))/C
 return {-c[1]/c[3],(c[4]-c[2]*fd)/c[3]}
 // return[1] = a, return[2] = b, line is y=ax+b

store all these coefficients in l1[1],l1[2]...l18[1],l18[2]
Then another fancy user-defined function to solve y=Ax+B and y=Cx+D (the built-in
solver does not output the result in a readily usable format, you would have to
remove the "x=", "and", and "y=" parts)
x=(-B-D)/(A-C) and y=(AD-BC)/(A-C)
There, you have all your points of intersection :-)

--
___     ______________________________________________________
 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
 |_/avid |ontaine               http://www.faricy.net/~davidf/

"Sitting on a cornflake, waiting for the van to come" -Beatles

Post a reply to this message

This is a macro I found somewhere on this:
#macro MakePlane(a,b,c)
  #local n=vnormalize(vcross((b)-(a),(c)-(a)));
  #local o=vdot((a),n);
  plane {n,o pigment { onion} }
#end

#declare a = <-1,1,0>;
#declare b = <1,0,-1>  ;
#declare c = <2,0,1>;
sphere { a 0.25 pigment { rgb <1,0,0> } }
sphere { b 0.25 pigment { rgb <0,1,0> } }
sphere { c 0.25 pigment { rgb <0,0,1> } }

MakePlane(a,b,c)

I know, too little, too late.

Josh

David Fontaine wrote:

> --
> ___     ______________________________________________________
>  | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
>  |_/avid |ontaine               http://www.faricy.net/~davidf/
>
> "Sitting on a cornflake, waiting for the van to come" -Beatles

--
Josh English
eng### [at] spiritonecom
"May your hopes, dreams, and plans not be destroyed by a few zeros."

Post a reply to this message

Josh English wrote:

> This is a macro I found somewhere on this:
> #macro MakePlane(a,b,c)
>   #local n=vnormalize(vcross((b)-(a),(c)-(a)));
>   #local o=vdot((a),n);
>   plane {n,o pigment { onion} }
> #end

Oh, I wasn't doing this in POV, I was finding numbers on my 89 to type
into POV...

--
___     ______________________________________________________
 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
 |_/avid |ontaine               http://www.faricy.net/~davidf/

"Sitting on a cornflake, waiting for the van to come" -Beatles

Post a reply to this message

On Wed, 23 Feb 2000 01:08:13 -0500, Serge LAROCQUE wrote:
>Tsk tsk. depending on a TI89.. Ah heck I admit it, I use a HP48G (no, not
>the GX)

I use a Radio Shack (Casio) EC-4023.  You kids today and your Turing Complete
calculators...

-- 
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

Post a reply to this message

Or just:

#macro MakePlane(a, b, c)

  plane {
    vcross((b)-(a), (c)-(a)), 0
    translate a
  }

#end // macro MakePlane


Tor Olav Kristensen

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


Josh English wrote:

> This is a macro I found somewhere on this:
> #macro MakePlane(a,b,c)
>   #local n=vnormalize(vcross((b)-(a),(c)-(a)));
>   #local o=vdot((a),n);
>   plane {n,o pigment { onion} }
> #end
>
> #declare a = <-1,1,0>;
> #declare b = <1,0,-1>  ;
> #declare c = <2,0,1>;
> sphere { a 0.25 pigment { rgb <1,0,0> } }
> sphere { b 0.25 pigment { rgb <0,1,0> } }
> sphere { c 0.25 pigment { rgb <0,0,1> } }
>
> MakePlane(a,b,c)
>
> I know, too little, too late.
>
> Josh
>
> David Fontaine wrote:
>
> > --
> > ___     ______________________________________________________
> >  | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
> >  |_/avid |ontaine               http://www.faricy.net/~davidf/
> >
> > "Sitting on a cornflake, waiting for the van to come" -Beatles
>
> --
> Josh English
> eng### [at] spiritonecom
> "May your hopes, dreams, and plans not be destroyed by a few zeros."

Post a reply to this message

In article <38b3dff2@news.povray.org>, ron### [at] povrayorg wrote:

> I use a Radio Shack (Casio) EC-4023.  You kids today and your Turing 
> Complete calculators...

I have a Casio CFX-9850G 3-color graphing calculator. I would rather 
have gotten one of the higher-end TI models though...

-- 
Chris Huff
e-mail: chr### [at] yahoocom
Web page: http://chrishuff.dhs.org/

Post a reply to this message