Ah, It seems you are not doing 1 - (x^2 +y^2). i.e. your parentheses are messed up.in you (mathematica ?) code you need to do (c^2)*(1 - ((x/a)^2+(y/b)^2))^0.5 i.e. sum the x and y terms and then subtract them both from 1. (Note: i don't know mathematica syntax, but I assume the above is valid.)
> Date: Sat, 7 Mar 2015 02:59:48 -0600 > From: s...@caveconsulting.com > To: programm...@jsoftware.com > Subject: Re: [Jprogramming] Plotting a 3D Ellipse > > Jon, > > Well that made it DIFFERENT, but still not an ellipse... > > http://bit.ly/17ZqbyM > > Skip > > Skip Cave > Cave Consulting LLC > > On Sat, Mar 7, 2015 at 2:38 AM, Jon Hough <jgho...@outlook.com> wrote: > > > I think I can see 2 issues:1. you need to multiply by c^2 , not c.2. you > > need to sqrt the whole thing. > > > > > > > Date: Sat, 7 Mar 2015 02:32:38 -0600 > > > From: s...@caveconsulting.com > > > To: programm...@jsoftware.com > > > Subject: Re: [Jprogramming] Plotting a 3D Ellipse > > > > > > Well, I tried plotting the equation > > > z = (c*(1 - ((x^2)%(a^2)) + ((y^2)%(b^2)))) > > > > > > And I don't get anything like a ellipsoid. Here's what I get... > > > http://bit.ly/17Zou4t > > > What is going wrong? > > > > > > Skip Cave > > > Cave Consulting LLC > > > > > > On Sat, Mar 7, 2015 at 12:04 AM, Skip Cave <s...@caveconsulting.com> > > wrote: > > > > > > > Yes, I just solved the Cartesian equation, and got the same answer. I > > just > > > > need the positive values of z, so I can take the absolute value of the > > > > equation for the plot. > > > > > > > > Now I need to see if I can plot the ellipse by simply running x from > > 1-10, > > > > and then stepping y after each x pass. I want to see the zero values > > of x > > > > as well, making a plane that the half ellipse sets on. > > > > > > > > Skip > > > > > > > > On Mar 6, 2015 11:20 PM, "Raul Miller" <rauldmil...@gmail.com> wrote: > > > > > > > > > > Of course you realize that there are either two or zero values of z > > > > > for every value of x and y. > > > > > > > > > > That said, > > > > > (((x^2)%(a^2)) + ((y^2)%(b^2)) + ((z^2)%(c^2))) = 1 > > > > > (((c^2)*((x^2)%(a^2)) + ((y^2)%(b^2)))+ ((z^2)) = c^2 > > > > > (z^2) = (c^2)*(1 - ((x^2)%(a^2)) + ((y^2)%(b^2))) > > > > > > > > > > a=:3 > > > > > b=:4 > > > > > c=:5 > > > > > > > > > > z=:13 :'c * ((1 - ((x^2)%(a^2)) + ((y^2)%(b^2))))^0.5' > > > > > z > > > > > 5 * 0.5 ^~ 1 - (9 %~ 2 ^~ [) + 16 %~ 2 ^~ ] > > > > > > > > > > Or: > > > > > z=:1 _1 */ c * 0.5 ^~ 1 - ((a^2) %~ 2 ^~ [) + (b^2) %~ 2 ^~ ] > > > > > > > > > > Does that help? > > > > > > > > > > Thanks, > > > > > > > > > > -- > > > > > Raul > > > > > > > > > > On Sat, Mar 7, 2015 at 12:10 AM, Skip Cave <s...@caveconsulting.com> > > > > wrote: > > > > > > Raul, > > > > > > > > > > > > Yes. What I need is a function f (x,y) using the Cartesian > > coordinates > > > > x & > > > > > > y that will produce the z dimension in the ellipse when I step x & > > y > > > > over > > > > > > the plane. > > > > > > > > > > > > Skip > > > > > > > > > > > > Skip Cave > > > > > > Cave Consulting LLC > > > > > > > > > > > > On Fri, Mar 6, 2015 at 11:03 PM, Raul Miller < > > rauldmil...@gmail.com> > > > > wrote: > > > > > > > > > > > >> I imagine they'd go something like this: > > > > > >> > > > > > >> X=. a*((sin P) */ cos T) > > > > > >> Y=. b*(((sin P) */ sin T) > > > > > >> Z=. c*((cos P) +/ T*0)%2 > > > > > >> > > > > > >> The assumption would be that when they are omitted they are 1. > > > > > >> > > > > > >> The trick is recognizing how these parametric equations > > correspond to > > > > > >> your original expression. > > > > > >> > > > > > >> Thanks, > > > > > >> > > > > > >> -- > > > > > >> Raul > > > > > >> > > > > > >> On Sat, Mar 7, 2015 at 12:00 AM, Skip Cave < > > s...@caveconsulting.com> > > > > > >> wrote: > > > > > >> > Ok now I'm confused. Nowhere do I see where we set the length > > of the > > > > > >> three > > > > > >> > axes a, b, and c. Also the step verb has lots of variables in > > it, > > > > like a, > > > > > >> > w, n, and z that I don't see defined anywhere. > > > > > >> > steps=: 3 : 'a+(w)*(i.n+1)%n[w=.z-a[''a z n''=.y' > > > > > >> > > > > > > >> > How do I change the lengths of the axes a, b,and c? > > > > > >> > > > > > > >> > Skip Cave > > > > > >> > Cave Consulting LLC > > > > > >> > > > > > > >> > On Fri, Mar 6, 2015 at 10:25 PM, Joe Bogner < > > joebog...@gmail.com> > > > > wrote: > > > > > >> > > > > > > >> >> I don't know what I'm doing other than copy/pasting, but the > > > > example > > > > > >> from > > > > > >> >> the plot demo looks pretty close: > > > > > >> >> > > > > > >> >> load 'plot' > > > > > >> >> pd 'clear' > > > > > >> >> steps=: 3 : 'a+(w)*(i.n+1)%n[w=.z-a[''a z n''=.y' > > > > > >> >> P=. steps 0 1p1 30 > > > > > >> >> T=. steps 0 2p1 40 > > > > > >> >> X=. ((sin P) */ cos T) > > > > > >> >> Y=. ((sin P) */ sin T) > > > > > >> >> Z=. ((cos P) +/ T*0)%2 > > > > > >> >> > > > > > >> >> pd 'backcolor blue' > > > > > >> >> pd 'new 0 0 1000 1000' > > > > > >> >> > > > > > >> >> pd 'type surface' > > > > > >> >> pd 'viewpoint 2 2 2;color grayscale' > > > > > >> >> pd X;Y;Z > > > > > >> >> pd 'show' > > > > > >> >> > > > > > >> >> > > > > > >> >> > > > > > >> >> On Fri, Mar 6, 2015 at 11:18 PM, Raul Miller < > > > > rauldmil...@gmail.com> > > > > > >> >> wrote: > > > > > >> >> > > > > > >> >> > This is something of an aside - I don't know what I'm doing > > yet, > > > > well > > > > > >> >> > enough to implement this via jhs, but here's an ellipsoid: > > > > > >> >> > > > > > > >> >> > https://www.shadertoy.com/view/XtlGDX > > > > > >> >> > > > > > > >> >> > You can tweak the a, b, and c radius values near the top of > > the > > > > script > > > > > >> >> > (which should display on the right side of the screen) and > > hit > > > > the > > > > > >> >> > play button to see the change. > > > > > >> >> > > > > > > >> >> > Thanks, > > > > > >> >> > > > > > > >> >> > -- > > > > > >> >> > Raul > > > > > >> >> > > > > > > >> >> > On Fri, Mar 6, 2015 at 10:38 PM, Skip Cave < > > > > s...@caveconsulting.com> > > > > > >> >> > wrote: > > > > > >> >> > > Looking a bit better, but no cigar: > > > > > >> >> > > > > > > > >> >> > > a=:3[b=:3[c=:3 > > > > > >> >> > > > > > > > >> >> > > X=:4 :0 > > > > > >> >> > > > > > > > >> >> > > a*(cos x)*cos y > > > > > >> >> > > > > > > > >> >> > > ) > > > > > >> >> > > > > > > > >> >> > > Y=:4 :0 > > > > > >> >> > > > > > > > >> >> > > b*(cos x)*sin y > > > > > >> >> > > > > > > > >> >> > > ) > > > > > >> >> > > > > > > > >> >> > > Z=:3 :0 > > > > > >> >> > > > > > > > >> >> > > c*(sin y) > > > > > >> >> > > > > > > > >> >> > > ) > > > > > >> >> > > > > > > > >> >> > > steps=: 3 : 'a+(w)*(i.n+1)%n[w=.z-a[''a z n''=.y' > > > > > >> >> > > > > > > > >> >> > > draw=:3 :0 > > > > > >> >> > > > > > > > >> >> > > angles=: steps _1p1 1p1 100 > > > > > >> >> > > > > > > > >> >> > > uangles =: steps _1.5708 1.5708 100 > > > > > >> >> > > > > > > > >> >> > > x=. uangles X"0 _ angles > > > > > >> >> > > > > > > > >> >> > > y=. uangles Y"0 _ angles > > > > > >> >> > > > > > > > >> >> > > z=. Z uangles > > > > > >> >> > > > > > > > >> >> > > 'surface' plot x;y;z > > > > > >> >> > > > > > > > >> >> > > ) > > > > > >> >> > > > > > > > >> >> > > draw'' > > > > > >> >> > > > > > > > >> >> > > > > > > > >> >> > > output at: http://bit.ly/1wNlQe3 > > > > > >> >> > > > > > > > >> >> > > > > > > > >> >> > > Skip Cave > > > > > >> >> > > Cave Consulting LLC > > > > > >> >> > > > > > > > >> >> > > On Fri, Mar 6, 2015 at 9:18 PM, Raul Miller < > > > > rauldmil...@gmail.com> > > > > > >> >> > wrote: > > > > > >> >> > > > > > > > >> >> > >> steps=: 3 : 'a+(w)*(i.n+1)%n[w=.z-a[''a z n''=.y' > > > > > >> >> > >> > > > > > >> >> > >> Thanks, > > > > > >> >> > >> > > > > > >> >> > >> -- > > > > > >> >> > >> Raul > > > > > >> >> > >> > > > > > >> >> > >> On Fri, Mar 6, 2015 at 10:08 PM, Skip Cave < > > > > > >> s...@caveconsulting.com> > > > > > >> >> > >> wrote: > > > > > >> >> > >> > Here's what I got whaen I ran Jon's code: > > > > > >> >> > >> > > > > > > >> >> > >> > a=:3[b=:3[c=:3 > > > > > >> >> > >> > > > > > > >> >> > >> > X=:4 :0 > > > > > >> >> > >> > > > > > > >> >> > >> > a*(cos x)*cos y > > > > > >> >> > >> > > > > > > >> >> > >> > ) > > > > > >> >> > >> > > > > > > >> >> > >> > Y=:4 :0 > > > > > >> >> > >> > > > > > > >> >> > >> > b*(cos x)*sin y > > > > > >> >> > >> > > > > > > >> >> > >> > ) > > > > > >> >> > >> > > > > > > >> >> > >> > Z=:3 :0 > > > > > >> >> > >> > > > > > > >> >> > >> > c*(sin y) > > > > > >> >> > >> > > > > > > >> >> > >> > ) > > > > > >> >> > >> > > > > > > >> >> > >> > draw=:3 :0 > > > > > >> >> > >> > > > > > > >> >> > >> > angles=: steps _1p1 1p1 100 > > > > > >> >> > >> > > > > > > >> >> > >> > uangles =: steps _1.5708 1.5708 100 > > > > > >> >> > >> > > > > > > >> >> > >> > x=. uangles X"0 _ angles > > > > > >> >> > >> > > > > > > >> >> > >> > y=. uangles Y"0 _ angles > > > > > >> >> > >> > > > > > > >> >> > >> > z=. Z uangles > > > > > >> >> > >> > > > > > > >> >> > >> > 'surface' plot x;y;z > > > > > >> >> > >> > > > > > > >> >> > >> > ) > > > > > >> >> > >> > > > > > > >> >> > >> > draw'' > > > > > >> >> > >> > > > > > > >> >> > >> > |value error: steps > > > > > >> >> > >> > > > > > > >> >> > >> > | angles=: steps _3.14159 3.14159 100 > > > > > >> >> > >> > > > > > > >> >> > >> > > > > > > >> >> > >> > Skip Cave > > > > > >> >> > >> > Cave Consulting LLC > > > > > >> >> > >> > > > > > > >> >> > >> > On Fri, Mar 6, 2015 at 8:56 PM, Jon Hough < > > > > jgho...@outlook.com> > > > > > >> >> > wrote: > > > > > >> >> > >> > > > > > > >> >> > >> >> > > > > > >> >> > >> >> I butchered Raul's script slightly. But the resulting > > > > graph is > > > > > >> >> still > > > > > >> >> > >> >> weird. Not sure if it's an improvement. > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> a=:3[b=:3[c=:3 > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> X=:4 :0 > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> a*(cos x)*cos y > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> ) > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> Y=:4 :0 > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> b*(cos x)*sin y > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> ) > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> Z=:3 :0 > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> c*(sin y) > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> ) > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> draw=:3 :0 > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> angles=: steps _1p1 1p1 100 > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> uangles =: steps _1.5708 1.5708 100 > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> x=. uangles X"0 _ angles > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> y=. uangles Y"0 _ angles > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> z=. Z uangles > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> 'surface' plot x;y;z > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> ) > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > >> >> draw'' > > > > > >> >> > >> >> > > > > > >> >> > >> >> > From: jgho...@outlook.com > > > > > >> >> > >> >> > To: programm...@jsoftware.com > > > > > >> >> > >> >> > Date: Sat, 7 Mar 2015 02:46:35 +0000 > > > > > >> >> > >> >> > Subject: Re: [Jprogramming] Plotting a 3D Ellipse > > > > > >> >> > >> >> > > > > > > >> >> > >> >> > It seems you are using [-pi,pi] as the range of all > > your > > > > > >> angles.I > > > > > >> >> > >> think > > > > > >> >> > >> >> you need to use [-pi/2,pi/2] as the range for the u > > > > argument (in > > > > > >> >> the > > > > > >> >> > >> >> wikipedia page). > > > > > >> >> > >> >> > > > > > > >> >> > >> >> > > From: rauldmil...@gmail.com > > > > > >> >> > >> >> > > Date: Fri, 6 Mar 2015 21:35:37 -0500 > > > > > >> >> > >> >> > > To: programm...@jsoftware.com > > > > > >> >> > >> >> > > Subject: Re: [Jprogramming] Plotting a 3D Ellipse > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > Hmm... > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > I notice that load'graph' no longer provides the > > steps > > > > verb > > > > > >> >> > >> mentioned > > > > > >> >> > >> >> > > in http://www.jsoftware.com/books/pdf/expmath.pdf > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > So here's a workalike: > > > > > >> >> > >> >> > > steps=: 3 : 'a+(w)*(i.n+1)%n[w=.z-a[''a z > > n''=.y' > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > and that gives us an example of a surface plot. > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > Next, we need a parametric representation of the > > > > ellipse, > > > > > >> and > > > > > >> >> > >> >> > > > > > > http://en.wikipedia.org/wiki/Ellipsoid#Parameterization > > > > > >> looks > > > > > >> >> > like > > > > > >> >> > >> a > > > > > >> >> > >> >> > > plausible approach there. > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > Using that, and > > > > > >> >> http://www.jsoftware.com/help/jforc/graphics.htm > > > > > >> >> > >> as a > > > > > >> >> > >> >> > > starting point, it seems to me that I ought to be > > able > > > > to > > > > > >> draw > > > > > >> >> an > > > > > >> >> > >> >> > > ellipse like this: > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > a=:3[b=:4[c=:5 > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > X=:4 :0~ > > > > > >> >> > >> >> > > a*(cos x)*/cos y > > > > > >> >> > >> >> > > ) > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > Y=:4 :0~ > > > > > >> >> > >> >> > > b*(cos x)*/sin y > > > > > >> >> > >> >> > > ) > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > Z=:4 :0~ > > > > > >> >> > >> >> > > c*(sin x)*/1: y > > > > > >> >> > >> >> > > ) > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > draw=:3 :0 > > > > > >> >> > >> >> > > angles=: steps _1p1 1p1 100 > > > > > >> >> > >> >> > > x=. X angles > > > > > >> >> > >> >> > > y=. Y angles > > > > > >> >> > >> >> > > z=. Z angles > > > > > >> >> > >> >> > > 'surface' plot x;y;z > > > > > >> >> > >> >> > > ) > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > draw'' > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > Sadly, that's not an ellipse. > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > But I do not have enough familiarity with plot to > > know > > > > > >> whether > > > > > >> >> > I've > > > > > >> >> > >> >> > > screwed up my math or if there's a defect in plot > > -- I > > > > don't > > > > > >> >> know > > > > > >> >> > >> how > > > > > >> >> > >> >> > > to isolate the problem. > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > That said, a quick test with a 3d model of a cube: > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > 'surface' plot ;/|:#:i.8 > > > > > >> >> > >> >> > > |NaN error: ncile > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > ...suggests that plot isn't really designed to > > > > represent 3d > > > > > >> >> > solids. > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > Still, that does not eliminate any potential > > errors on > > > > my > > > > > >> part. > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > On the other hand, maybe the right approach would > > be > > > > to use > > > > > >> jhs > > > > > >> >> > and > > > > > >> >> > >> >> > > generate a distance field renderer along the lines > > of > > > > what > > > > > >> you > > > > > >> >> > see > > > > > >> >> > >> at > > > > > >> >> > >> >> > > shadertoy.com. > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > I'll have to think a bit to see if I can pull off > > > > something > > > > > >> >> like > > > > > >> >> > >> that. > > > > > >> >> > >> >> > > (I think that that would only work for people who > > have > > > > > >> adequate > > > > > >> >> > >> >> > > graphics hardware support. But I think you have a > > > > suitable > > > > > >> >> > graphics > > > > > >> >> > >> >> > > card?) > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > Thanks, > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > -- > > > > > >> >> > >> >> > > Raul > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > > > > > > >> >> > >> >> > > On Fri, Mar 6, 2015 at 7:10 PM, Skip Cave < > > > > > >> >> > s...@caveconsulting.com> > > > > > >> >> > >> >> wrote: > > > > > >> >> > >> >> > > > I want to plot a 3D ellipse (ellipsoid) and then > > be > > > > able > > > > > >> to > > > > > >> >> > change > > > > > >> >> > >> >> the > > > > > >> >> > >> >> > > > lengths of the three axes. The equation of an > > > > ellipse with > > > > > >> >> axis > > > > > >> >> > >> >> lengths of > > > > > >> >> > >> >> > > > a, b, & c is: > > > > > >> >> > >> >> > > > > > > > > >> >> > >> >> > > > ((x^2)%(a^2)) + ((y^2)%(b^2)) + ((z^2)%(c^2)) = > > 1 > > > > > >> >> > >> >> > > > > > > > > >> >> > >> >> > > > How can I arrange this so it can be plotted in a > > 3-D > > > > plot > > > > > >> in > > > > > >> >> J, > > > > > >> >> > >> and > > > > > >> >> > >> >> then be > > > > > >> >> > >> >> > > > able to experiment with the lengths of the axes? > > > > > >> >> > >> >> > > > > > > > > >> >> > >> >> > > > Skip > > > > > >> >> > >> >> > > > > > > > > >> >> > >> >> > > > Skip Cave > > > > > >> >> > >> >> > > > Cave Consulting LLC > > > > > >> >> > >> >> > > > > > > > > >> >> > >> >> > > > > > >> >> > > > > > ---------------------------------------------------------------------- > > > > > >> >> > >> >> > > > For information about J forums see > > > > > >> >> > >> >> http://www.jsoftware.com/forums.htm > > > > > >> >> > >> >> > > > > > > > >> >> > >> > > > > > >> > > ---------------------------------------------------------------------- > > > > > >> >> > >> >> > > For information about J forums see > > > > > >> >> > >> http://www.jsoftware.com/forums.htm > > > > > >> >> > >> >> > > > > > > >> >> > >> >> > > > > > > >> >> > > > > > ---------------------------------------------------------------------- > > > > > >> >> > >> >> > For information about J forums see > > > > > >> >> > >> http://www.jsoftware.com/forums.htm > > > > > >> >> > >> >> > > > > > >> >> > >> >> > > > > > >> >> > > > > > ---------------------------------------------------------------------- > > > > > >> >> > >> >> For information about J forums see > > > > > >> >> > http://www.jsoftware.com/forums.htm > > > > > >> >> > >> >> > > > > > >> >> > >> > > > > > > >> >> > > > > ---------------------------------------------------------------------- > > > > > >> >> > >> > For information about J forums see > > > > > >> >> > http://www.jsoftware.com/forums.htm > > > > > >> >> > >> > > > > > >> > > ---------------------------------------------------------------------- > > > > > >> >> > >> For information about J forums see > > > > > >> >> http://www.jsoftware.com/forums.htm > > > > > >> >> > >> > > > > > >> >> > > > > > > > >> > > ---------------------------------------------------------------------- > > > > > >> >> > > For information about J forums see > > > > > >> http://www.jsoftware.com/forums.htm > > > > > >> >> > > > > > ---------------------------------------------------------------------- > > > > > >> >> > For information about J forums see > > > > > >> http://www.jsoftware.com/forums.htm > > > > > >> >> > > > > > > >> >> > > > > ---------------------------------------------------------------------- > > > > > >> >> For information about J forums see > > > > http://www.jsoftware.com/forums.htm > > > > > >> >> > > > > > >> > > > > > ---------------------------------------------------------------------- > > > > > >> > For information about J forums see > > > > http://www.jsoftware.com/forums.htm > > > > > >> > > ---------------------------------------------------------------------- > > > > > >> For information about J forums see > > > > http://www.jsoftware.com/forums.htm > > > > > >> > > > > > > > > ---------------------------------------------------------------------- > > > > > > For information about J forums see > > http://www.jsoftware.com/forums.htm > > > > > > > ---------------------------------------------------------------------- > > > > > For information about J forums see > > http://www.jsoftware.com/forums.htm > > > > > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
