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
