z = (c*(1 - ((x^2)%(a^2)) + ((y^2)%(b^2)))) is different from
c * ((1 - ((x^2)%(a^2)) + ((y^2)%(b^2))))^0.5 When solving for z you need to take the square root of something. The equation you're working with looks like it got part of it chopped off. Perhaps it would be clearer if we reorganized things a bit: z =: c*(1 - rest) ^ 0.5 where rest=: ((x%a)^2) + (y%b)^2 There's other ways of doing this, but basically you're working with a root-mean-square type of equation. Thanks, -- Raul On Sat, Mar 7, 2015 at 3:32 AM, Skip Cave <s...@caveconsulting.com> wrote: > 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
