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 <[email protected]> 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" <[email protected]> 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 <[email protected]> > 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 <[email protected]> > 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 <[email protected]> > > >> 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 <[email protected]> > 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 < > [email protected]> > > >> >> 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 < > [email protected]> > > >> >> > 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 < > [email protected]> > > >> >> > 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 < > > >> [email protected]> > > >> >> > >> 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 < > [email protected]> > > >> >> > 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: [email protected] > > >> >> > >> >> > To: [email protected] > > >> >> > >> >> > 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: [email protected] > > >> >> > >> >> > > Date: Fri, 6 Mar 2015 21:35:37 -0500 > > >> >> > >> >> > > To: [email protected] > > >> >> > >> >> > > 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 < > > >> >> > [email protected]> > > >> >> > >> >> 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
