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
