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
