Message Boards Message Boards


[GIF] Ruled (doubly ruled surface)

Posted 5 years ago
1 Reply
6 Total Likes

One-parameter family of hyperboloids


I made this for this month's MCCC. The theme is "lines", which immediately made me think about ruled surfaces, so this is just a family of ruled hyperboloids.

Here's the code for the corresponding Manipulate[]:

MCCCcols2 = {RGBColor["#F07B3F"], RGBColor["#FFD460"], 
  RGBColor["#EA5455"], RGBColor["#2D4059"]}

 n = 99;
    Table[{MCCCcols2[[Mod[t, 3, 1]]], 
      InfiniteLine[{{Cos[2 \[Pi] t/n], Sin[2 \[Pi] t/n], 
         0}, {Cos[2 \[Pi] t/n], Sin[2 \[Pi] t/n], 
          0} + {-Cos[\[Theta]] Sin[2 \[Pi] t/n], 
          Cos[\[Theta]] Cos[2 \[Pi] t/n], Sin[\[Theta]]}}]}, {t, 1, 
      n}]}, PlotRange -> 2, Boxed -> False, ImageSize -> 540, 
   ViewAngle -> \[Pi]/6, ViewCenter -> {.46, .5, 1/2}, 
   Background -> MCCCcols2[[4]]], {\[Theta], 0, \[Pi]}]

The fact that the hyperboloid is squared-off when \[Theta] is small is due to the bounding box. This bothered me for a while, but I made a version where the line segment endpoints always formed a circle and found it a little too boring. The transition from squared-off to round adds visual interest that I think enhances the animation.

(Incidentally, to make alternate round version I ended up converting to ParametricPlot3D so that I could use RegionFunction, but it would have been nicer to be able to do it in Graphics3D. Is there any way to mimic the behavior of RegionFunction in a Graphics3D object?)

enter image description here -- you have earned Featured Contributor Badge enter image description here Your exceptional post has been selected for our editorial column Staff Picks and Your Profile is now distinguished by a Featured Contributor Badge and is displayed on the Featured Contributor Board. Thank you!

Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
or Discard

Group Abstract Group Abstract