Doubly Ruled Hyperbolic Paraboloid


Is there a way this can be done in Blender?

If so, where’s a good place to start?

Has someone already done it?

Is there a Math XYZ or Z function for this?

like that ?

happy bl

No, that’s the saddle.

The example is different.

Here’s another example:
Note: The only rounding is in the center, not around the edges.

Subdivide plane and rotate ends then.

Here’s one way, I’m not sure if it is 100% mathematically correct, though.

  1. Create a plane
  2. Rotate one edge along it’s perpendicular axis by 30 degrees.
  3. Rotate the opposite edge along the same axis, but by -30 degrees.
  4. Select all subdivide. ( I used 9 cuts).


Edit: I see Eppo beat me to it! You guys/gals are just too fast!! And of course, Eppo’s way seems much easier. :confused: After seeing Eppo’s post, I have revised my post with the easier method.

like this?

each stick is stright. nothing is curved. if you Subdevide a Plane, you might get curved edges.

PS: i intentionally made the sticks slightly different length, cause they where not even in the exsample you posted.


Without making any adjustments to the default settings of the plane, wouldn’t the default perpendicular
axis be “Z”?

Rotating before or after subdividing, isn’t giving me what you got.

Got it! Used the X axis instead.

Been looking EVERYWHERE on this.

Thank you SO much!

The formula is stated as:

“A doubly ruled hyperbolic paraboloid with equation z=xy”

[I]but, I have no idea how that translates into a Math Function

Seems there ought to be a way to do it.

There’s already a working formula for a Saddle
hyperbolic curve, but, it’s a Saddle, not the same.


sorry but hyperbolic paraboloid is a saddle !
see wiki
so may be you don’t have right name for the curve your have here!
also you want sticks to follow the curve so it is not really a curve as such!

happy bl

Ricky, it’s not my grammar I’m going by.

This is the language from the wikipedia site on “ruled surface”:

“A doubly ruled hyperbolic paraboloid with equation z=xy”

Not that your saddle is NOT a hyperbolic paraboloid. It IS.

It’s just not as specifically stated (or shown) at the site:

A “doubly ruled” hyperbolic paraboloid - what I’m looking

Your saddle and the example shown are NOT the same.
They are BOTH hyperbolic paraboloids, but, by appearance
alone, they are NOT the same.

Now I’m no math whiz, so, I’m not here to argue credibly
about the difference. I’m just repeating what I found.

You might want to take it up with someone considerably more
math literate.

Wouldn’t this method, also work with an array?

A bar, replicated 8 or nine times along the x and y axes,
joined (I think - haven’t tried this), then bent comparably
along the perpendicular?

Just another way of getting to the same end.

That would allow for more flexibility per your example

(Or, is that what you did, thereby proving the point?)


Here’s an example of what I had in mind:

Little more work than I thought.

Added a cylinder
Scaled it
Rotated it
Array Modifier - x9 w/offset (3.5) / Applied
Broke into separate parts (Edit / P)
Set Origin (via Transform to center/end of cylinder)
Ctrl-A (Reset Rotations)
Rotated up (multiples of 8 along the y axis - 8, 16, 24, 32, etc)
Selected All
Duplicated Twice - Shift-D
Rotated around as you see

Not sure if it’s a true hyperbolic paraboloid, but, it
looks neat.

Addon Add Mesh:Extra objects.
Write “x*y” where it says Z Equation (Z Math Surface).
Select straight edge loops, separate and convert to curves, give fill type Full, Bevel and Resolution.

ok I check the wiki page
and it says
for some specific parameters
we see that the hyperbolic paraboloid is congruent to the surface Z = X Y

I will make a new script to test that !
and see results of the 2 surfaces!


here is drawing of Z = XY in green
and the saddle in blue

and the surface Z = XY fit right above the saddle so it is congruent !

happy bl

Gorillas and chimpanzees are congruent.

Horses and Jackasses are congruent.

Men and Women are congruent.

Raspberries and blackberries are congruent.

But, they AIN’T the same.