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I have tried and failed to use the Bezier Curve tool to create a 3D saddle shape only managing to bend a plane in one direction.

Is this the best way to do so and how should I go about doing it?

This is the shape i'm trying to create:

picture from http://erikdemaine.org/hypar/

Thanks

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    $\begingroup$ can you add a picture of what you want to create? Are you struggling with trying to get the plane to bend "around the horse" and arch front to back? $\endgroup$ – David Feb 15 '17 at 23:04
  • $\begingroup$ I guess a subdivided plane driven by a lattice modifier would do the job perfectly, I'll make you a more detailed answer later. $\endgroup$ – Ahmed Ali Feb 16 '17 at 21:35
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Bezier curves are not the proper tool for this, curves are useful mainly for extrusion based geometries, or sections-swept-along-paths shapes.

NURBS surfaces may be closer to what you need, though they will require some considerable manual modeling work, and they are a half-baked tool in Blender that wont help much.

You may also model this manually using meshes and subdivisions, but again will require a lot of manual modelling and not necessarily yield a mathematically accurate surface.

The best way to model such thing is using the builtin addon Add Mesh: Extra Objects Python script

Start by opening File > User Preferences > Addons then search for Extra and activate the Add Mesh: Extra Objects addon.

Then in the 3D View press Shift+A > Add > Mesh > Math Function > Z Math Function

According to Wikipedia the mathematical function for a simple Saddle Point surface is Z = X^2 - Y^2 so in the operator properties change the input formula to the desired function using Python notation which should be (x**2 - Y**2)

Blender Saddle Point Z function

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If you're just going for that look, and don't need mathematical precision,
Subdivide a plane then add a Simple Deform modifier using a sphere.

Do this twice. Once along the X-axis, and once along the Y-axis.

Set the Deform Angle positive for one of 'em,
and negative for the other.

You can see the technique illustrated here:
https://www.youtube.com/watch?v=x77mvrmI0ck

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