For me, a hyperbolic paraboloid is one of those things that has to be seen to be believed. As Mike mentions, it is a "ruled surface". That means that you can make a grid on the surface formed by straight lines, all lying on the surface.
There are oompty-oomp ways of constructing one in TC.. In the attached drawing, made in TC V17, I've done it by Twist Extrude (2" height, 45 degree twist) of a straight line, and by lofting two straight lines, then, after exploding, shelling to a small thickness. The 3D lines in the "Rules" layer were constructed by 'make copy' of a single 2D line, moving +Z=0.2 and rot Z=4.5.
Edit 10/5/15: It has come to my attention that there is an error in the original post. The definition of the surface is Y=aXZ, so that Z=(Y/aX) and the rotation angle for constant Z should be ArcTan(Y/aX). Anyway, for those (apparently few) interested people, I'm replacing the original .tcw file with a corrected and 'beautified' version.
« Last Edit: October 05, 2015, 12:20:00 PM by Don Ritchie »
TC 11.2 and 17.2 Platinum