TurboCAD Forums
Turbo Talk => General Discussion => Topic started by: Mike Hall on September 29, 2015, 06:01:32 AM

I think TC will do this. I want to create a modified 3D saddle shape. Could someone point out which tools to use for this.
thanks
Michael

A picture or sketch would be a great help.

I think TC will do this. I want to create a modified 3D saddle shape. Could someone point out which tools to use for this.
thanks
Michael
The object shown here was lofted.
Henry H

How about using the Revolve tool on some arcsnlines, then reduce the Rotation Angle?

Thanks Henry and John
You guys are way over my head. :) Anyway, I was thinking TC had creation tools for ruled objects such as a hyperbolic paraboloid (aka saddle). With a little effort I can create one in SU, but I have not figured out how to round the corners yet. I would prefer to do it in TC. Back to the TC drawing board....
thanks again

probably won't be accurate enough for your needs (and may be completely useless), but you could have a look at deform to point, not automatic but can create odd shapes.

I wouldn't swear to this, but I think you can generate a hyperbolic paraboloid by revolving a line about an axis that is neither parallel to it nor in the same plane.
Henry H

Thanks again Henry and Andy
I think one of 1 of those 2 suggestions will work for me. Outstanding tips!

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 oomptyoomp 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.

Those few who downloaded Hyperbolic Paraboloid.tcw that I posted on 9/30/15 might want to take a look at the edited post and the new file.
Don

That came out great, Don.
I tried using the smesh tool. It took about a minute to create the object though the nodes can be edited > for adjusting the shape.

The hyperbolic paraboloid created by revolving a line about an axis that is neither parallel to it nor in the same plane can be converted to the conventional saddle shape by 3DIntersecting it with a Cylinder.
Henry H

Dean: The 'smesh' tool apparently came out in V19? I had thought of using the 3D mesh in V17, but the loft of two lines was much faster.
Henry: Hmmmm ... you're devious; that's one I never thought of!!
I first ran across the hyperbolic paraboloid surfaces in some work that I was doing in 1960 (!!!) and was fascinated by the underlying simplicity. I still am.
Don

I wouldn't swear to this, but I think you can generate a hyperbolic paraboloid by revolving a line about an axis that is neither parallel to it nor in the same plane.
Henry:
Your construction of a "saddle surface" intrigued me. After some thought, followed by some Googling, I found that your construction produces a "onesheeted hyperboloid", which is not the same as a "hyperbolic paraboloid". See
http://mathworld.wolfram.com/Hyperboloid.html
According to Wolfram, there are only three "doubly ruled" surfaces, a plane, a onesheeted hyperboloid, and a hyperbolic paraboloid. I didn't know that before you showed it to me.
Don

I wouldn't swear to this, but I think you can generate a hyperbolic paraboloid by revolving a line about an axis that is neither parallel to it nor in the same plane.
Henry:
Your construction of a "saddle surface" intrigued me. After some thought, followed by some Googling, I found that your construction produces a "onesheeted hyperboloid", which is not the same as a "hyperbolic paraboloid". See
http://mathworld.wolfram.com/Hyperboloid.html
According to Wolfram, there are only three "doubly ruled" surfaces, a plane, a onesheeted hyperboloid, and a hyperbolic paraboloid. I didn't know that before you showed it to me.
Don
Live and learn. Thanks, Don.
I shoulda realized that a hyerbolic paraboloid cannot be a surface of revolution.
Henry H

This Web page implies a way to create a hyperbolic paraboloid in TCad:
http://www.cutoutfoldup.com/902hyperbolicparaboloid.php (http://www.cutoutfoldup.com/902hyperbolicparaboloid.php)
Example is attached.
Henry H

Henry:
It's easy to draw hyperbolic paraboloids. It's considerably more difficult to draw geodesics (shortest paths on the surface) between points. In the attached image, drawn with MAPLE, the blue lines are geodesics between the three points viewed along the Zaxis of Z=XY. Numerical integrations are necessary for any two points not on the straight lines of the surface.
Don

Henry:
It's easy to draw hyperbolic paraboloids. It's considerably more difficult to draw geodesics (shortest paths on the surface) between points. In the attached image, drawn with MAPLE, the blue lines are geodesics between the three points viewed along the Zaxis of Z=XY. Numerical integrations are necessary for any two points not on the straight lines of the surface.
Don
Challenging.
Henry H