Hyperbolic paraboloids. Very easy to create in tS.

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Galane
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Hyperbolic paraboloids. Very easy to create in tS.

Post by Galane » 22 Sep 2009, 08:26

It's easy to make a hyperbolic paraboloid shape in trueSpace.

1. Start with a primitive with four or more sides, an even number of sides works best.
2. Scale it so it's quite thin.
3. Select every other vertical edge, change to World Coordinate System then move those edges straight up a ways.
4. Poke the Quad Divide button ONCE.
5. Inspect the object to ensure it placed an edge from the middle of all the edge faces to the center point, on top and bottom. If it missed any, use Add Edges to put them in.
6. Poke Quad Divide 3 or 4 more times.
7. Pop in a cube, move it out of the way and boolean subtract it to delete all the excess edges from the edge faces.
8. Triangulate. None of those faces are flat, rendering holes everywhere without being triangulated.

If you want to make it like a stretched piece of fabric or canvas, use an n-sided flat polygon to start with.

This method doesn't quite make a true "hypar" when using over four sides because the lines aren't perfectly straight from any point on one edge to its mirror opposite point. I'm curious if a straightedge could be run over one of these with 6 or more sides, if it'd show it being flat between any two mirror opposite points.

A 4 sided one IS a correct hypar because every line can be traced straight across.

I first made these with tS 2.1a, was inspired by an old article in Popular Science where some college students made frames from steel re-bar then made the surface out of strips of fiberglass window screen. Various surface coatings such as polyester resin and concrete were applied to make lightweight yet extremely strong structures. One broke loose from its moorings during a windstorm and totaled a VW Bug in the campus parking lot. The Hypar structure wasn't damaged.

Physical hypar structures don't have to have straight side edges and with some fiddling they can be created with an odd number of sides. Might be possible with nurbs? I've tried using an odd number of sides but the geometry just goes really wrong with the quad divide.

I've attached a tower made from four, 4 sided hypars. Could also be a flower vase or ???
hypar tower.zip
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clintonman
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Re: Hyperbolic paraboloids. Very easy to create in tS.

Post by clintonman » 22 Sep 2009, 15:40

Wow. I remember that article. It was a looong time ago. Maybe this thread should be in the tips section of the forum.
Clinton Reese

http://clintons3d.com

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RAYMAN
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Re: Hyperbolic paraboloids. Very easy to create in tS.

Post by RAYMAN » 22 Sep 2009, 17:05

Galane wrote: Might be possible with nurbs? I've tried using an odd number of sides but the geometry just goes really wrong with the quad divide.

I've attached a tower made from four, 4 sided hypars. Could also be a flower vase or ???
The attachment hypar tower.zip is no longer available
You bet it is possible !
Here I made it with nurbs and network tools...
Attachments
without the lid.jpg

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RAYMAN
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Re: Hyperbolic paraboloids. Very easy to create in tS.

Post by RAYMAN » 22 Sep 2009, 17:11

5 sided ..... you want more ?
Attachments
5 sided.jpg

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