Sierpinski tetrahedron

Yay, it's here! My first Shapeways model, not very original I guess, just the first thing I wanted to try, it has lots of air inside, so it's not too expensive for a model this size


(EDIT: the current model has been enlarged: sides 18 cm, 14.5 cm high)
The sides are about 12 cm, it's 9.5 cm high. The model has 499.994 faces, there are 4096 struts. It feels pretty sturdy, no flexibility at all of course.

(EDIT: this problem has been resolved by making the model bigger)
Though I'm pleased with the result, there are a few issues due to the thinness of the struts: struts that are in the plane of the printing layers are noticeably thicker, some of the thinnest struts (<10) didn't make it through printing and cleaning, see below:


Another view:


and another:


Finally, I'd like to thank the good people behind POVRay and MeshLab for enabling me to make the model, and of course everybody at Shapeways, without whom this wouldn't have been possible
Oh, and I almost forgot Sierpinski himself...

Looks amazing,

well done.

Great photos! The graph paper background is a nice touch.

Big model. Between level 5 and level6. Small price. Every single polygon used.
Very nice job. Congratulations!

For some reason I still think these things are optical illusions.

Thanks all!

Here's a detail of the model in MeshLab, as you can see the use of faces/polygons is not extremely efficient, that's why I used so many:



No two struts are the same, it took a lot of time to draw them all by hand

To reduce the polygons use Rectangular trusses instead of spherical. It takes 2 polygons to make the face of a rectangle (four faces would be 8 polygons not counting the ends because your trusses are all joined), where depending on your resolution it could take hundreds (in your image it looks to be around 20) polygons to make the outside face of a cylinder.

Lowering the polycount is not an issue, as long as it's below the Shapeways limit.

Actually the method I used is more suited to circular cross sections, as it will smooth everything anyway. Note the way the trusses join, in the original POVRay model those are regular cylinders joining with sharp edges.

I scanned the model in POVRay resulting in a point set of 750.000 points with normals, which MeshLab turned into a mesh of 2.000.000 faces, which I had it reduce to 500.000.

So nothing by hand of course, that would be silly...

What does "scanned the model in POVRay" mean?

"it took a lot of time to draw them all by hand"

This made me laugh, and rember a time when I was the young guy at the old aircraft factory... an old timer had to learn the new technology called CADAM, which was a drawing package at the time. He was drawing the dashed line needed for the cross section he was drafting, one little dash at a time. (like you'd do by hand right?) Later he quoted, "this cad thing will never catch on, it takes forever just to draw a dashed line". It took us a while to stop laughing, before we could tell him it was just a line type, and only one "line" was needed, not hundreds. Now I'm the old timer and the last laugh is on me I guess. Ha!

Ha ha ha, hilarious!

@WelshDesigns: that's classic! :laughing:

@stannum: I used the povray "trace" command, which you can use to trace any line through an object. It returns both the intersection point of that line and the objects surface, as well as the surface normal at that point.

So if you use this to scan an object from the x, y and z directions you get a lot of surface points with normals, which I let povray save as an ascii .ply file, which MeshLab can read and turn into a mesh.

So scanning in the z direction means tracing rays at the model along the z axis, starting from a grid in the x/y plane. If a point is found, a new trace is started from just behind that point until no more points are found on that line. If you do this in x and y directions as well, all surfaces will be hit sufficiently.

The scanning can take quite a while, depending on the resolution and the complexity of your object, this took 1 or 2 hours.

If anyone gives a hoot I could do a tutorial with pics and code which will explain it a little better...

Thanks a lot. I used POVRay long ago, I think at that time trace was missing, because I don't remember anything like that. Time wouldn't be a new problem to me... raytraced images taking overnight was common then.