Get the two circles. I used a more involved way, starting with the oloid script and lofting the lines, then mirror the surface twice, and make two 3-point circles.
Loft the two circles. without closure option.
Shell the surface with centerline option.
Fillet the 4 edges, one by one, with a small fillet.
Done. (?)
Correctly done?
- Brian
3d printing will have to wait until my 3d printer is finished. Have not worked on it for about a year :-(
Walmart and Costco have no TP, and many shelves are nearly bare. Weird.
Can you confirm that this anti oloid has 2 surfaces against a Moebious ribbon who have only one surface ?
Seems yes but as I have not a real solid on the hands...only virtual... :)
The Tetrahedron, Reuleaux Tetrahedron, MeissnerVBody, and MeissnerFBody may all be constructed using MoI commands.
The Reuleaux Tetrahedron is not quite a body of constant width. The width for opposite edges is larger than the other widths.
The two Meissner bodies have three edge wedges of the Reuleaux Tetrahedron replaced by a wedge portion of a spindle torus, and are of constant width. https://www.researchgate.net/publication/225748121_Meissner's_Mysterious_Bodies
I tried the following last night, and was almost done, but mixed up the radius and diameter, so will try again later.
Probably would work for diameters by multiplying the equation by 2 ?
Symmetric Spheroform Tetrahedron
The symmetric spheroform tetrahedron with uniform width begins with a tetrahedron of side one, easily built in MoI.
The Reuleaux tetrahedron is created using Trim on intersecting spheres of radius one, centered at the corners of the tetrahedron. Circular array 3 is helpful.
The Reuleaux tetrahedron is not quite of uniform width.
To achieve uniform width, areas near the 4 edges must be rounded over by
replacing each of four "wedge" areas near each edge, by trimming in a particular solid formed of a swept SPHERE (NOT vertical circle).
To form the swept circle solid, in MoI Top View, sweep a vertical circle placed at the center of two rail curves, along the two rails.
Rail one is the line between x = -0.5 and x = +0.5.
The "bottom" of the SPHERE (NOT circle) sweeps along rail_1.
The SPHERE (NOT circle) shrinks down to zero radius at the ends.
The vertical SPHERE (NOT circle) to be swept is of radius "r". It's center is located at (x,y) = (0,r), which is the center of rail_2.
The center of the SPHERE sweeps along rail_2.
Using Max Smirnov's MoI script FxGraph, rail_2 may be easily plotted.
The formula for the rail_2 NURBS curve is given in the pdf, by the equation:
y = f(x) = ((4 * sqrt(2) - 8) * x*x + 2 - sqrt(2)) / 8 ;
min(x) = -0.5;
max(x) = +0.5;
The number of points plotted was 100.
Tab pasting the following to the command window accomplishes the same radius curve: (If _FxGraph is in command folder, or use FxGraph without _)
_FxGraph ((4*sqrt(2)-8)*x*x+2-sqrt(2))/8;-0.5;0.5;100
MoI does not have SweepSphere command, so some other method must be found and used...
The Sphere to "fake-sweep) can be placed in the middle of the wedge to be.
Place a point at the top of the SPHERE to assist with future alignment of the swept_wedge.
Then perform the fake_sweep with some new method..
Draw appropriate alignment lines, (bothsides setting), from edge center to opposite edge center to place one swept_wedge.
Trim the swept_wedge and the tetrahedron edge area. The trimmed swept_wedge should be tangent to two adjoining faces of the tetrahedron. Perform circular array (3) of the trimmed swept_wedge.
Place appropriate CPlane, to permit circular array of one of the trimmed swept_wedge, along bottom face of the tetrahedron.
Join will now form the Symmetric Spheroform Tetrahedron.
After several attempts, it became clear that an array of spheres centered on the radius curve has an envelope that is larger than that of a swept vertical circle, as described in the previous post.
The previous post was modified to correct mistaken understanding.
So I will have to find some way of finding the envelope of an array of spheres centered on the radius curve, with decreasing radii.
Maybe with Scaling the array of spheres with coordinate values of points on the radius curve, and then ???
There might be some kind of formula or moving frame???
Found a couple of papers on Canal (Channel) surfaces, from spheres of varying radii, which look promising...depending upon the math load.
So more study to come...
Some mention is made of rolling ball blends and the R4, 4th dimension...
Attached is a spheroform uniform width, symmetric tetrahedroid. [See next post for update.]
Despite being very careful, somehow the corners get out of wack. So the model does not appear to be quite perfect.
There seems to be a problem with a very slight lack of symmetry with maybe the circular array command, or something.
The canal surface "wedges" were made with loft of only 21 numpoints.
Using a Vee trimming tool object on the 4 master spheres, and the wedges, enabled the joining of the parts.
A script which arrays objects in a tetrahedral layout would be helpful.
AntiOloid2Ring01.7z
