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15-23
From: bemfarmer
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???
- Brian
Attachments:
WedgeCaterpiller01.7z
From: Frenchy Pilou (PILOU)
Maybe all these things will be fun in Node Editor for have variable forms!
Carterpiller curves
From: bemfarmer
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...
- Brian
From: Michael Gibson
Hi Brian, maybe something related in this previous thread? :
http://moi3d.com/forum/index.php?webtag=MOI&msg=8430.1
- Michael
From: bemfarmer
Thank you Michael.
Yes, it is related.
I still remember doing experiments with booleans and "jaggies":-)
I found papers with the needed math...
- Brian
From: bemfarmer
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.
- Brian.
Message 9722.21 was deleted
Message 9722.22 was deleted
From: bemfarmer
A cleaner version of the uniform width, symmetric spheroform tetrahedron, starting with the 4 corner points of a tetrahedron of edge-length 2√2 from wikipedia. Later scaling to edge-length 1. Trimming the 4 spheres was laborious, whereas previously it was near onestep. The orientationn of the spheres must matter a lot. Added one canal wedge trimmed with angle Vee. Lots of trimming. Used Orient Line/Line multiple times, which generally placed surfaces with correct orientation, without resorting to cplane.
- Brian
Attachments:
SpheroformTetrahedron20.7z
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15-23
