bo198214 wrote:if you have 'H's before 'E's then you get some strange objects like two solid squares or so. If the system should be complete I would assume we want to get all strange objects for example 4 vertices together with a solid square or so. But this can not be accomplished by the E/H system. So it is incomplete.
Even if you introduce round objects its usually only necessary to give dimensional thickness of the boundaries ...
PWrong wrote:I think I understand this system now, at least when applied to 3D objects. It does seem pretty natural, although I think it should be used alongside RNS, rather than replacing it. Is there a list somewhere of all the objects up to 4D along with their CSG notation?
I do have a problem with the M, R and S operations. These could be made more general and less redundant by using matrices. Adding a vector translates the object, and multiplying by a matrix rotates/stretches the object.
I'm not sure if (EL#EL)E is the same as EL#(ELE) or EL#ELE, hence the brackets. What is ELE anyway?
Talking about a duocylinder, does it really have a hole? On this page it is projected as having a hole and it is the only 4D rotope that I can't visualize (other than the tiger, which is based on the duocylinder anyway )... And if it does, is it a pocket or a normal hole?
(EL#EL)E would be an extruded torus. EL#(ELE) and EL#ELE would be the same object since # takes precedence, but I don't know what this would be since I don't really know how to spherate by a cylinder...
moonlord wrote:Unfortunately, LEE is not a cylinder. That's... well... an artefact... . L gives two points, which, after extrusion, give two squares... opposite faces of a cube.
I'm not sure. It might depend which form of the duocylinder you mean. I think the margin is topologically equivalent to a hollow torus, so it has both a hole and a pocket.
I understand this notation, except for one thing...
What does the # mean?
I was talking about the duocylinder that was shown on the page I linked to, if there are other forms of it then that's even more confusing. hehe.
the CSG expression for a duocylinder is as yet unknown
PWrong wrote:the CSG expression for a duocylinder is as yet unknown
Isn't the duocylinder something like a rotated cylinder? Rotate one way, and you get a spherinder, rotate the other way and you get a duocylinder.
EELL is the spherinder, so maybe the duocylinder is ELEL. Or spherinder could just as easily be ELLE. That might be more sensible
moonlord wrote:Let's take it otherwise. I'm reffering to cartesian product in the following.
A tetraframe duocylinder is disk x disk.
A triframe duocylinder is disk x circle or circle x disk, I don't think it matters.
A diframe duocylinder is circle x circle.
I believe we can gather information about holes from these.
A tetraframe duocylinder has no hole of any kind. Disks are full, and we don't spherate anything.
A triframe duocylinder needs some more thinking. I'm not yet sure which product is the correct one.
A diframe duocylinder is even more problematic.
Now you've got some fresh ideas. Maybe you can help.
You lost me at R<sup>k</sup>.
By the way - I already asked this, but where does thie EL notation come from? I haven't seen it anywhere...
Rob wrote:You lost me at R<sup>k</sup>.
A triframe duocylinder is disk x circle or circle x disk, I don't think it matters.
PWrong wrote:The cartesian product is supposed to be commutative. That is, disk x circle = circle x disk
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