CSG should start with a point. You can extrude it and get a segment, or lathe it and get two points. This way, the number of letters in the shape's CSG notation will reflect its dimensionality.
Now about the naming. Some shapes (I suspect, all do) have different "flavours". For example (CSG abbreviations):
RNS has the same problem. The simplest solution I see is, as I've already mentioned, to specify the dimensionality of the considered body.
I saw on the duocylinder wiki page that all these components are considered different "flavours" of the same body. I'd only consider them, well, components.
PWrong wrote:I'm still getting the hang of CSG notation. It's harder to understand a notation you didn't help to invent.
PWrong wrote:But "flavour" is an interesting word for it.
PWrong wrote:For instance, the area of the 2D form of a cylinder is the sum of the areas of its two cells.
PWrong wrote:What do you mean by components?
Doesn't it have three cells? Two disks and a rolled up rectangle?
I'll give an example: two disks, a rolled up rectangle and a cylindrical interior are components of a cylinder (full).
PWrong wrote:Here's the three forms of a cylinder:
1D form: S2*S1 - one cell
2D form: B2*S2, S2*B2 - two cells
3D form: B2*B2 - one cell
PWrong wrote:Here's the cubinder, so you can see the pascal's triangle develop; note the number of cells in each form.
1D form: one cell
S2*S1*S1 = four circles
2D form: three cells
B2*S1*S1 = four disks
S2*B1*S1 = two hollow cylinders along x direction
S2*S1*B1 = two hollow cylinders along y direction
3D form: three cells
B2*B1*S1 = two solid cylinders along x
B2*S1*B1 = two solid cylinders along y
S2*B1*B1 = hard to visualise. The squares are solid, but the circles are hollow.
4D form: one cell
B2*B2*B1 = solid cubinder
Here's where I lose it. I don't have the time to read the thread you provided right now, but I'll try to do it in the evening. Which of the two cells in the 2D form is which component? I ask because I'd expect the two disks to be B2*S1 and the rolled up rectangle to be S2*B1. Again, isn't the 3D form B2*B1? Or do I misunderstand the * product?
As I see it, S1 is two points, S2 is a circle, B1 is a segment and B2 - a disk. I interpreted the * product as simple cartezian product of two perpendicular components.
Again, I'd expect the 4D form to be B2*B1*B1 (disk extruded two times). How about S2*B1*B1? Isn't it a hollow cylinder, extruded?
moonlord wrote:CSG should start with a point. You can extrude it and get a segment, or lathe it and get two points. This way, the number of letters in the shape's CSG notation will reflect its dimensionality.
Now about the naming. Some shapes (I suspect, all do) have different "flavours". For example (CSG abbreviations):
aa. A circle is LL or, in Cartesian equations, x2 + y2 = r2. A circle is one-dimensional, as it is, in fact, a "curved" segment.
b. A disk is EL or, in Cartesian equations, x2 + y2 <= r2. A disk is, obviously, two-dimensional.
a. EEE is a full cube (|x| <= h, |y| <= h, |z| <= h). It's 3D.
b. A hollow cube, or a box can not be represented with the actual CSG notation. It is something like LEE+LEE+LEE, with the first lathing oriented along x, the second along y and the third along z. Or any permutation of these. This is why I'd use a parameter for lathing and extruding, to show the direction it is performed in. A box becomes LxEyEz+LyExEz+LzExEy. A box is 2D.
c. A wireframe cube is also bogus. It can not be represented even in the extended CSG. So I ask, whether CSG is really useful.
I'd also note that line is sometimes incorrectly used for segment. One is finite, one is not.
Rob wrote:EHL = Hollow cylinder (...)
EH = Hollow square (...)
EEH = Hollow cube
EHH = Wireframe cube
moonlord wrote:It is a good idea, although it does not actually represent the creation method for the above. That is:
EHL generates the two disks, HLE generates the curled up rectangle, so the hollow cylinder should be EHL+HLE. Same for the others: EH+HE - hollow square, EEH+EHE+HEE - hollow cube, EHH+HEH+HHE - wireframe cube.
moonlord wrote:Why ironic?
Rob wrote:nullframe
monoframe
biframe
triframe
tetraframe
Rob wrote:nullframe
monoframe
biframe
triframe
tetraframe
wendy wrote:The tradition of latin and greek names, and not mixing them, greatly limits what might be said, and tends to add unnecessary confusion to the subject.
houserichichi wrote:Bi and duo are both latin prefixes. The greek equivalents are di or dy. The actual greek numeral 2 is "duo" (or dyo or di) though but the prefix isn't.
Numerical equivalent = Greek prefix -- Latin prefix
1 = mono -- uni
2 = di/dy -- bi/duo
3 = tri -- tri
4 = tetra -- quadri/quart
If we insist on using "tetra" then you must stick with tri, di/dy, and mono for consistency. (think unilateral, bilateral, trilateral, quadrilateral versus monad, dyad, triad, tetrad)
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