periodic surface -- what is it?

Replies to This Discussion

Permalink Reply by Pep Tornabell on October 19, 2009 at 4:07am

I'm not an expert, but seems like a surface that has a periodicity at the "v" parameter, for expample the moebius belt, has one direction limited (the "u" direction, the wide of the belt) and the other is somehow infinite.

Hope it helped

if that's not correct, excuse me, I think it is :)

Permalink Reply by Giulio Piacentino on October 19, 2009 at 4:23am

Hi Ognek,
yes, Pep is close to the mathematical sense of it.
v periodic means that the 2 edges of the surface in the v direction are joined without kinks (the surface is "closed in the v direction"). The difference between being closed and periodic is just the existence of the kink. You can see pictures at "Periodic Curve" and "Periodic Surface" in the Rhino help.

Hope this helps,
Giulio

Permalink Reply by Damien Alomar on October 19, 2009 at 7:55am

To go even further into it mathematically, a Nurbs surface (or curve) has a degree, which represents how many control vertices will influence a surface (in a given direction) or curve at any given point. In the middle of the surface or curve, when there are plenty of vertices to either side, this is fairly consistent. However, towards and at the end of a non-periodic surface or curve you will see that the influence of those ending CVs become more significant because there are no more CVs to influence the curve or surface. You can see this if you actually look at the Basis function of the curve....Figure 4.9 from Focus on Curves and Surfaces

Page 67-Figure 4.9

With periodic surfaces or curves, the basis function will stay constant because the vertices "wrap around". This means that the end points of the curve now have the same influence as the curve in the middle, making it very smooth and without a kink. You can see this if you look at the basis function of a periodic curve. Figure 4.10

Page 68-Figure 4.10

Not sure whether that helps a lot, but its worth knowing. BTW, the book that I referenced, Focus on Curves and Surfaces, is a great resource for some of the math going on behind the scenes in regards to NURBS.

Permalink Reply by Ognek Kciroks on October 19, 2009 at 8:39am

dear pep, giulio, damien,

thank you very much for time.
i think i understand -- does a v-periodic surface mean it is closed without kink in the v-direction (like pep is saying, a cylindrical strip); and would a uv periodic surface be.. a sphere?

ognek

Permalink Reply by Giulio Piacentino on October 19, 2009 at 11:30am

Well, no... the sphere has two singularities as a NURBS: two edges are "shrunk" into two points. A torus, or a shape similar to it in its topology, would be u+v periodic as a NURBS. Btw, nice book Damien (besides the cover)!

Permalink Reply by Damien Alomar on October 19, 2009 at 12:55pm

Yea, the book is a little dated, but it presents a lot of the NURBS/math stuff in an pretty straight forward, easy to understand way. There's still math involved, but not any of the cryptic Chinese that's typically presented. Funny enough, the book comes with a CD that has a trial of Rhino 2.0 :)