Surprising sub-surface result, it doesn't space the iso-curves proportionally.

I was always under the impression that if you use divide interval component on a surface, it actually divides that surface with proportionally spaced iso-curves along the U and V directions. So each iso-curve is divided into say 10 proportional lengths by its intersecting perpendicular iso-curve over the length of each respective iso-curve, but the intersection points are not decided by total length of each iso-curve but seems to be decided on the original surface's "elastic" pull. In this extreme example you can see it clearly but I was not able to notice this before because its difficult to see the proportions of the spacing of the iso curves on an "organic" surface.

This interests me because I am sure I have seen some paneling definitions that made the same assumption I did but they just can't see the deviation in proportion, and this could change that approach.

Though I'd share that since it wasn't that obvious to me.

Attachments:

Grasshopper.jpg, 73 KB

Replies to This Discussion

Permalink Reply by Vicente Soler on October 14, 2009 at 10:18am

The divide interval divides the domain of the surface in equal chunks. The surface's domain doesn't directly relate to the final shape surface has in 3d space. For example, if you create a rectangular planar surface and you nudge a row of control points (not the first or last row, but one in the middle), the geometry in 3d space is still the same but the parameter space of the surface has been compressed at one side and expanded on the other.

Since the UV domain already acts as an underlying grid over the surface, there are several components that extract sub-surfaces or grids of points directly from the UV domain simply because it's easy. But this is not necessarily the best way to do it.

There are several rhino commands that allow you to modify the surfaces parameter space so that it has some relationship to the actual 3d space like -reparametrize, -rebuild, -moveuvn.

Permalink Reply by Theunis du Toit on October 14, 2009 at 11:23am

I thought reparametrize would maybe make a difference but it doesn't. With rebuild you obviously need more iso-curves to maintain shape within a tolerance, but it still changes the shape on the surface however small it may be. And moveuvn didn't want to do anything for me.

I have no problem with how it works, I just never thought about it properly before. I guess if the interval component would make new iso-curves, it would also have to change the shape of the surface? Or not?

Anyways, thanks for the reply.

Permalink Reply by Damien Alomar on October 14, 2009 at 12:54pm

Reparameterize does not equalize the structure of the surface so that they are all equidistant. All it really does is set the surface domains in both directions to be between 0 and 1.

The interval component can make new isoCurves, and since those are derived from the surface, it won't change it. What you're trying to get around is that the parametric space of the surface is not constant in regards to its physical distance or the actual shape of the surface. About the only thing that is really going to make this more consistent is to rebuild the surface as it will take the physical shape of the surface and try to redefine the surface in a much more even way.

Permalink Reply by Vicente Soler on October 14, 2009 at 1:46pm

When i referred to "reparametrize", i meant the rhino command not grasshopper's reparameterize option.
If you execute the reparameterize command and select "automatic", the uv domain will try to correspond to the surface's actual size.

For example: Create a rectangular surface with a size of 10x5 units. The uv domain will be (0-10, 0-5). Scale the surface in the x axis only by 2, now the uv domain is still (0-10, 0-5) but the size of the rectangle is 20x5. Now execute reparameterize and select "automatic". The domain will be 0-20,0-5. I hope that makes sense. This is all fine and dandy for planar surfaces, but there is no unique right way to reparameterize an organic surface.

Permalink Reply by Scott Davidson on October 14, 2009 at 2:49pm

I know we get in the habit of using UV because it is easy, but not very accurate. It also imposes some servere constraints on how the surface is modeled. Does a Geodesic work better? See this image:

http://grasshopper3d.ning.com/photo/forforum-1?context=album&al...

Permalink Reply by Theunis du Toit on October 16, 2009 at 1:54pm

Definitely, thanks.

RSS