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In this video, we'll build our knowledge of curve and surface degree by changing the degree of various entities. As I've mentioned before, the simplest explanation of degree is its smoothness. For proper editing of curves, we'll need a degree of three. For surfaces with their two directions, we require degree of three for each of those two directions. These directions are labeled as U and V by Rhino and are visually represented by the Surface Isocurves you can see when in shaded mode. So, we'll start off by exploring two new commands, Rebuild and Change Degree.
When I zoom in on to this degree 1 polycurve that has six control points and we'll select it and these two commands we'll be discussing now are right together. This is Edit > Change Degree. Not too many options here. It just says currently it's degree one and Deformable = No. So, we want to make sure that the new version will be deformable, so we would say Yes, and then I'll type in 3. Hit Enter. Notice the curve change. I'm going to hit the F10 and there is the control points, so it's now a completely degree 3 curve with no kinks. Pretty handy.
Now let's mix it up with the second command we're going to be looking at called Edit > Rebuild. We'll do this on the degree 2 curve. I'm going to select it, go to Edit > Rebuild. Now, I have quite a bit more options. For example, it tells me that the Point count is 19 and the Degree is 2. That's why they are in parenthesis. We can then change either of those. I'm going to just leave it as let's say 12. Degree 3 is okay. You would probably want to delete the input every time.
We don't need the original. That's why we are rebuilding it. And then the Preview option is very handy. It will show us again the Maximum deviation. That's 1.7 and it's occurring in right this position. So, that degree 2 polycurve is now degree 3 and fully editable with a new number of control points. And finally, in a third case, let me select this degree 3 curve. I go to use the command Edit > Rebuild, and you'll notice here that it's got 30 points.
I'm going to cancel out of this and hit F10. You'll see exactly what's going on, and this is pretty bad news. However, this happens fairly often and especially when you get geometry from other software applications, you'll end up with a ridiculous amount of control points here. That's okay. We're going to need to change them, but as long as you remember the general rule, the fewer the points the better. So, make control points off F11, go back to Edit > Rebuild, select the curve, and I'm going to use the same numbers as earlier. Degree three.
That's not changing. It's just the point count that's changing. We'll preview it. Here's your maximum deviation. I'm going to hit OK. Now in these situations let me turn the control points back on. If it deviates too much, not a problem. There is always a little bit of tweaking involved. You can push and pull back so that it gets closer to what your wanting, or you can actually delete the control points whenever needed. They can be deleted anytime and the curve just gets a little bit simpler. I'm going to switch over to surfaces.
I have another layer here. I'm going to turn that on and zoom out. When you start off with a common primitive, the sphere. You may not realize this, but it is not degree three by default. In either of the directions. It is degree two and two. And I want to prove this by turning on the control points and just dragging them a little bit, and you can see we have a very sharp seam. I think the reason for this being degree two is it that it's generated internally by Rhino as being an arc that is somehow rotated but so an arc is a degree two curve.
Let's take another sphere I've just built that is also degree two and two by default. Place the Edit > Rebuild command to change the degrees. Okay. We've got now point counts in two directions. Those are represented by the isocurves. I'm not sure which is which. It doesn't really matter. We are going to keep this symmetrical. I'm just going to go with six and six for the point count. Degree in the U and V is three and three. That looks good. Go ahead and say OK, and you notice the isocurve has changed, but the real proof here is turning on the control points.
It really had to seam in the earlier one. I'll nudge these over. We have no seam here. All thanks to degree three. Let's try this again with the Extrude example. Now this is an odd mixture. We've got a surface that is degree 1 and 3. Let's analyze how that could happen. I'm going to select this curve that generated it. Turn on the control points and we can see that's obviously a degree curve there. It's very smooth, but then we extruded it in one direction, which is actually a straight line.
So, that is your degree one in that direction. So, if we wanted to generate maximum editability, we can do a quick rebuild on this as well. I'll select the surface, Edit > Rebuild, and here you see the differences. U and V are 3 and 1. We can change the point count. Let's just add a few more. Take a look, and it's pretty close. I don't see much deviation there. Hit OK, and that should now be a degree three in both directions.
Now you'll notice that edge looks straight and just like the degree one. However, it's degree three and can be completely deformed in any direction. Meaning I can turn on the control points. I can select one or many and just nudge them up, and it should be maintaining perfect smoothness. Okay the final case is a Revolve. This is another unexpected result from a built in commands with Rhino. Just like the sphere was degree 2 and 2, this ends up being degree 2 and 3.
So, we have a seam. If we turn on the control points, you can already see it. I've predeformed it. So, if we move those over, that's a problem. We've got a sharp edge. We get around this by looking for an option in the command for Revolve. So, it's under the Surface menu > Revolve. It's asking for the axis, so this is pretty much the same way we do it. Usually I'm going to stop right here, and this is where people blow right by and forget to check the options. We have the Deformable, and that's something I mentioned earlier.
We are going to select Yes. Now we can select the beginning and ending. I just say FullCircle. The one other option you want to be aware of is the Point count. That's how many increments around. That's defaulting to 10. Let's just try eight. Let's get this selected right on those hyperlinks, type an 8 now. So, we have Deformable = Yes, Point count = 8, just click FullCircle. That will prevent you from having to enter the beginning and ending angles.
Okay it looks pretty much the same. I do see a different number of isocurves. It looks like it's eight as I requested. Let's turn those control points on, and zoom above the top, and a little nudging. And what do you know? It stays perfectly smooth. So, if you didn't notice it before, all NURBS surfaces  no matter how simple or curvy  will have two direction and only two directions.
These can be seen via the surface isocurves, which always cross at 90 degrees, thus confirming the whole twodirection idea. So, whenever converting either a curve or surface to another degree, remember these two commands. Change degree, which will keep the same number of control points, while the Rebuild command provides additional options for modifying the number of control points.



Released
4/8/2010 Understanding 3D terminology
 Viewing a 3D model in Rhino 4.0
 Manipulating objects with commands
 Creating curves, surfaces, and solids
 Applying transformations to 3D objects
 Creating unique shapes with Boolean operators
 Snapping to objects and planes
 Defining curve and surface degree
 Prototyping a 3D model
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Video: Using Rebuild and Change Degree