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In Rhino 4.0 Essential Training, author Dave Schultze shows how the 3D NURBS-based modeling tools in Rhino 4.0 are used to engineer products from toy robots to full-sized aircraft. This course concentrates on using Rhino 4.0 for industrial design and rapid prototyping, with a review of common 3D terminology using specific examples. Along with a comprehensive exploration of the Rhino interface, the course includes an introduction to building 3D objects with Rhino's three primary entities: the curve, the surface, and the solid. Exercise files are included with the course.
In this video, we'll define and explore the meaning of degree and why it is so important to NURBS-based modeling. The concept of curve and surface degree may sound a little technical, but it's actually very straightforward and absolutely mandatory to understanding and controlling your designs. The simplest explanation I can give you is smoothness. Why do we care about smoothness? A couple of reasons. It's for editability, elegance and the underlying math. I think elegance, to me, is one of the more important ones because we want surfaces that are clean and error-free.
So, for true NURBS-modeling, we need to always have a degree 3 minimum curve. Let's take a look at a couple of examples of degrees 1, 2, and 3, and see the attributes of each. I am going to zoom in on this degree 1 curve. This was created by the polyline command, but you could also edit it individually by segments that were then later joined. Both would form a polyline. I am going to turn the control points on by selecting it, hitting F10. We can see sharp corners wherever lines meet. So, if I were to pull one of these around, it stays sharp.
That's degree 1, pretty simple. It's just a sharp corner with multiple straight segments. Let's take a look at degree 2. It's almost like a hybrid. This is constructed with straight lines and arcs. This would be the result of a fillet operation. So, let's hit F10 to turn the control points on. Now, it technically looks smooth in its current state. But we'll find out pretty quickly, if we grab one of these corners, there is a kink. So, it's no longer smooth, so that's why it's classified as degree 2. Put that back into place with Ctrl +Z. Now, let's check out degree 3.
This could have been constructed with a control point curve or several segments joined with the Blend command. So, let's select the curve and turn the control points. Notice as I move these around, no kinks will appear, no matter what I do. Even have it go around in circles, and it will still stay smooth. Another attribute of degrees is the ability to reduce itself to individual components.
We've talked about this being individual segments. If we hit the Explode button, it's now broken in individual pieces. Same as a degree 2. You can see it has got individual components. They can explode into individual pieces. The degree 3 cannot be reduced. So, when we explode it, we basically get an error message here at the top, "cannot explode a single curve segments." We would like selecting one of these and try to explode that. So, I am going to undo those last two explodes and make sure these are joined back up.
Okay, now let's create some surfaces. That's why we are modeling with NURBS in 3D, the ability to create surfaces. So, we'll do a quick Extrude and see what the result is. I am going to try to turn the control points for this surface by selecting and hitting F10. It looks like we have an error message. I can't turn on points for poly surfaces. Because of these individual components joined at the edge, it's no longer editable. So, that's another shortcoming of the degree 1 curves, and therefore the surfaces.
Also, since the curve could be exploded, we can select this and explode those individual faces. Let's try it again with the degree 2. We'll do a quick Surface Extrude. I am going to turn the control points for this surface with the F10. That lets him come on, so this is barely meeting the minimum requirements. But let's try that same problem corner. I am just going to use the nudge key here. Sure enough, we have generated a very sharp kink in the surface. So, it's no longer got the characteristic of a free-flowing surface.
Let's go over to the degree 3 surface. Now, I could extrude this, and it's very tempting to do so. But if we stop for a moment to think, that would be going up in a straight line, which would be degree 1. It would actually be generating a mixed degree surface. It would be degree 3 in one direction, degree 1 in the other direction. So, when building surfaces from degree 3 curves, you got to be careful which surfacing command you use. In this case, I am going to switch over to the Surface > Sweep 2 Rails. Both of these rails are degree 3 curves as is the profile.
So, I can select this. This should not explode according to the command line. If I turn the control points, I should be able to edit this until the cows come home. I'll grab a couple of points here, just using the nudge. So, no seams will occur. I'll show you one further analysis tool. I'll turn the control points off, so I can select the entire surface. Control points on is F10, control points off is F11.
Let me select the surface. Now, we have kept this Properties window over here in the right side dock. Here is a great reason why. If I select the details, it's going to give us a very technical report, and so there is a lot of math in there. But I want to direct your attention to the U and V. These are just the Isoparms or Isocurves going in the two different directions, which is the characteristics of all NURBS surfaces. It's telling us it is degree 3 in one direction. Let's call it U. And degree 3 in the opposite direction. Let's call it V.
So, that's another way to verify we have got a surface that is fully editable and degree 3 in both directions. So, there is your scary technical background to curve and surface degrees, which is hopefully not all that scary. One more caveat to add for degree 3 curves. You need to have a minimum of 4 control points. That's to satisfy the mathematical requirements. A degree X curve always needs X+1 control points. This is never an issue with degree 1 or 2 curves, but now as you know, always plan to have 4 control points for curves if you plan on building editable NURBS surfaces from them.
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