What are degrees and why should I care? - Rhino Tutorial

- [Instructor] Next up, we cover one of the foundations of modeling in Rhino. Yes, it's time to talk about degrees! If you've never heard the term, it's not really that complicated. We use the word "degrees" to measure the smoothness of our geometry. And a higher degree number will be smoother. Pretty simple. The best news about this is it works the same for curves and surfaces. However, curves have one value, surfaces, as we'll see in a minute, have two values. Let's cover three examples of degrees using curves. I'm going to zoom in here. This is a classic Degree 1, which is your basic straight line. Now another thing to notice. as we go down the line of degrees, the degree equals that number plus one giving you the number of control points, and a lot of times that's how you can tell what degree it is. So, I'm going to turn on the control points here. We going to go to, over here on the main Toolbar, Show Control Points, and as you would have guessed, anything we do is pretty limited. We're just moving endpoints, 'cause that's all you get in Degree 1. Let's move over to Degree 2. Three control points here. Or I can turn this guy on. And then control points on there. And there's the three control points. Now the definition of this is better described as an arc. This is not a freeform curve at all. So, an arc is defined as something with a constant radius. That's a Degree 2. Only used occasionally for fillets, or when you need something precise and geometric. When you're doing something much more organic, you will be using Degree 3 curves. And using your new knowledge of math, we have four control points for a Degree 3 curve. I'm going to put the control points on here again just so we can see. Now the beauty of these guys, besides being smoother, is they're editable. So we can move these points around and the curve just flows. No sharp edges. Let's now take this knowledge and apply it to surfaces. Going to come over here. And starting with Degree 1,1. Remember, we've got two values, and the reason is the surface has area. And as a reminder, you have iso curves that go in two directions. That means you have two values. This one was created with these blue lines on the outside, then was surfaced from plainer curves. Since they're all straight, and Degree 1 curves, the surface resulting from it is Degree 1 and 1 in both directions. The next example is Degree 2 and 1. And we have a blue curve here. That was obviously an arc, because it's Degree 2. And then it was extruded which, since there's no line there, but it's the same result. Though this surface is a mixture of Degree 2 and 1. Another example that's fairly related is we have a Degree 3 curve. I'm going to go ahead and make an extrusion just to verify this. So we select the curve there, go to Surface, Extrude Curve, Straight. Pretty much is the world's most basic command. And as we move out, we're going along a straight line. That's kind of the definition of an extrusion. Now I can just eyeball this. As a reminder, you can snap to other stuff in this scene, so always remember that if that's important and you want to make it accurate. And finally, let's go to the highest quality level: Degree 3 and 3. These are three curves. They're all Degree 3. So if we make a surface from these guys, they will be a Degree 3,3 surface. Remember, the extrusion was a straight line. That's what kept it to Degree 1. So we can't use the Extrusion command. I'm going to pick all three of these curves and just go to the Surface, Loft command. This is actually one of my favorite commands because it gives you the smoothest, quickest, easiest surface from any series of input curves. I'm going to go hit Ok, and we move in. You'll notice that this is a very simple surface. Also, since it's Degree 3 and 3, remember the editability of the Degree 3 curve over here? We now get that same advantage on the surface. Let's turn on control points there. And this nice little cage is editable, so we can move things around. Lot of times it's nicer to do it with the gumballs, so I'm going to turn that on at the lower level there. And we can move the control points or a group of control points. That's why we care about degrees and how curves play a big role in the degrees on a surface. So degrees may seem technical and not worth the effort many times, but it's really important to understand them if you want higher quality surfaces and to avoid problems. So keep these ideas in mind whenever you build something where you care. This gives you cleaner models and avoids the problems of openings and edges when you finish and get ready to prototype and then, ultimately, manufacture.