Title of this video is surface modeling. So in this video, I'm going to talk more about this thing called surface modeling. And in a sense, we've already been doing it when we use sweep or extrude or revolve, we're doing surface modeling. But in this video and the subsequent tutorials, I'm going to get deeper into more sophisticated tools in the area known as surface modeling. And this series of tools allows us a great variety of creating, editing and working on surfaces. And we're going to look at four types, lofting, surfaces from 2 or 3 edge curves, something called a patch surface and then a surface from a network of curves. Lofting is a term like spline that comes from the discipline of boat building. And lofting in boat building is the process where I'm taking a drawing and I'm transposing it into full size jigs or molds to build a boat from, and typically in a boat building factory which is very dirty. The cleanest place and the biggest place to be able to do that was the same place that I made the sales in which was the loft sort of above the building floor. Thus the term lofting. Now, lofting also involves something called splints, which we've talked about, which were translated from the process of boat building and car design into 3D modeling. And splints are these little pieces of wood that give me a kind of fair curve when I make this translation. So it's really fascinating to understand that our 3D modeling tools are connected to a much longer history of design, drawing and fabrication. Now when we loft in a computational manner, we're setting up a series of profiles in space that we generate the surface between. So in a sense we're sort of kind of sketching the form of a thing in space by positioning those profiles. Now there's a couple of things we have to watch out for when we do that. Every curve and shape that I create has a start and an end point and I need to be cognizant of those start and end points, where they are in relation to each other along the profiles. Because if they're out of sync with each other, I can get a real sort of severe twisting in my surface that I produce. The other thing that I have to look out for is the direction of the curve. So the direction of all of these is going the same way, if I happen to have one that was going another way I might get something called hourglassing within the surface. So that's where I get a twist and it kind of makes the form look like an hourglass. Now, a pretty interesting thing about a loft is that there are a number of different ways that I can translate the profiles into a final form. So a normal or tight way, the surface that's created. It heres as close as possible to those profiles that I position. I can also create a kind of loose interpretation which generally holds to my beginning and end profiles, but has a looser interpretation of the profiles in the middle. And then I can also do something called straight, which creates a straight section geometry between the different profiles. You'll also notice that I can, the loft allows me to translate between radically different types of profiles. I can have smooth profiles, I can have angular profiles and it's going to generate good geometry translating between those things. Now, why would I choose the loft tool over something like sweep or revolve? Well, if I don't have, let's say if I'm trying to create an object that doesn't have a specified rail for example, I don't have a sort of central rail that I can sweep my profiles or position my profiles down. Then I might choose loft. In this example, I'm showing this glass and we'll run through this in the lofting lecture. And normally, I would think of a glass form as something which I could produce through revolve. But this glass form happens to have a circle at the top and a square at the bottom, so it would be impossible to do it through revolve. So it's a very good candidate for using lofting to create it because I'm going to get that translation from the circle to the square at the bottom. And then I use, actually use a revolve to get the inside of the glass because that has a smooth form from top to bottom and I can revolve it around that central axis. So lofting is different than sweep in the sense that I'm kind of sketching the model out through these kind of positions of these profiles in space. And I'm really working on it through the positioning and manipulation of these 2D lines to really as accurately as possible create the form that I'm trying to get to. The next tool surface from 2, 3, or 4 curves. Edge curves is a really interesting tool because it has two poles, I can be super precise with it or I can be kind of sketchy with it. So on the left hand side we're looking at 4 lines, they're not in the same plane, they're not even touching and they run sort of past each other and I can select those 4 lines. And the computer is going to generate a surface from them no matter what those 4 lines are. So that's pretty interesting. I can generate surfaces from stuff that I just kind of quickly sketch in space and not really worry about precision with it or on the right hand side, I can be super precise about these curves that I'm creating. The bottom ones are created within the same plane, the 2 end ones are created in plane and they all sort of meet at their, they're joined together at their endpoints. And so I can create a very kind of precise surface from that. Now what if I wanted to create a surface with more than 4 edge curves? Well if I wanted to do that, I would need to use something called a patch surface. So a patch surface allows me to create a surface from any number of edge curves and they should be joined and they can be any form, they don't have to be in plane and it will generate a surface from that. And so for this form which is a form that I've showed before, this sort of complex tree form involves 4 patch surfaces. And each one of those patch surfaces requires 6 lines to create it. And so it's a very complicated piece of geometry. Now when I create a patch surface, there's a couple of things that I have to look out for and I need to be cognizant of when I'm creating this geometry. One of the things to recognize is that because I have a geometry that doesn't have sort of clear angular edges. My UV grid has nothing to align to, it doesn't have an edge to align to. So if we look at the image on the left, we'll see that my U and my V sort of run diagonally across that surface. They don't align to anything. And with the middle image, if I turn on my control points, I'll see that the computer actually understands that surface as in terms of his equation as something which extends far beyond the boundaries of that surface that I'm looking at. And that's why sometimes we refer to a NURB surface as a B-rep. A B-rep is a boundary representation. So I'm looking at a representation of the surface that the computer understands is actually something that's much much larger, that's represented by this control points. Now, why this is important is if I look at the image all the way on the right is, if that control lattice isn't fine enough for the geometry that I'm creating. At the edge conditions, I can get these sort of gaps or splits within my geometry which doesn't make good geometry. If I tried to join all these surfaces together, they wouldn't join and I wouldn't be able to do something like 3D print this form because I had these sort of gaps in my geometry. Now, a remedy for that is to make a denser UV grid and that usually works, but it also creates a computationally heavy model. Now that might not matter for 6 surfaces but if I have 1000 surfaces that have very dense UV grids, it can be cumbersome to work with. And so with actually our final assignment, we'll look at a different alternative for this kind of geometry. And the last one surface from a network of curves. It's a bit like lofting on steroids. It gives us a lot of control over the shape of the form that we're creating. This is a quick sketch model I did of my computer mouse nothing to scale or anything. I just quickly sketch the profiles that I needed to use to generate this. And what a network of curve surface from a network of curves is, is that there are sets of curves that are going in two directions and they can either be all open or all closed. So this is all open curves and we can see there's one here, this is split in the middle. So I have one on the other side because I can't close that thing because that would be all one curve. So I have three curves going this way and I have three curves going the other way. And I noticed a couple other things about this sketch, these construction lines as I have these 90 degree lines here and I've drawn a sort of axis that I've organized everything along. These lines have helped me position my C plane where I wanted and so I'm able to manipulate these curves. And these curves are actually produced from, I only produced one and then I copied it and I manipulated it to create the form that I wanted. And that's very important. That's actually in the surface of network of curves, creating your sections through duplication and manipulating them into the form. You'll have better success because those curves are essentially based on the same equation. They have the same number of control points and usually have better luck with that. So we're going to work on some things similar to this, a kind of ergonomic form and we're going to use some different processes in creating a very smooth form. Probably made of a couple different types of surfaces and a couple of different operations and we'll do that in the next assignment.