The name of this video is vectors. If we look at our surface that we've been working with, if we selected and type in Dir, we're going to get these arrows which represent as the normals of that surface showing us its front face, so it's directionality. If I put my mouse over the surface, you'll see that that arrow, the direction arrow changes slightly with the curvature of the surface. So it's really staying perpendicular to that surface, and what this normal is on the surface, is really a vector. What I can do is I can find these normals or I can find these vectors at any evaluated point within the surface. I can use that vector which is going in a positive direction; I can also use it in a negative direction to create another point matrix in space that I can also create geometry too. So that's really when we begin to create three-dimensional geometry from the surface. But the problem is that we don't really know what a vector is yet, what constitutes a vector and how do we work with it? So there's a couple of things that I have to go through in terms of vectors before we can start to work with a surface in that way. So let's start with some basics, I'm just going to hide this and we'll go to a top view. To create a vector from scratch, I'm going to need two points. So let's create two points in space here. One of these points is going to be a to point and one of them is going to be a from point. So a vector always has directionality to it, has magnitude, which is its length, and then it also has directionality. If I go into my code and I've created a simple little code here, no functions or anything, and I'm inputting two points, my to point and my from point. Then I'm not creating a vector yet, but I'm creating a line which represents a vector. Because another thing about vectors is, like planes, you don't see them in space. So you really have to create or use geometry with them in order to see them, to see what they're doing. So I'm going to add this line and we'll go ahead and do that. So select a to point, and select that point as my to point and this point as my from point. So it's just creating a line, and that line represents our vector. Now let's actually create a vector from those two points. If you look under rhinoscript and you look under point in vector, you'll see that there's a lot of different functions that are related to vectors. So I've vector create, which is what we're going to start using. Vector add, vector angle, vector compare. We'll only go over a couple of them. Some of them are pretty self-explanatory, like vector length. But we're going to start with vector Create. So vector create takes two points, first a to point and then a from point. So it's very specific about that, and do that. So point one is my to point, point two is my from point. Then in order to see the vector, and this brings up a critical point about vectors. What a vector is, is a point in space. There's really no difference between a vector and a point. Well, there is one difference and that's its relationship to the world coordinate center. So let's go ahead and do this. We'll run this and we'll select our to point and our from point. So I've created a line and then I've also created a point in space which represents our vector. So there's our line and there's our point, which is strange because you wonder about what's the relationship of that point to these two points in space? I can describe that relationship by moving this line. So if we move that line over to our world coordinate center, we'll see what defines a vector. A vector is a point whose magnitude and direction are defined by its relationship to the world coordinate center. That's going to be true for any points in space that I create these vectors. So if I move these up in space off the plane and input them again. So my to point, my from point. Now I'm creating that point. Doesn't allow me to grid snap to that. Let's do this. There we go. So we can see that that line between those two points is identical from a line from the world coordinate to the point, which is the vector. Now, there's a couple of things I can do with a vector. The first one you might be asking is, well, what good does that do me if a vector is always in relation to the world coordinate, what good does that do me because then I'm only going to be able to work around the world coordinate system? Well, you usually use a vector or VectorCreate in conjunction with another function. So if I create a third point in space, we're back to our top view. So if I create a third point and say up here, and that's a point that I'm going to add to. So I can add my vector to a point in space. Okay? So I can use this function and we talked about this a little bit fore when I was talking about points, not to confuse PointAdd with AddPoint. PointAdd is something very different, PointAdd allows me to add two points together. If I see, if I click on PointAdd here, it says it adds a 3-D point or a 3-D vector to a 3-D point. So up here I'm going to input that third point, the point to add to. Then I'm going to add to at the vector and then I'm going to save that in a variable called new-point and then I'm going to plot that out. So my to point, my from point and then my point to add to. Now we can see if I just copy this and I need a point here again. So that's my vector. Then I added that vector to this point. So it's added that vector point to that point, so I can move a vector anywhere in space. So in the next lesson, I'm going to talk a little bit about how we could change the magnitude of the vector, its length, to a precise distance.
