Title of this video is vectors lesson. In this video, I'm not going to go over everything that you need to know about vectors. What I want to do and what I want to convey in this video is what a vector is in a fundamental way. Once you understand that, then in the software demo, I'm going to go through all the things that you could do with vectors, different ways that you can create them, extract them from things, how you add them, so on and so forth, how you move them around. What I want to convey in this video is what makes a vector fundamentally. If you look at the data of a vector, it doesn't look any different than a point. It's three values, X, Y, Z coordinate values, and that's what a vector is. A vector is essentially a point. The thing that which defines it as a vector is its relationship to the world coordinate center. So the world coordinate center, which I've drawn in this diagram here, is that point that's at 0, 0, 0. If I have a point in space, let's say out here, and it's just an X, Y, Z location, and I've defined that. I've said that point is a vector, its magnitude and its direction as a vector are defined by its relationship to this world coordinate center. We can imagine the vector as a line that runs from that 0, 0 point to that point having that direction. The magnitude of the vector is this distance from that point to that point, and its angle, its direction is defined by that relationship. Fundamentally, that's it. That's what a vector is. It's a point in space that has a relationship to the world coordinate center. It's as simple as that. The confusion comes in in thinking that that's somehow a limitation to the vector, and it's not because the first assumption is that, well, what can I do with a point that always has to be in a specific relationship to that world coordinate center. That's where a second or another function comes in called PointAdd. PointAdd is a critical function relative to the use of vectors. All PointAdd does, now it's different than addpoint, we've been using addpoint up until now, which renders points within the scene. PointAdd adds two points or two vectors together. Typically, what we're doing is we're adding a vector to a point in space. I find a vector, either I create a vector or I find it and then essentially what I'm doing is I'm moving it by adding it to another point in space. If I either created or found this vector that I've drawn here and then I wanted to relocate it someplace else, let's say to a point out here, then I would add this vector, and let's call this, let's say that's point 01, and I'm going to add it to that point, which is let's say point 02. I'm not seeing this line. Well, oftentimes if I'm teaching with vectors, I'm going to draw a line because you don't see a vector. It's another thing. It's like planes. You don't see planes. You would have to actually create a rectangle or a surface something to see the plane. But if I'm adding that point to that point, it's going to create the point out in space this distance and at that exact angle, and it's going to create that new point. So that's what that new point has created there. This is added there, this is added there and it creates that new point. That's it. That's really a fundamental thing about vectors. Now, we can use something called VectorCreate, and I'm going to go over this in the demo where we can input two points in space and they're essentially going to create that angle, that relationship, that magnitude, let's call this D2, relative to that world coordinate center. I'm going to show that it's not often how we use vectors. I just want to quickly talk about the two ways that we typically we're going to use vectors. One I already mentioned, and that's from a line. When we were finding a plane on a curve, what we were evaluating or finding was the normal at a point on that curve in order to find a plane. What that normal is is a vector. Anytime you hear the term normal, normal is also a vector. If I'm to return that normal on that curve, it's going to give me a point. The point that would return that normal would be a point relative to the world coordinate center. The other normal or vector that we find is from a surface. We can evaluate a point or parameter and find a normal along any surface at any parameter on that surface, and that's also a vector. Those are more likely the two ways that we're going to be creating vectors is we're going to be extracting them from geometry and then doing something with them, creating geometry from that. That's what we're going to talk about when we talk about the 3D surface point matrix.
