Understanding coordinate systems - Rhino Tutorial

- The coordinate systems in Rhino for Mac, help us figure out where things are in Rhinos 3D space. To help us get oriented in our coordinate system, I've got the Exercise File, modeling coordinates.3dm open. You might be familiar already with commands in Rhino that prompt us to enter points in the form of coordinates. One example of that, is the Polyline command. Let's go to the Curve menu, and under Polyline, I'll click that Polyline command to activate it. So, this command just takes points as its input, and we can click anywhere in the viewport to start setting points. But we could also set those points by typing into the command prompt. When we enter points this way in a Rhino command, we can do it in two different ways. We can set Cartesian coordinates or polar coordinates. Cartesian coordinates are probably the more familiar set, the XYZ configuration. So, for example, if I wanted the next point to be right about here, at -10, -10, 0, I can just type that in. So, -10 and I separate each coordinate by a comma, - 10 and then 0 and hit Return to set that point. So, there you can see, I get my second point, exactly where I specified. I could also do Cartesian coordinates with just the X and the Y values. So, let's zoom into the top here a little bit, and let's say, I wanted to go somewhere, right around here, so, maybe -5 X, and be careful as you're doing this, because if you type Spacebar into the command prompt, Rhinos, thinking that you're hitting Enter. So, you want to make sure that you just do a comma -5 comma, - 8, and no space in between, hit Return. And so, I didn't even specify a Z-coordinate, but Rhino is just assuming, if it's left off, that it's zero. So, Cartesian coordinates are pretty straightforward. We're just typing in the X, Y, and Z location of the point, and we can also get some clues to where that might end up, by checking down here in the status bar, you'll get an XYZ readout of wherever the cursor happens to be. So, you can see as I'm moving around, in any of the viewports, those locations will be changing. So you can kind of crib that, and type it into your command line if needed. Now, in addition to Cartesian coordinates, I can also enter what are called polar coordinates. So, these are formatted a little bit differently. With a polar coordinate you enter a distance and an angle. So, let's try a polar coordinate. So, first I'm going to enter a distance, let's say 30 units, and just like with Cartesian coordinates, that's relative to the coordinate system origin. So, right now we're saying, 30 units from the origin. And then we'll type in an angle, and to tell Rhino I'm typing in an angle, I'll use the less than sign, and then we'll type in an angle, and let's say that I want that angle to be 45 degrees. So, that less than sign is an angle of 45 degrees. And you can see my preview is already going to that point. So, I'm 30 units from the origin, at an angle of 45 degrees from the last point. Go ahead and hit Enter, and that's my point. Okay, I'll just hit Escape to get out of that Polyline command. And let's talk a little bit more about polar coordinates, cause I know, that one can be pretty confusing. This might be the first time you're ever exposed to it working in Rhino. Let's go over to our layers panel, and click to make the Polar Coords layer, the current layer. Also go ahead and double-click on my top viewport to maximize, just so we can see a little bit easier. So, here we have a little visualization to help illustrate, how the angles are set up in Rhino when we're working with polar coordinates. So, let's go ahead and bring up just a single line command. So from Curve, I'll go to Line and just click to select Single Line. We'll start the line right at the origin. And here I can snap, right to that world origin because my grid snaps are active. A nice little shortcut if you ever want to specify the origin, just type zero into the command line, and hit Return, and again, Rhino is going to assume, that anytime you're leaving off coordinates, they are set to zero. So, simply by typing in zero Rhino is assuming that we mean zero for all of the dimensions. So, maybe I want the end of my line to end up right around here. So, I would need to break that down into a distance, and an angle. And looking at the circle, I can see the radius is about 20, so my distance would probably be 20, and my angle is going to be somewhere between zero and 90. So, you can see the coordinates on the circle go counterclockwise. So we start here at zero, we go up to 90, 180, 270, then all the way back around to 360. So, if I want to set a point somewhere over here, it's going to be... I'm going to say probably about 75 degrees. So, let's use a polar coordinate, to specify the end of that line. So, it's going to be 20 units from the origin, and then we will type in the less than sign to say that we're typing in an angle, and let's say 75 degrees. And there I can see, that's pretty close, and this is nice that we get the preview cause I can kind of tweak it still, and then go ahead and click done. So, we've got a little bit of exposure, to different ways of setting coordinates. To put that into practice, let's go ahead back to our layers panel and let's set this Maze layer to be the current layer and let's turn off, Polar Coordinates layer. The challenge here is to make a polyline, that goes completely through the Maze, without clicking in the viewport, so, just by typing in coordinates into the command prompt. I'll get us started here, but I'm hoping you can use your knowledge to actually get all the way through the Maze, it's really good practice. So, I'll go ahead up to the Curve menu, under Polyline, let's bring back Polyline, and I want to start right at the origin. So again, anytime we need to start at the origin, we can just type in zero, hit Return, okay? So, that is my first point. Let's work on setting some additional points using some of the tricks we've learned. So, I know for the first one, I'd like to go right about here. So, that looks like about zero in X direction, maybe five in the wide direction and zero in the Z direction. So, we type in 0,5,0. Okay, that's our first point. So, it looks like we needed to come over this direction. And of course we can come down here to our status bar. We can crib those points. So, I see that it's -27,5. So, -27 in the X, comma five hit Enter, and since the Z is zero, we can just leave that off, Rhino assumes that it's zero. Now, so far, all of the points that we've been entering into the command line, have been relative to that world origin, so, two, zero, zero, zero right here. One cool trick we can do in Rhino, when we're entering coordinates, is to enter them relative to the previous point. So, rather than specifying everything relative to the world origin, I can treat the previous point, as sort of a temporary origin. And with that in mind, I'm thinking this next point, this needs to be... Oh, it looks like maybe about 25 units above the previous point. So, to tell Rhino that we are working relative to the last point, all we do is type a letter r to begin our set of coordinates. And that makes the whole set of coordinates that we'll enter, relative to the last point. So, I want to go zero in X, 25 in Y. Oops, and that was a little bit too far. Let's click the Undo. Let's make it more like 20. So, r for relative, we're not moving horizontally. So we'll set that to zero and let's make that more like 20. There we go. And I can even look more closely at the preview to make sure that that's what I want. That's great. Now, we can also, of course, do that with polar coordinates. So, if I'm wanting to set this next point using a relative polar coordinate, let's think that through. First of all, I need to type in r, my length, let's say that's going to be probably eight units, and then we'll specify an angle, and that angle is going to be 180 degrees. Hey, that looks pretty good. Go ahead and click Return. So, I'm going to keep chugging here, you should do the same. It's a really helpful way to get some practice in terms of thinking about where things are in 3D space, and this will really help you get quicker, as you're executing commands that can take in coordinates.