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Understanding the Cartesian coordinate system

From: AutoCAD 2013 Essentials: 02 Drawing Fundamentals

Video: Understanding the Cartesian coordinate system

AutoCAD is a vector-based application. This means that all of the geometry that we see in a drawing is tied to an underlying coordinate system. This coordinate system allows AutoCAD to know with a high degree of precision where everything spatially exists in a file. In this lesson, we're going to take a behind-the-scenes look at model space to better understand how AutoCAD manages our geometry. Generally speaking, model space represents an infinitely large grid, much like a sheet of graph paper. We draw our geometry on this grid and AutoCAD uses the grid to maintain the accuracy of the file. It does this through the use of baselines. The first is an East-West baseline called the x axis.

Understanding the Cartesian coordinate system

AutoCAD is a vector-based application. This means that all of the geometry that we see in a drawing is tied to an underlying coordinate system. This coordinate system allows AutoCAD to know with a high degree of precision where everything spatially exists in a file. In this lesson, we're going to take a behind-the-scenes look at model space to better understand how AutoCAD manages our geometry. Generally speaking, model space represents an infinitely large grid, much like a sheet of graph paper. We draw our geometry on this grid and AutoCAD uses the grid to maintain the accuracy of the file. It does this through the use of baselines. The first is an East-West baseline called the x axis.

The x axis is also a number line. Everything to the right of zero is considered positive X. Everything to the left of zero is considered negative x. There is a second baseline that runs North-South. It's called the y axis, and it also represents a number line. Everything above the x axis is considered positive y. Everything below the x axis is considered negative y. AutoCAD uses these intersecting baselines to identify all points on the grid.

It does this through the use of coordinates, and AutoCAD references coordinates using the format x, y. The first coordinate we're going to talk about is the location where the x and y axis intersect. This point has a coordinate value of 0,0. This location is also considered the origin; all other coordinates are measured from this point. For instance, if I pick a point over here, this location would have a coordinate value of 6,2. It's six units in the x direction and two units in the y direction. Let's try another. This point would have a coordinate value of -4,5.

It's negative four units in the x direction and five units in y. Remember, the format is always x, y. We'll do one more. How about this one? This point has a coordinate value of 9,-3. Nine units in the x, negative three units in the y. Knowing this, when I create a line onscreen, AutoCAD views this object as an entity that was drawn from coordinate -8,-3 to a coordinate of -9,7. Having these coordinates, AutoCAD can easily calculate the length of the line and the direction in which it was drawn. AutoCAD views all geometry within the context of coordinates. Let's return to model space.

As you can see, I'm sitting in the default template file. I'm going to zoom out slightly, and I'll pan the drawing up a little bit. Notice the grid that we see onscreen. This is a visual reminder of the underlying coordinate system. In fact, you can easily identify the location of the baselines. The x axis appears red and the y axis appears green. Take a look at this icon. This is called the UCS icon. UCS stands for User Coordinate System, and this icon identifies the direction of positive x and positive y. Notice down here in the lower-left corner of the screen. As I move my cursor, you can see it's coordinate location updating in real time. So, everything we create is based on an underlying coordinate system.

At this point, you may be wondering if it's possible to create geometry using coordinates. The answer is yes you can, although we don't do it very often. Let's try it. Since we're going to be drafting using coordinates, I'm going to make one quick change. I'm going to come down and turn off the Dynamic Input. Dynamic Input tends to take some liberties with our coordinates, and I don't want to get into that right now so we'll toggle that off momentarily. I'm going to create a circle first. I'll launch the command and rather than picking my center point onscreen, I'm going to enter the coordinate value 10,5, and I'll press Enter. I will then create the circle with a radius of 3. Then I'll press Enter. Now, let's say I'd like to create another circle, twenty units to the right of this one. Well, using coordinates, that's very easy. I'm going to press the spacebar to relaunch the Circle command, and this circle's center point would have a coordinate value of 30,5.

I'll press Enter, and then I'll press Enter again to create a circle the same size as the last one. Let's do one more thing. Maybe I'd like to draw a line from the center of this circle to the center of this one. Once again, this is very easy because I know those coordinates. I'm going to move up and launch the Line command. I will start my line at the coordinate 10,5. I'll press Enter, and I'll draw this to coordinate 30,5. Enter. When I'm finished, I'll press the Escape key.

As you can see, since this drawing is based on an underlying coordinate system, AutoCAD can easily maintain the accuracy of the line work. And it allows us to create new geometry with a high degree of precision.

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AutoCAD 2013 Essentials: 02 Drawing Fundamentals

27 video lessons · 9345 viewers

Jeff Bartels
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