A coordinate system consists of numbered scales that identify an initial, or base, point and the direction for measuring subsequent points on a graph. The Cartesian Coordinate System, named after the philosopher René Descartes, who defined the x,y-coordinate system in the 1600s, consists of three numbered scales, called the x-axis, y-axis, and z-axis, that are perpendicular to each other and extend infinitely in each direction. Each pair of axes (xy, xz, yz) forms a flat plane. Most of your time using AutoCAD will be spent drawing in the xy plane.

The point where the scales intersect is called the origin. For each axis, all values on one side of the origin are positive, all values on the other side are negative, and values that fall in line with the origin have a value of 0 (zero). The divisions along the scales may be any size, but each division must be equal. The axes divide the coordinate system into four regions called quadrants. Quadrant I is the region above the x-axis and to the right of the y-axis. Quadrant II is the region above the x-axis and to the left of the y-axis. Quadrant III is the region below the x-axis and to the left of the y-axis. Quadrant IV is the region below the x-axis and to the right of the y-axis. Most of your work in AutoCAD will be done in Quadrant I, and this is the area shown when you first open a drawing.

Any point on a graph can be specified by giving its coordinates relative to the origin given as a combination of the X value and the Y value delineated with a comma. For example, a coordinate of 5,7 means a point on the coordinate system that is 5 units in the positive X direction and 7 units is the positive Y direction. Figure 2.9 shows a typical Cartesian coordinate system and the default region used as the drawing area in a new AutoCAD file.

In this next exercise, you'll try using the Line command again, but instead of picking points in the drawing area with the mouse as you did before, this time enter x- and y-coordinates for each point from the keyboard. To see how to do this, follow these steps:

You can also start the Erase command by entering e

Figure 2.9. The x- and y-coordinates of the drawing area

Now begin drawing lines again by following these steps:

The lines are similar to those you drew previously, but this time you know where each point is located relative to the 0,0 point. In the drawing area, every point has an absolute x- and y-coordinate. In steps 2 through 8, you entered the x- and y-coordinates for each point. For a new drawing such as this one, the origin (0,0 coordinate) is in the lower-left corner of the drawing area and all points in the drawing area have positive x- and y-coordinates.

Let's explore how the cursor is related to the coordinates in the drawing.

The drawing area of a new drawing is preset with the lower-left corner of the drawing at the coordinates 0,0.

Once you understand the coordinate system used by AutoCAD, you can draw lines to any length and in any direction. Look at the shape shown earlier in Figure 2.1. Because you know the dimensions, you can calculate, by adding and subtracting, the absolute coordinates for each vertex—the connecting point between two line segments—and then use the Line command to draw the shape by entering these coordinates from the keyboard. However, AutoCAD offers you several tools for drawing this box much more easily. Two of these tools are the relative Cartesian and the relative polar coordinate systems.

When you're drawing lines, these coordinate systems use a set of new points based on the last point designated, rather than on the 0,0 point of the drawing area. They're called relative systems because the coordinates used are relative to the last point specified. If the first point of a line is located at the coordinate 4,6, and you want the line to extend 8 units to the right, the coordinate that is relative to the first point is 8,0 (8 units in the positive x direction and 0 units in the positive y direction), whereas the actual—or absolute—coordinate of the second point is 12,6.

The relative Cartesian coordinate system uses relative x- and y-coordinates in the manner shown, and the relative polar coordinate system relies on a distance and an angle relative to the last point specified. You'll probably favor one system over the other, but you need to know both systems because you'll sometimes find that, given the information you have at hand, one will work better than the other. A limitation of this nature will be illustrated in Chapter 4, "Developing Drawing Strategies: Part 1."

When entering relative coordinates, with the Dynamic Input tool turned off, you need to enter an "at" symbol (@) before the coordinates. In the previous example, you would enter the relative Cartesian coordinates as @8,0. The @ lets AutoCAD know that the numbers following it represent coordinates that are relative to the last point designated. When the Dynamic Input tool is turned on, relative coordinates are employed and the @ symbol is not required.

Relative Cartesian Coordinates

The Cartesian system of coordinates uses a horizontal (x) component and a vertical (y) component to locate a point relative to the 0,0 point. The relative Cartesian system uses the same components to locate the point relative to the last point picked, so it's a way of telling AutoCAD how far left or right and up or down to extend a line or to move an object from the last point picked (see Figure 2.11). If the direction is to the left, the x-coordinate will be negative. Similarly, if the direction is down, the y-coordinate will be negative. Use this system when you know the horizontal and vertical distances from point 1 to point 2. To enter data using this system, use this form: @x,y.

Figure 2.11. The relative Cartesian coordinate system

Relative Polar Coordinates

This system requires a known distance and direction from one point to the next. Calculating the distance is straightforward: it's always positive and represents the distance away from the first point that the second point will be placed. The direction requires a convention for determining an angle. AutoCAD defines right (toward three o'clock) as the default direction of the 0° angle. All other directions are determined from a counterclockwise rotation (see Figure 2.12). On your screen, up is 90°, left is 180°, down is 270°, and a full circle is 360°. To let AutoCAD know that you're entering an angle and not a relative y-coordinate, use the less-than symbol (<) before the angle and after the distance. Thus in the previous example, to designate a point 8 units to the right of the first point, you would enter @8<0 or simply 8<0 when the Dynamic Input tool is active.

Figure 2.12. The relative polar coordinate system

Note

Remember, use the relative polar coordinates method to draw a line from the first point when you know the distance and direction to its next point. Enter data using this form: @distance<angle.

You can also draw lines by placing the cursor at any angle relative to the last point and entering a distance value at the command prompt. The line is drawn from the last point toward or through the cursor location at the length specified. The Direct Distance method is often used when either Ortho mode or polar tracking is turned on.

To begin drawing the box, use the same drawing:

Figure 2.13. The first four lines of the box

To prepare to draw the box again, use the Erase command to erase the four lines you just drew:

Note

You've been introduced to two methods of selecting lines to be erased: typing all

When you move the cursor over an object, AutoCAD highlights the object. This is called rollover highlighting. It tells you that clicking while the object is high-lighted selects that object. You have some choices as to how this highlighting appears:

Now draw the shape again using the relative polar method by following these steps:

You can see from this exercise that you can use either method to draw a simple shape. When the shapes you're drawing get more complex and the amount of available information about the shapes varies from segment to segment, one of the two relative coordinate systems will turn out to be more appropriate. As you start drawing the floor plan of the cabin in Chapters 3 and 4, you'll get more practice using these systems.

Now draw the box once more, this time using the direct input method by following these steps:

You can see from these exercises that you can use multiple methods to draw a simple shape. When the shapes you're drawing get more complex and the amount of available information about the shapes varies from segment to segment, one method or another will turn out to be more appropriate. As you start drawing the floor plan of the cabin in Chapters 3 and 4, you'll get more practice using these systems.

Some additional tools make the process of drawing simple, orthogonal lines like these much easier. I'll introduce these tools in the following three chapters.

The next task is to create the lines that represent the inside walls of the box. Because they're all equidistant from the lines you've already drawn, the Offset command is the appropriate command to use. You'll offset the existing lines 0.5 units to the inside.

The Offset command involves three steps:

Here's how it works:

This command is similar to the Line command in that it keeps running until it's stopped. With Offset, after the first offset, the prompts switch between Select object to offset or [Exit/Undo] <Exit>: and Specify point on side to offset or [Exit/Multiple/Undo] <Exit>: until you press

The inside lines are now drawn, but to complete the box, you need to clean up the intersecting corners. To handle this task efficiently, you'll use a tool called the Fillet command.

Specify offset distance or [Through/Erase/Layer] <Through>:

The Fillet command lets you round off a corner formed by two lines. You control the radius of the curve, so if you set the curve's radius to zero, the lines form a sharp corner. In this way, you can clean up corners such as the ones formed by the lines inside the box. You must pick points on the filleted lines on portions that will remain after the fillet is implemented; otherwise the wrong portion of the line may be retained.

Follow these steps to establish the precise position of the opening:

Figure 2.25. Offsetting the second line of the opening

You now have two new lines indicating where the opening will be. You can use these lines to form the opening using the Extend and Trim commands.

You use the Extend command to lengthen (extend) lines to meet other lines or geometric figures (called boundary edges). Executing the Extend command may be a little tricky at first until you see how it works. Once you understand it, however, it will become automatic. The command has two steps: first, you pick the boundary edge or edges; second, you pick the lines you want to extend to meet those boundary edges. After selecting the boundary edges, you must press

You can also start the Extend command by entering ex

Figure 2.28. The lines are extended to the boundary edge.

You can also start the Trim command by entering tr

The final step is to trim away the horizontal lines to complete the opening and the unneeded portions of the two most recent vertical lines that you offset. To do this, you use the Trim command. As with the Extend command, there are two steps. The first is to select reference lines. In this case, they're called cutting edges because they determine the edge or edges to which a line is trimmed. The second step is to pick the lines that are to be trimmed.

Figure 2.29. Lines selected to be cutting edges

Figure 2.30. Lines selected to be trimmed.

The opening is trimmed away (see Figure 2.31).

Figure 2.31. Lines are trimmed to make the opening.

Now let's remove the extra part of the trimming guidelines.

Congratulations! You've just completed the first drawing project in this book and covered all the tools in this chapter. These skills will be useful as you learn how to work on drawings for actual projects.

A valuable exercise at this time would be to draw this box two or three more times, until you can do it without the instructions. This will be a confidence-builder to get you ready to take on new information in the next chapter, in which you'll set up a drawing for a building.

Figure 2.32. Lines picked to be cutting edges

Figure 2.33. Lines picked to be trimmed.

The box you drew was 6 units by 5 units, but how big was it? You really don't know at this time because the units could represent any actual distance: inches, feet, meters, miles, and so on. Also, the box was positioned conveniently on the screen so you didn't have any problem viewing it. What if you were drawing a building that was 200′ (60.96 meters) long and 60′ (18.29 meters) wide or a portion of a microchip circuit that was only a few thousandths of an inch or millimeters long? In the next chapter, you'll learn how to set up a drawing for a project of a specific size.

Figure 2.34. The completed trim

A completed version of this exercise can be found in this book's web page, www.sybex.com/go/autocad2010ner, as Chapter02 Shape Completed.dwg.

You can save the file by clicking the Save button on the Quick Access toolbar or exit AutoCAD now without saving this drawing. To do the latter, expand the Application menu, and then click the Exit AutoCAD button in the lower-right corner. When the dialog box asks if you want to save changes, click No. Alternatively, you can leave AutoCAD open and go on to the following practice section or the next chapter.