Coordinate Systems

No matter what kind of drawing you do in AutoCAD, you need a systematic method of specifying points. Points define the beginnings and endpoints of lines, the centers of circles and arcs, the axis points of ellipses, and so on. The capability to place points accurately is important. When an AutoCAD command prompts you for a point, you can either specify a point on the screen with the mouse or pointing device, or enter coordinates at the command line. When entering points, AutoCAD uses a three-dimensional Cartesian, or rectangular, coordinate system. Using this standard system, you locate a point in 3D space by specifying its distance and direction from an established origin measured along three mutually perpendicular axes: the X-axis, Y-axis, and the Z-axis. The origin is considered to be at 0,0,0. Figure 6.1 illustrates such a coordinate system. Only two dimensions are depicted with the Z-axis projecting up, perpendicular to the page. If you are concerned only with two-dimensional drawings, this is the presentation of AutoCAD’s coordinate system that will be seen.

In Figure 6.1, the 4,6 coordinate indicates a point 4 units in the positive X direction and 6 units in the positive Y direction. Points to the left or below the origin have negative X and Y coordinate components, respectively. Figure 6.2 illustrates the same coordinate system, only now the third dimension and the Z-axis are shown. To specify 3D points, you add a third element to the coordinate designation. The point 4,6,6 in Figure 6.2 is located 4 units in the positive X direction, 6 units in the positive Y direction, and 6 units in the positive Z direction. The system of reckoning coordinates is independent of the units used so that distances can be in any measurement; for example, the X direction could be Imperial feet or inches, or metric centimeters or kilometers.

Later in this chapter, you will learn about the various ways that you can change the origin as well as the orientation of the three axes of AutoCAD’s rectangular coordinate system. No matter how the coordinate system is oriented, you must know how to enter points.

Coordinate Point Entry Methods

Many of the drawings you make in AutoCAD—regardless of their eventual complexity—consist of a few relatively basic AutoCAD objects such as lines, circles, and text elements. These objects require that you enter points that specify their location, size, and direction. Additionally, many editing operations also require that you specify points. There are four ways to enter points or coordinates in AutoCAD:

• Using absolute coordinates

• Using relative coordinates

• Using direct distance entry

• Using coordinate display

Using Absolute Coordinates

Absolute rectangular coordinates are always measured from the origin point: 0,0,0. In AutoCAD, you specify an absolute coordinate from the keyboard by typing in the X-, Y-, and Z-axis values separated by a comma: X,Y for 2D points, or X,Y,Z for 3D points.

You don’t need to use a plus sign (+) if the displacement from the origin is positive. You must, however, place a minus sign (-) in front of displacements in the negative direction: -2,3 or 4,-6,3.

Absolute polar coordinates also treat a 2D coordinate entry as a displacement from the origin, or 0,0, but you specify the displacement as a distance and an angle. The distance and angle are separated by a left-angle bracket (<) with no spaces: distance<angle (for example, 25<135).

Positive angles are measured counterclockwise from an assumed 0 degree that lies, by default, along the positive X axis as shown in Figure 6.3.

In the following exercise, you use both absolute rectangular and absolute polar coordinates to draw the outline of a fastener.

Exercise 6.1 Using Absolute Rectangular and Absolute Polar Coordinate Entry

LINE Specify first point: 4.5,5 
Specify next point or [Undo]: 6.5,5 
Specify next point or [Undo]: 9<38.34 
Specify next point or [Close/Undo]: 7.8<25.36 
Specify next point or [Close/Undo]: 6.5,4 
Specify next point or [Close/Undo]: 4.5,4 
Specify next point or [Close/Undo]: C
								

This short exercise demonstrates the limitations of absolute coordinates. Although absolute coordinates are adequate for designating the beginning of a line, measuring subsequent points in relation to the drawing’s origin is cumbersome and often inaccurate. When the lines outlining an object (such as the fastener in the preceding exercise) are not orthogonal, absolute coordinates are inadequate if any degree of accuracy and efficiency is desired. The use of relative coordinates solves this problem.

Using Relative Coordinates

In almost any kind of drawing, after you have established the beginning of a line, you usually know the X and Y displacement or the distance and angle to the next point. Relative coordinates do not reference the origin point but are determined relative to the last point. You can use this more straightforward method with either relative rectangular or relative polar coordinates. To distinguish relative coordinate entry from absolute entry, you precede relative coordinates with the @ symbol (for example, @1.5,3 for relative rectangular entry or @2.6<45 for relative polar entry).

In the preceding relative rectangular entry, the point specified lies at a displacement of 1.5 units in the X-axis direction and 3 units in the Y-axis direction from the previous point. In the relative polar entry, the point lies 2.6 units at an angle of 45 degrees from the previous point.

In the following exercise, the usefulness of relative coordinates is shown in drawing a fastener similar to the one in the previous exercise.

Exercise 6.2 Using Relative Coordinates

Continue from the previous exercise.

LINE Specify first point: 9,5 
 (Note this is an absolute coordinate.) 
Specify next point or [Undo]: @2<0 
 (Note this is a relative polar coordinate.) 
Specify next point or [Undo]: @.8<46 
Specify next point or [Close/Undo]: @0,-2.2 
 (Note this is a relative rectangular coordinate.) 
Specify next point or [Close/Undo]: @.8<134 
Specify next point or [Close/Undo]: @2<180 
Specify next point or [Close/Undo]: C
								

As you can see, relative coordinate point entry is much easier to use and permits more accuracy than absolute rectangular entry. Even when your drawing involves purely orthogonal displacements, relative coordinate entry is the superior and usually the only accurate method.

Direct Distance Entry

A variation of relative coordinate entry, called direct distance entry, is supported in AutoCAD. In direct distance entry, rather than entering coordinate values, you can specify a point by moving the cursor to indicate a direction and then entering the distance from the first point. This is a good way to quickly specify a line length. This method is used primarily when the displacements involved are orthogonal and you can have the ORTHO drawing aid turned on. The following exercise demonstrates the use of direct distance coordinate entry.

Exercise 6.3 Using Direct Distance Coordinate Entry

LINE Specify first point: 7.5,7.5 (Enter) 

Specify next point or [Undo]: <Ortho on> 2.3 (Enter) 

Specify next point or [Undo]: @.8<46 (Enter) 

Specify next point or [Close/Undo]: 2.2 (Enter) 

Specify next point or [Close/Undo]: @.8<134 (Enter) 

Specify next point or [Close/Undo]: 2.3 (Enter) 
Specify next point or [Close/Undo]: C (Enter) 

The outline should be similar to that completed in the previous exercises.

Direct distance entry provides a more direct and easier method of entering relative coordinates when the point lies in an orthogonal relationship to the previous point—a common situation in most drawings. Of course, if the point you want to designate lies on a snap point, whether or not orthogonal to the previous point, you can bypass keyboard entry by simply snapping the cursor to and clicking on the point. (The concept of snapping is covered later in this chapter.)

Coordinate Display

The coordinate display window located at the bottom left of the status bar is useful when entering coordinates, whether you type them at the command prompt or pick points on the screen with the screen cursor. Figure 6.6 shows this display with two variations of the format.

The upper display shows decimal units while the lower display shows architectural units. The are three types of coordinate displays, which can display either absolute or relative coordinates, depending on the one selected and the command in progress. You can cycle through the various display types in four ways: by pressing either F6 or Ctrl+D, or by clicking or right-clicking in the display area itself. The three coordinate display types are as follows:

• Static Display. Displays the absolute coordinates of the last picked point. The display is updated whenever a new point is picked.

• Dynamic Display. Displays the absolute coordinates of the screen cursor and updates continuously as the cursor is moved. This is the default mode.

• Distance and Angle. Displays the distance and angle relative to the last point whenever a command prompt requesting either a distance or angle is active.

When Static Display is selected, the coordinate display appears grayed-out, although the coordinates of the last selected point are still visible. At an empty command prompt (one with no command in progress) or at an active prompt that does not accept either a distance or angle as input, you can only toggle between Static Display and Dynamic Display. At a prompt that does accept or require either a distance or angle as input, you can cycle among all three display types. Pay particular attention to the coordinate display window during the following exercise.

Exercise 6.4 Cycling Through Coordinate Display Types

Specify next point or [Undo]: 6,7 (Enter) 

Specify next point or [Undo]: 2,3 (Enter) 

In this exercise, you saw the three types of coordinate displays and how they can aid you in selecting points. You also manually used the four methods available to you for cycling through the three display types. Although the absolute rectangular read-out type is of limited usefulness, it can, for example, be used to specify the starting point of an object such as a wall or to specify a set of known points in a surveying data context.