Chapter 7 Computer-Aided Drafting and Design
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drawn using coordinates in relation to the last
coordinate specifi ed (or the origin, if a previous
point has not been specifi ed). For example,
entering the relative coordinate (@5,4) after
entering the absolute coordinate (2,2) places
the next point fi ve units along the positive X
axis and four units along the positive Y axis
“relative” to the absolute coordinate (2,2)
or at the absolute coordinate (7,6). Refer to
Figure 7-9B.
When using polar coordinates, coordinates
are located at a given distance and angle. Polar
coordinates are entered using a format such as
(distanceangle). This format specifi es a linear
distance and angle in the XY plane relative
to the previous point or the origin. Angles
are most commonly measured counterclockwise,
with the positive X axis representing 0°. Entering
the @ symbol before the polar coordinate
locates the point relative to the previous point.
If the @ symbol is not entered before the
polar coordinate, the point is located relative
to the origin. Referring to Figure  7-9C, the
polar coordinate entry (545) locates the point
fi ve units away from the origin at an angle
of 45° in the XY plane. The polar coordinate
entry (8120) locates the point eight units
away from the origin at an angle of 120° in the
XY plane.
Each of the different types of coordinate
entry can be used when creating a drawing. The
entry used typically depends on the object
drawn. For example, it may be useful to use
absolute coordinates when a given point is
known, or when drawing straight lines. Relative
coordinates may be used when locating points
from a common feature. Polar coordinates are
useful for drawing inclined lines and round
objects.
User Coordinate Systems
As previously discussed, the default world
coordinate system in a CAD program has the
origin located at 0,0,0. This is typically suffi cient
for most 2D drawings, since coordinates for
2D objects can be drawn on the XY drawing
plane without specifying a third coordinate
along the Z axis.
axis, the Z axis, is required for 3D drawings.
See Figure 7-8. This axis is used for coordinate
entry above or below the XY plane. A point
with a positive Z coordinate, such as (0,0,1), is
located “above” the XY drawing plane. When
looking at a drawing on screen, this location
can be thought of as a point projecting out
of the monitor toward you. A point with a
negative Z coordinate, such as (0,0,–1), is
located “below” the XY drawing plane. When
looking at a drawing on screen, this location
can be thought of as a point projecting into
the monitor away from you. In order to draw
objects in 3D space with a CAD system, it is
important to be able to visualize objects in
three dimensions and understand how points
are located along the three coordinate axes.
Refer to Figure 7-6.
A basic way to locate points when drawing
objects is to pick points on screen using the
mouse. In addition, there are three common
forms of coordinate entry used to specify
point locations. Coordinates can be entered as
absolute coordinates, relative coordinates, or
polar coordinates. See Figure 7-9. When using
absolute coordinates, objects are drawn using
points in relation to the coordinate system origin
(0,0). The absolute coordinate (2,2) indicates
that the point is located two units from the
origin along the positive X axis and two units
from the origin along the positive Y axis.
When using relative coordinates, objects are
Goodheart-Willcox Publisher
Figure 7-8. A third axis (the Z axis) is needed to
generate three-dimensional drawings like the one
shown. The ability to visualize objects in 3D space is
fundamental to creating 3D drawings.
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