Chapter Four
Planes
Objectives
Upon completion of this chapter the student will be able to:
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Describe the difference between a surface and a plane.
List the four ways that the boundaries of a plane may be defined.
List the three types of planes encountered in descriptive geometry.
Use AutoCAD to determine if two objects reside on the same plane.
Determine the location of a point on a plane.
Determine the location of a line on a plane.
Locate the piercing point of a line and a plane using the auxiliary view and
cutting
plane methods.
Use the cutting plane method in AutoCAD to determine the intersection of
two planes.
Locate the piercing point using the point command and app osnap option.
Locate the intersection of two planes.
Determine the angle between two planes.
Defining a Plane
There are four ways in which a plane’s
boundaries can be secured.
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a line and a point
three points
two intersecting lines
two parallel lines.
Line and a Point
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The line and the point must both reside
on the plane that they are defining.
The point cannot reside on the line. If the
point is on the line then only one possible
boundary can be established.
Line and a Point Example
Three Points
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All three points must reside on the plane that
they are defining.
It must not be possible to connect all three
points with a single, straight, line segment.
Three Points Example
Two Intersecting Lines
Two intersecting lines or line segments drawn
at any length and intersecting at any angle may
be used to define the boundaries of a plane if
both lines reside on the plane that they are
defining.
Two Intersecting Lines Example
Two Parallel Lines
To define a plane using two parallel lines, both
line segments must reside on the plane that they
are defining.
Two Parallel Line Example
Normal Planes
• If a plane is parallel to one of the three
principal planes of projection (frontal,
horizontal, profile) then the plane is referred to
as a normal plane.
• There are three subcategories of normal
planes: horizontal, frontal, and profile.
Normal Plane Example
Inclined Plane
• When a plane is not classified as a normal
plane but appears as a line (edge view) in
one of the principal views and distorted in
the remaining two, then this plane is known
as an inclined plane.
• The true shape and size of an inclined
plane can only be found by constructing
one or more auxiliary views
Inclined Plane Example
Oblique Planes
• When a plane does not appear in edge view
in any of the three principal views then it is
known as an oblique plane.
• The true shape and size of an oblique plane
can only be determined in one or more
auxiliary views
Oblique Planes Example
XY Plane
• When an object is created in AutoCAD, it is
created on the XY-plane.
• Theoretically, the XY-plane extends
indefinitely in both directions along the Xand Y-axes, but does not contain a
thickness. Without a thickness an infinite
number of XY-planes could be stacked
upon one another.
Sketch Plane
• A sketch plane, in Mechanical Desktop, is
one that extends infinitely in two directions
and is used to construct the twodimensional outline of a part’s features.
The orientation of the X- and Y-axis on the
sketch plane
Locating Point on a Plane
• A point will either coexist with a plane or
outside the boundaries of the plane (above or
below an established plane).
• When a plane containing a point is projected
into a view where the plane appears as a line,
then the point contained on that plane will
appear as a point on the line.
Locating Lines on a Plane
• The principles, techniques, and theories
discussed in the previous section regarding
the location of points on a plane can also
be applied when transferring the location of
a line from one view to another.
Locating the Piercing Point of a Line and a Plane
• This point can either fall within or somewhere
outside the established boundaries of the
plane.
• If a line does not coexist on the plane or is
parallel to that plane, then a piercing point will
exist; because in theory a line extends
indefinitely in both directions unless a
boundary has been established.
Locating the Intersection of Two Planes
• When two or more planes intersect, they will
share more than one common point.
• In fact, they will share a series of points that
may be connected by a straight-line (line of
intersection), and every point along that line
will be common to both planes.
Determining the Angle between Two Planes
• When two planes intersect, they form an
angle known as the dihedral angle (see
Figure 4–57).
• This angle appears in true size in any view
where the two planes appear in edge view, or
any view in which the line of intersection
appears as a point
Determining the Angle between Two Planes
Example