Download Descriptive Geometry

Fundamentals of
Descriptive Geometry
Department of Applied Technology
And Technology Management
September 9, 2013
Point View of a Line
• What you see when
you look down the
length of a line.
• Experiment:
– Take a pencil and
look at it from various
directions, keeping in
mind the rotations
between line of sight
directions.
Principles of Descriptive
Geometry Rule #2
If the line of sight is parallel to a truelength line, the line will appear as a
point view in the adjacent view.
Corollary
Any adjacent view of a point of view of
a line will show the true length of the
line.
Points on a Line
• If a point is
on a line, it
will appear
on the line
in all views
and be at
the same
location on
the line.
Not All Points that APPEAR to
be on a Line actually are!
• Two
orthographic
views are
required to
see where
any given
point lies.
Planes
• Planes are surfaces that can be uniquely
defined by:
–
–
–
–
Three non-linear points in space,
Two non-parallel intersecting vectors,
Two parallel vectors, or
A line and point not on the line.
Plane Definitions
Plane Classifications
• Planes are classified as
– Horizontal
– Vertical
• Profile
• Frontal
– Inclined (perpendicular to a principle plane)
– Oblique (not perpendicular to a principle
plane)
• Horizontal and Vertical planes are
principle planes.
Examples
• Orthographic
representations
of planes as
they appear in
the principle
views
Principles of Descriptive
Geometry Rule #3
Planar surfaces of
any shape always
appear either as
edges or as
surfaces of similar
configuration
Principles of Descriptive
Geometry Rule #4
If a line in a plane appears as
a point, the plane appears as
an edge
Principles of Descriptive
Geometry Rule #5
A true-size plane must be
perpendicular to the line of
sight and must appear as an
edge in all adjacent views.
Drawing a Plane in Edge View
A Corollary to Rule #5
If a plane is true-size then all
lines in the plane are true
length and all angles are true.
Finding the Angle Between Two
Intersecting Planes
• The key is to create a view where BOTH
planes are in edge view.
– The common line between the planes is the
intersecting line.
– Create a view where the intersecting line
appears as a point.
• Start by drawing a view of the line in true length
• Then draw the desired view.
Finding an Angle