Fundamentals of
Descriptive Geometry
(Text Chapter 26)
UAA ES A103
Week #12 Lecture
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Introduction
• Most of the concepts of this chapter have
already been touched on in prior lectures
and exercises.
• The intent of this lecture to provide another
view of the principles and concepts from
an analytical standpoint.
Descriptive Geometry
• Descriptive geometry is the graphic
representation of plane, solid, and analytical
geometry used to describe real or imagined
technical devices and objects.
• It is the science of graphic representation in
engineering design.
• Students of technical or engineering graphics
need to study plane, solid, analytical, and
descriptive geometry because it forms the
foundation or grammar of technical drawings.
Uses of Descriptive Geometry
• Descriptive geometry principles are used to
describe any problem that has spatial aspects to
it.
• For example the application of descriptive
geometry is used in:
– The design of chemical plants. For the plant to
function safely, pipes must be placed to intersect
correctly, and to clear each other by a specified
distance, and they must correctly intersect the walls of
the buildings.
– The design of buildings
– The design of road systems
– The design of mechanical systems
Methods of Descriptive
Geometry
• There are three basic methods
– Direct View
– Fold Line
– Revolution
• The differences is in how information is
transferred to adjacent views.
Direct View Method
• Reference
plane is used
to transfer
depth info
between
related views.
• Length
information
comes by
projection
lines from the
adjacent view.
Fold-Line Method
• A variation on
the Direct View
method.
• The reference
line is moved
between the
views to
represent the
folds in a glass
box.
Revolution Method
• The projectors from
the adjacent view are
not parallel to the
viewing direction (as
related to the object)
• Need to rotate the
length information
about an axis before
projecting it to the
new adjacent view.
Reference Planes
• The reference
plane is
perpendicular
to the line of
sight project
lines. It
appears as a
line in related
views.
• Gives a
reference for
measuring
depth
information for
related views.
Basic Elements
• The basic elements used in descriptive
geometry include:
– Points
– Lines
– Planes
• Coordinate systems are mathematical tools
useful in describing spatial information
– Cartesian coordinate systems are the most
commonly used.
Cartesian Coordinate System
• Points are
located
relative to
the origin
of the
coordinate
system.
Points
• A point has no width, height, or depth.
• A point represents a specific position in
space as well as the end view of a line or
the intersection of two lines.
• The graphical representation of a point is a
small symmetrical cross.
Lines
• Lines represents the locus of points that are
directly between two points.
• A line is a geometric primitive that has no
thickness, only length and direction.
• A line can graphically represent the intersection
of two surfaces, the edge view of a surface, or the
limiting element of a surface.
• Lines are either vertical, horizontal, or inclined.
A vertical line is defined as a line that is
perpendicular to the plane of the earth (horizontal
plane).
Multi View Representations of
Lines
True Length Lines
• A true length line
is the actual
straight-line
distance between
two points.
• In orthographic
projection, a truelength line must
be parallel to a
projection plane
in an adjacent
view.
True Length Lines
• True length lines are
ALWAYS parallel to
the reference plane in
ALL adjacent views.
• To find the true length
of a line, draw a view of
the line where the
reference plane is
parallel to an adjacent
view of the line.
Principles of Descriptive
Geometry Rule #1
If a line is positioned parallel to
a projection plane and the line
of sight is perpendicular to
that projection plane, then the
line will appear as true length
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