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Orthographic
Projection
UnitEngineering Graphics
Principles
Copyright 2002
Brigham Young University
All Rights Reserved
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Foreword
Orthographic projection (sometimes referred to as multi-viewprojection), is a geometricprocedure used in the engineering disciplines to project multiple graphic images of three-
dimensional objects, onto a single two-dimensional plane. The procedure is also calledengineering drawingor drafting, and is the primary means of communication used bydesigners and engineers in the design process. Multiple views in an orthogonal orientation(each rotated 90 from the other), is fundamental to the definition of feature and partcharacteristicssuch as size, location, orientation, and functional relationships.
In its simplest form, orthographic projection provides a range of six orthographic-specificviews of an object. In your mind, imagine a physical stationary object that has beensuspended in the center of a glass cube. Each of the six sides of the box represents aviewingorprojectionplane. The orientation of the observers line of sight must alwaysbeperpendicular or normalto the planes on the glass box, and the sides of the box must alsobe perpendicular to their adjacent sides. That being the case, the object could onlybeviewed from the front, top, right side, left side, back, or bottom. With the images indelibly
fixed on the planes, and the box unfolded, the projected images or viewswould always beoriented orthographically, and aligned with each other, from view to view on the drawing.
The process of orthographically projecting parts and/or feature characteristics is notnecessarily complicated, but it is complex. It is essential to the delineation of featuregeometry as an aide to the manufacturing process. This unit will give you practice usingthese principles, and will increase your ability to understand and visualize the process.
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How to Proceed
In order to produce mechanical parts, detailed design information must be provided to the
craftsmaninformation that defines and describes relevant geometry and relationships of
descriptive elements on the part. Graphic images or views, developed from specific
orientations, are major elements in this communication process. A primary objective of thisunit is to acquaint you with the process of generating multiple (albeit, geometrically related)
views of mechanical components. The basic theory, rationale, and production techniques
are presented in a systematic order. It is anticipated that you will complete this unit in one
or possibly two sessions (more time and practice may be required if you are new to the
science of engineering graphics).
Begin with a thoughtful preview of the unit objectives, and carefully consider the related
vocabulary words and terminology. As each topic is considered, keep in mind an overall
objective of being able to read an engineering drawing, or to construct correctly projected
views that would be required to describe part features, thus facilitating the manufacturing
process.
Follow each explanation, and practice each technique as outlined for solving orthographic
projection problems. Review concepts that seem unclear, and do each of the exercises that
are providedespecially the self assessment exercises at the end of the presentation. As
you complete the exercises, carefully compare your own sketched solutions with the those
provided, and review the governing principles where necessary.
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Unit Objectives
When you have completed this unit, you will be able to:
Explain the principles upon which orthographic projection is based.
Recognize and identify horizontal, frontal, and profile planes in engineering drawings, and explain
their relationships to standard planes of projection.
Identify the six principal views which may be generated, using the concept of the viewing cube, and
explain their specific orientation and relationships to each other.
Identify normal, inclined, and oblique planes relative to the six principal projection planes.
Read an engineering drawing, and explain the necessity for creating multiple views.
Use graphic tools such as reference planes and fold lines to solve orthographic projection problems.
Apply standard line and view conventions on an engineering drawing.
Solve orthographic problems using at least two techniques of locating and applying data.
Explain and illustrate the differences between first- and third-angle projection.
Demonstrate the appropriate applications for center lines and hidden lines in multi-view drawings.
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Orthographic Projection -- Theory and Practice
Terminology / Vocabulary
Orthographic Projection Theory (Third Angle Projection)
Glass Box Theory
Orientation of Object Features in Orthographic ProjectionDirections and Orientation in Orthographic Projection
Orthographic Projection Principles Review
Orthographic Projection Theory (First Angle Projection)
Multi-view Projection Techniques
Miter Line (1)
Miter Line (2)
Miter Line (3)
Miter Line (4)Solid Example Problem
Compass Projection Technique
Projection Orientation -- View Selection
Pictorial Visualization
Measure and Transfer Method (1)
Measure and Transfer Method (2)
Measure and Transfer Method (3)Measure and Transfer Method (4)
Pictorial Visualization (Pyramid4a)
Measure and Transfer Method (5)
An Alternative Solution (5a)
Inclined Surfaces in Orthographic Projection
Oblique Surfaces in Orthographic Projection
Additional Examples (Practice Problems in Orthographic Projection)
Concept Mastery Examination (Self Evaluation)
Orthographic Projection Table of Contents
Table of ContentsTopics:
To assist you in your study of the contents of
this presentation, a Table of Contentshas
been prepared. The topics listed are linked
to the specific content by topic. When
selected with the mouse (in show mode), the
presentation materials will open at the
requested location. The navigation bar at the
bottom of the screen allows you to return tothis slide at any time. Similar tables have
been included in all of the presentations that
follow.
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Terminology / Vocabulary
Orthographic Projection
Station Pointany location in 3-dimensional space that is infinitely displaced from the
object being viewed.Line of Sight(LOS)the orientation of an observer relative to a specific object.
Projection Plane(also called a Viewing PlaneorPicture Plane)the plane onto which
the image of an object is projected.
Visual Raysan infinite number of parallel theoretical projectors which emanate from
an object, to form the image of the object on the projection plane.Pierce Pointsintersections created by theoretical visual rays as they pass through or
collide with a projection plane.
Graphic Imagea symbolic representation of a 3-dimensional part or assembly of
parts, or a schematic layout or organization of entities, projected onto a 2-
dimensional plane.
Normal Viewsviews of features or part characteristics that are oriented perpendicular
to the observers line of sight.
Contiguous Viewsadjacent, orthographically projected views of an object.
Orthogonal Viewsprojected, orthographically aligned views of an object.
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Viewing CubeGlass Box concept; six projection planes configured as a cube.
Fold Linesthe representation of intersections between the sides of the viewing cube.Reference Planesa base line for taking and applying measurements.
Principal Viewsalso referred to asPrimary Viewstypically the front, top, and rightside views.
Surface Viewsnon-normal views of feature surfaces that display 3-dimensional areas.
Edge Viewsall points on a planar surface aligned parallel to the line of sight.
Inclined Surfacesperpendicular to 2 of the 6 viewing planes; parallel to none.
Oblique Surfacesneither parallel nor perpendicular to any of the 6 viewing planes.
Line Weightsthere are three distinct line weightson engineering drawings; thin linesapproximately .007 - .010 wide, medium lines, approximately .015 - .020wide, and thick lines approximately .030 - .040 wide.
Line Typesthere are many line typesthat are used on mechanical drawings, but thereare only six distinct line types that will be used in our discussions regardingorthographic projection: construction, object, center, hidden, phantom, andextension lines (also known as projection, or witness lines).
Terminology / Vocabulary
Orthographic Projection
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Orthographic Projection Theory
Observation of an object begins with the direction from which the object is to be
viewedthe line of sight.
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Viewing Station
at Infinity
Orthographic Projection Theory
The viewing station for the observer is always an infinite distance from the object.
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Line of Sight
Viewing Station
at Infinity
Projection Plane
(Picture Plane
Viewing Plane)
Orthographic Projection Theory
The plane of projection is located between the viewing station and the object (third
angle projection).
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Line of Sight
Viewing Station
at Infinity
Projection Plane
(Picture Plane
Viewing Plane)
Orthographic Projection Theory
The line of sight is always normal to the plane of projection
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Object
Line of Sight
Viewing Station
at Infinity
Projection Plane
(Picture Plane
Viewing Plane)
Orthographic Projection Theory
The object may be located anywhere behind the plane of projection
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Parallel Visual Rays
Orthographic Projection Theory
Object
Line of Sight
Viewing Station
at Infinity
Projection Plane
(Picture Plane
Viewing Plane)
Because the observation location is at infinity,parallelvisual rays extend from the
object to the plane of projection, and produce the image on the projection plane.
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Viewing an Object From an Infinite
Distance
Assuming a position at infinity, and
looking towards the object, we would see
the image of the object on the projection
plane (notice the line contrast between
object, center and hidden lines).
Projection Plane
A permanent image of the
object is formed on the
projection plane by visual
rays as they pierce theplane.
Parallel Visual Rays
Line of Sight
Projection Plane
Object
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Visualizing orthographic views using pictorial views
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Three-dimensional (pictorial) views of objects are frequently easier to understand thanmulti-view orthographic projections of the same object. Sketching the object in a mannershown can often help students visualize the details of the part. Students who are new tothese concepts are encouraged to use sketches.
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GLASS BOX CONCEPT
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The glass box concept theorizes that an object is suspended inside a six-sided glass cube
(notice the use of hidden lines on the glass box, depicting lines that would not be visible
from the given perspective).
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As the object is viewed from a specific orientation (perpendicular to one of the sides of the cube) visual
rays project from the object to the projection plane. These projectors arealwaysparallel to each other.
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The objects image is formed on the projection plane by the pierce points of the visual rays.
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The process is repeated to construct the right side view on the profile plane
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Similarly, the top view is projected
to the horizontal plane
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For many three-dimensional objects, two to three orthographic views are sufficient
to describe their geometry.
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The box can be unfolded to show the
multiple views in a single x-y plane
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FRONT
TOP
RIGHT SIDE
Notice that the projectors or extension lines,are perpendicular to the folding lines of theglass box. (Fold lines and extension lines aredrawn very lightly, when used, and are notpart
of the finished drawing.)
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The Glass Box Concept
Click on image to animate - click outside for next slide
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H i h hbj / i i i h hi j i
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Height = h
Width = w
Depth = dIn each of the six principal orthographic views,two specific dimensional characteristics are
provided
Object/Feature Orientation in Orthographic Projection
Directional Orientation in Orthographic ProjectionH i h h
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RIGHT SIDE
d
h
FRONT
TOP
d
w
w
h
Directional Orientation in Orthographic Projection
Two or three views of a 3-dimensionalobject are often sufficient for a complete
definition of part geometry. Width and
depth are displayed in the top view; height
and width in the front view, height and
depth in the side view.
Height = h
Width = w
Depth = d
Directional Orientation in Orthographic Projection H i ht h
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RIGHT SIDEFRONT
TOP
Directional Orientation in Orthographic Projection Height = h
Width = w
Depth = d
Two of the three size characteristics aredisplayed in each view. Because contiguousviews are always projected 90 to eachother, all three dimension characteristics canbe displayed in a single two-dimensionalplane.
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Direction and Orientation
In each projection plane, specific directionalorientation is described.
(Forward, or infront of)
BACK
BACK
LEFT
(To the left of) RIGHT(To the right of)
FRONT
UP
DOWN
FRONT
UP
DOWN
LEFT RIGHT
H
F P
(Behind, or in
back of)
(Forward, or in
front of)
(Behind, orin back of)
(Above, or
on top of)
(Below, beneath,
or lower than)
(Above, or on
top of)
(Below, beneath
or lower than)
(To the left of) (To the right of)
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REVIEW
ORTHOGRAPHIC PROJECTION PRINCIPLES
(Third-Angle Projection)
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The viewing station is an infinite distance from the object.
The line of sight is always perpendicular to projection plane.
The projection plane is always betweenthe object and viewing station.
Visual rays are always perpendicular to the projection plane.
Projectors (visual rays for a specific view) must always be parallel to each other, and
perpendicular to projectors from adjacent views.
Orthographic Projection Theory
REMEMBER,For Third-Angle Projection Solutions,
Review
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FIRST-ANGLE PROJECTION
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Line of Sight
Viewing Station
at Infinity
Projection Plane
(Picture Plane
Viewing Plane)
The basic difference between third- and first-angle projection is that infirst-angle
projection, the objectis placed between the observer and the projection plane.
First-Angle Projection
The image is always projected onto the projection plane but in the case of first
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Line of Sight
Viewing Station
at Infinity
Projection Plane
(Picture Plane
Viewing Plane)
The image is always projected onto the projection plane, but in the case of first-angle projection, it is actually projected away from, instead of towards theobserver. The image would be projected directly behind the object in each case.
Object
The image of the front view is formed as the projectors intersect the projection plane It is
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Projectors
(Visual Rays)
Line of Sight
Viewing Station
an infinite distance
from the object
Projection Plane
(Picture Plane
Viewing Plane)
The image of the front view is formed as the projectors intersect the projection plane. It is
important to note that the front view actually ends upbehindthe back surface of the object.
Let me try to illustrate the concept using three planes of the glass box theory.
Object
Object oriented in first angle
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An illustration of
first-angle
projection. (The
traditional horizontal
(top), frontal, andprofile (right side)
panels of the glass
box have been
removed for clarity.)
You are looking
down on theremaining three
sides of the boxa
birds eye view.
Object oriented in first-angle
projection framework
A bj t h bObject oriented in first angle
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= Line of Sight
An object has been
suspended in the glass
box. Top, front, and
right side views will be
generated using first-
angle projection.
Object oriented in first-angle
projection framework
Fi t A l P j ti Th ll i di t th li
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Front View
First Angle Projection The yellow arrow indicates the lineof sight. The image of the frontview is projected to the projectionplane behind the object.
The top (horizontal) view is projected from above the object but is created on the planeb l
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Front View
Horizontal
or Top View
below.
As with the previous two projections, the right side view is projected to the opposite side of
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Profile or
Right Side
View
Front View
Horizontal
or Top View
the glass box.
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The reference frame can be
unfolded to show the multiple
views in a single X-Y plane
Profile or
Right Side
View
Front View
Horizontal
or Top View
First-angle projection requires that
the box unfold awayfrom theobserver rather than towards the
observer.
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The reference frame can be
unfolded to show the multiple
views in a single X-Y plane
Profile or
Right Side
View
Front View
Horizontal
or Top View
As the box becomes fully two-dimensional, the differencesbetween first- and third-angleprojection become obvious. Theviews are reversed in their order
from third-angle projection; the topview is below the front view and theright side view is to the left of thefront view. If they had beendeveloped, the left side would be tothe right of the front view, the
bottom view would be above thefront view, and the back or aft viewwould be associated with any viewother than the front view.
The United States and Canada are the only two major countries that use third-
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Right Side ViewFront
View
Top
View
angle projection. All other industrial nations throughout the world use first-angle
projection. It is important that you understand the differences because many U.S.
companies are now internationally established. They will expect you to be able to
read and interpret either method used in engineering documentation.
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MULTI-VIEWPROJECTION TECHNIQUES
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Orthographic ProjectionExample Number 1
This is an example of how to use a miter (45) line to assist in constructing an
orthographic solution for the top or horizontal view. The front and right side
views are given.
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Explanations regarding solution techniques may vary between instructors, but the
results are the same. Verify the projection by placing extension lines between the
end points of the lineview to view, and label the points (care should be taken to
label the separate views consistently).
Establish a fold line somewhere between the views (make certain that the fold line
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(
is perpendicular to the projection lines between the two views). Although the fold
line does not necessarily have to be betweenthe two views, the problem is
simplified by placing it there. Later on, we will discuss placement alternatives.
A second fold line should be constructed perpendicular to the first at some
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A second fold line should be constructed perpendicular to the first, at some
convenient location, and extended to overlap both front and side views.
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P j t th i t th t d fi th li (1 2) i th i ht id i i di ti
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Project the points that define the line (1,2), in the right side view, in a direction
that isperpendicularto the fold line that is between the view and the 45 miter
line. Remember, when developing a new view, projectors between the views must
alwaysbe perpendicular to the fold lines that separate the two views.
Th i t f d b th i t ti th 45 it li i th j t d
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The point formed by the intersection on the 45 miter line is then projected across
the vertical fold line into the horizontal view.
P j t i t 1 d 2 f th f t i i t th h i t l (t ) i N ti
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Project points 1 and 2 from the front view into the horizontal (top) view. Notice
that an intersection is formed by this projection line and the horizontal line
projected from the point on the 45 miter line.
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Where the two projectors intersect, is the point (end) view of line 1,2. All of the
points are now accounted for in all three views. Label the points.
From a viewing position above the fold line, with the line of sight perpendicular to the
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1,2
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g p , g p p
projection plane (represented by the fold line), point 1 would be closer to your eye.
Thus, point 1 is in front of point 2 in the labeling of the horizontal or top view.
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Miter Line Technique (Example Number 2)
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Position a fold line at some convenient location between the views. Remember, in
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Position a fold line at some convenient location between the views. Remember, in
everycase where fold lines are constructed between adjacent orthographic views,
they must be perpendicular to the projectors.
At some location along the vertical fold line construct a horizontal fold line
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At some location along the vertical fold line, construct a horizontal fold line.
Construct a miter (45) line through the intersection of the two fold lines
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Construct a miter (45 ) line through the intersection of the two fold lines.
Project points 1 and 2 from the right side view, up to intersect with the miter line.
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Project points 1 and 2 from the right side view, up to intersect with the miter line.
At the points where the intersections are formed on the miter line project lines
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At the points where the intersections are formed on the miter line, project lines
into the horizontal (top) view.
F h f i j i 1 d 2 i h h i l i l
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From the front view, project points 1 and 2 into the horizontal view to complete
the projection of the line.
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Clean up the drawing by eliminating the construction lines.
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The resulting views represent the correct solution for the top, front, and right side
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view of line 1,2.
Miter Line Technique Example Number 3
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Miter Line TechniqueExample Number 3
This drawing represents the top and front views of a line. Construct the right side
viewusing the miter line technique. Label the end points on the line.
Verify the projection of the two views by extending parallel lines which connect
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Verify the projection of the two views by extendingparallel lines which connect
the points of the line.
Construct a fold line between and perpendicular to the views of the line
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Construct a fold line between and perpendicular to the views of the line.
Next, construct a second fold line perpendicular to the horizontal one, thus
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Next, construct a second fold line perpendicular to the horizontal one, thus
establishing the location for the right side view.
Establish the miter line through the point of intersection of the two fold lines.
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Project points 1 and 2 in the top view horizontally across the fold line until they
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intersect with the miter line.
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Project points 1 and 2 from the front view, across the vertical fold line, into the
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right side view.
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Clean up the drawing by removing the projection lines between the views.
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The drawing is now complete, showing the front, top, and right side views of the
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line.
Miter Line TechniqueExample Number 4
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In this problem, front and top views of a skewed planar triangle in 3-D space is given.
An orthographic projection of the right side view is required. Verify the projection.
Set up the right side view by constructing a projection plane.
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Project the points from both views into the right side view.
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j p g
Connect the points the same way they are connected in the parent views.
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Clean up the construction lines.
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The required right side view is now complete.
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Mit Li Fl ibilit A S lid Obj t
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Miter Line FlexibilityA Solid Object
Front and right side views are given. Use a reference plane off of the back of the
object to determine the location of the miter line, and project the top view of thissolid object.
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Project vertically from the front view.
Project the back surface vertically from the right side view.
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Establish a horizontal line at a reasonable location along these projectors.
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Where the two projectors (representing the back surface) intersect, construct a 45 line.
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Project the front surface from the right side view until it intersects with the miterline, then project the point of intersection to the horizontal view to complete the
boundary outline of the top view.
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boundary outline of the top view.
The boundary in the top view can be established with object lines, and the drawing
cleaned up.
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