ERT249 CAD FOR BIOSYSTEMS
ENGINEERING
2-D Transformation And
Projection
Geometric Transformation
Graphics is at the core of any CAD/CAM system to produce the
functionality and interactivity of the system. Some are:
• geometric transformation
• modelling and object hierarchy
• algorithms for removing hidden edges and surfaces,
shading and colouring, and clipping and windowing
1. 2D Transformation: Scaling
2. 2D Transformation: Rotation
(a) Rotation about Coordinate Origin
(b) Concatenation
(c) Rotation about an Arbitrary Point
(a)
(b)
(c)
3. 2D Transformation: Translation
Examples of Transformation in
AutoCAD
3-D Transformation And
Projection
Planar Geometric Projections
Standard projections project onto a plane
Projectors are lines that either converge at a center
of projection and are parallel.
Such projections preserve lines but not necessarily
angles
Non-planar projections are needed for applications
such as map construction
Taxonomy of Planar Geometric
Projections
Planar Geometric
Projections
Parallel
Perspective
Multiview
orthographic
Axonometric
Oblique
isometric
dimetric
trimetric
1 point
2 point
3 point
1. Parallel Projection
a. Orthographic Projection
Projectors are orthogonal to projection plane
Multiview Orthographic
Projection
 Projection plane parallel to principal face
 Usually form front, top, side views
isometric (not multiview
orthographic view)
front
in CAD and
architecture,
we often display
three
multiviews plus
isometric
top
side
b. Axonometric projection
Same as perspective projection except
that the projectors are parallel.
This means that there are no vanishing
points.
Depending on the orientation of the
object, Axonometric projection can be
divided into three classes:
• 1.Trimetric.
• 2.Dimetric.
• 3.Isometric.
di: means there are
two sets of axes.
iso: means similar
c. Oblique Projection
 The object is aligned such that one face (the
front face) is parallel to the picture plane.
 The projection lines are still parallel but they are
not perpendicular to the picture plane.
2. Perspective Projection
Projectors converge at center of projection
Vanishing Points
Parallel lines (not parallel to the projection plan) on the object
converge at a single point in the projection (the vanishing point)
Drawing simple perspectives by hand uses these vanishing
point(s)
vanishing point
a. One-Point Perspective
 One principal face parallel
to projection plane
 One vanishing point for
cube
b. Two-Point Perspective
 On principal direction
parallel to projection
plane
 Two vanishing points for
cube
c. Three-Point Perspective
 Three-point
perspective is usually
used for buildings seen
from above (or below).
 In addition to the two
vanishing points from
before, one for each
wall.
 This third vanishing
point will be below the
ground
Some Frequently used 3D Terms
Model
• 3D objects made in AutoCAD
called models
• 2D work referred to as
drawing/drafting
Model in 3D
1. Wireframe Model
• Object by its edges only
• Wireframe cannot hide object that are behind
them
• Hole has no meaning in a wireframe model
because there is nothing in which to make a
hole
2. Surface Model
• Surface model; solid + empty shell
• Surface model often use wireframe
models as a frame for their surfaces
• Surface model; part wireframe + part
surface
3. Solid Model
• Wireframe, surface model &
computer-calculated mass;
• eg: volume, centre of gravity, mass
moment of inertia
• Solid models look like wireframe
unless a hidden line removal command
is in effect
4. Rendering
• Shaded, realistic-looking picture of a surface
solid model is called a rendering
• Two type:
• Grayscale rendering
• Fully capable of colour rendering
Reasons For Using 3D
Closer to representing real object than a 2D
Show design more clearly
Good for verifying design as well as for use in
presentation and documentation as well.
Multi-view Drawing
Projection Theory
 Engineering and technical
graphics are depend on
projection methods.
 Two methods primarily
used:
a) Parallel: object positioned
at infinity & viewed from
multiple points on an
imaginary line parallel to
the object.
b) Perspective: object
positioned at finite distance
& viewed from a single
point.
Multi-view Projection
 Multi-view projection is
an orthographic
projection for which
the object is behind the
plane of projection.
 The object is
orientated such that
only two of its
dimension are shown.
 Orthographic projection:
 A parallel projection technique.
 The projection plane is placed between observer and object.
 The projection plane is also perpendicular to the parallel line
of sight.
 Multi-view drawings
 Employ multi-view projection technique
 Generally 3 views of an object are drawn
 Each view is a 2D flat image
Example: Multi-view
Projection
Multi-view Lines
Multi-view: Planes
Multi-view: Planes
View Placement
View Placement
Angle Projection
 There are two standard arrangement of all
six views of an object
 First-angle projection
 Third-angle projection
 Each uses different symbol
 The names are derived from the method
used to view the object being drawn
 In 1st angle projection, the
object is placed in the first
quadrant.
 In 3rd angle projection, the
object is placed in third
quadrant.
 Rules:
1st angle
projection
3rd angle
projection
View from above
is placed
underneath
View from above
is placed above
View from below
is placed above
View from below
is placed below
View from left is
placed on right
View from left is
placed on left
View from right
is placed on left
View from right
is placed on right
 Symbols
(a) 1st angle projection (b) 3rd angle projection
Example: 1st and 3rd angle view
projection
1, 2 and 3 view drawing
View Selection
View Selection
Natural position
Unnatural position
View Selection
Sectioning
PREPARED BY: SAMERA BINTI SAMSUDDIN SAH
SCHOOL OF BIOPROCESS ENGINEERING
Outline
Cutting Plane
Section Lines
Several Types
of Section
Drawings
Purpose
To demonstrate the proper use of section views
which show internal features of objects that are
not easily understood in standard multiview
drawings
To demonstrate the use of CAD tools in
generating section views
Sectioned Drawings
Definition: A multiview technical drawing that reveals
details about internal features by displaying the part as
if cut by an imaginary cutting plane.
Objective: To make the drawing more understandable,
especially the internal details of the part
Since the sectioned drawing shows internal features
there is generally no need to show hidden lines
Especially helpful for assembly drawings
The Cutting Plane
The Cutting Plane
 Cutting planes may be
labeled at their endpoints
if multiple cutting plane
lines are used
 When using multiple
cutting planes each
sectioned drawing is drawn
as if the other cutting plane
lines do not exist
 The cutting plane line
takes precedence over
center lines
 Occasionally cutting plane
lines are not shown when
their location is obvious
Section Lines
 Section lines are drawn where
the object passes through the
cutting plane
 If a saw was used to cut the part
then section lines represent the
cutting marks left by the saw
blade
 Different materials may be
represented by the use of
different section line types
 The general section line type
which may be used for any
material is the line type for iron
Section Lines
 Section lines should not be parallel




or perpendicular to object lines
Section lines are generally drawn at
45 degrees unless this conflicts with
other rules
Section lines should be oriented at
different angles for separate parts
Occasionally section lines are only
drawn on the perimeter of large
areas
Section lines are not used for thin
parts rather they are filled in solid
(Do not use closely spaced section
lines)
Section Drawing Types
 Full Section
 Half Section
 Assembly Section
 Offset Section
 Broken-Out Section
 Revolved Section
 Removed Section
 Special Section Conventions
Full Section
 The cutting plane passes completely through
the part as a single flat plane
Half Section
 The cutting plane only passes half way through




the part
The other half is drawn as usual
Hidden lines are not shown on either half of the
part
A center line is used to separate the two halves
Mostly used on cylindrical parts
Assembly Section
 Shows how parts fit together
 Different parts have different
section line orientation
 Different materials use different
section line types
 Standard parts (shafts, pins,
dowels, rivets, screws, washers,
gears, etc.) are not sectioned
Assembly Section
 Cut each part of the
assembly and section each
part with the appropriate
section line type
 Put the parts together in
their assembled position
Assembly Section
 The shaft is not sectioned
because it is a standard part
and section lines would
provide no additional
information
 The other two part are made
from the same material
 The orientation of section
lines clearly shows the
location of the different
parts
Assembly Section
 The top and bottom mating part are made from
different materials in the part shown below
 A center line is added to the shaft to show that it is
a circular feature
Offset Section
 The internal features of
many part can not be
shown using a single
straight cut to create
the sectioned drawing
 An offset section is
used for such parts
Offset Section
 The multiview drawing is often difficult to
interpret when there are several hidden
features on the object
 A sectioned view makes the object much
easier to understand
Offset Section
 An offset section allows the cutting plane to
pass through all of the internal features
 There may be several bends in the cutting plane
Offset Section
 The actual part would show a new visible line at
the bend in the cutting plane
 Since the cutting plane bend is arbitrary, do not
show the line representing this bend in the
sectioned drawing
Offset Section
 The sectioned view does not
show the bend in the cutting
plane
 Hidden lines are not shown
 Be sure to include object lines
that are behind the cutting plane
Broken-Out Section
 Only a portion of the
view is sectioned
 A jagged break line is
used to divide the
sectioned and
unsectioned portion
of the drawing
Revolved Section
 A cross section of
the part is revolved
90 degrees and
superimposed on
the drawing
 A jagged break line
may be used to
divide the revolved
section from the
rest of the drawing
Removed Section
 Similar to the revolved
section except that the
sectioned drawing is not
superimposed on the
drawing but placed next to
it
 The view and the cutting
plane are labeled (Section
A-A)
 The removed section may
be drawn at a different
scale
Special Section Conventions
 There are special rules
(conventions) that are
followed to make some
parts more
understandable
 Some features are rotated
to their true radial position
in sectioned views
Special Section Conventions
 The object is difficult to understand using
standard multiview drawings where hidden
lines are used to represent internal features
Special Section Conventions
 If the part is sectioned as it
would actually appear if cut
the details of the ribs and
holes would not be clear
 Since the objective is to
make the drawing easy to
interpret the drawing is
modified following
standard conventions
Special Section Conventions
 The cutting plane shows that the




features are revolved to their true
radial position
Hidden features are not shown
The sectioned drawing produced is
a distorted but clearer picture of
the object
The section drawing appear as a full
section
The arrows show the direction of
the view
Special Section Conventions
 Ribs are not sectioned when the cutting plane passes through
them lengthwise
 Ribs are sectioned if the cutting plane passes through them at
other orientations
Special Section
Conventions
 The front view is replaced by a full




section view
The cutting plane shown in the
top view shows the direction of
the line of sight
The holes and ribs have been
revolved to their true radial
position
The ribs are not sectioned in this
orientation
The section lines are all drawn at
the same angle since the object is
one solid part
Sectioning With Solid Models
 Slice
 cuts the solid object at the specified
cutting plane using the current color
 breaks the objects into two parts
 one part may be deleted or moved
 Section
 creates a 2-D drawing of the section
 only draws the portion of the object
that is cut (i.e. the portion of the
object that has section lines)
Sectioning With Solid Models
 SLICE command
 SECTION command
Sectioning With AutoCAD
 Use BHATCH
 Use the correct scale
 Default line orientation is 45
degrees
 The general line type is
ANSI31
 Use different line types for
different materials
 Use PICK POINTS to select an
internal point in the
sectioned portion of the
drawing
THE END…