Download 3-D Transformation and Projection

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PTT 105/3: Engineering Graphics
TAXONOMY OF PLANAR
GEOMETRIC PROJECTIONS
Planar
Geometric
Projections
Parallel
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Perspective
Multiview
orthographic
Axonometric
Oblique
Isometric
Dimetric
Trimetric
PTT 105/3: Engineering Graphics
1 point
2 point
3 point
Parallel Projection
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PTT 105/3: Engineering Graphics
Perspective Projection
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PTT 105/3: Engineering Graphics
Orthographic Projection
Projectors are orthogonal to projection surface
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PTT 105/3: Engineering Graphics
Orthographic Projection
Advantages and disadvantages
 Preserves both distance and angle
- shapes are preserved
- can be used for measurements:
 Building plans
Manufactured parts
• Cannot see what object really looks like because
many surfaces hidden from view.
- often we add the isometric
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PTT 105/3: Engineering Graphics
Multiview Orthographic Projection
 Projection plane parallel to principle face
 In CAD and architecture, we often display three multiviews
plus isometric.
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PTT 105/3: Engineering Graphics
Axonometric Projections
 Move the projection plane relative to object
 Classify by how many angles of a corner of a projected cube
are the equal to each other.
 Types of axonometric projections:
 Three angle equals: isometric
 Two angle equals: dimetric
 None angle equal: trimetric
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PTT 105/3: Engineering Graphics
1. ISOMETRIC PROJECTION
 The isometric projection has a standard orientation
that makes it the typical projection used in CAD.
 In an isometric projection, the width and depth
dimensions are sketched at 30° above horizontal.
 In an isometric projection all angles between
the axonometric axes are equal.
 This results in the three angles at the upper
front corner of the cube being equal to 120°.
 The three sides of the cube are also equal, leading
to the term iso (equal) -metric (measure).
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PTT 105/3: Engineering Graphics
 Isometric drawings work quite well for objects of
limited depth.
 However, an isometric drawing distorts the object
when the depth is significant.
 In this case, a pictorial perspective drawing is better.
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PTT 105/3: Engineering Graphics
2. DIMETRIC PROJECTION
 In a dimetric projection two of the objects axes make
equal angles with the plane of projection and the third
angle is larger or smaller than the other two.
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PTT 105/3: Engineering Graphics
3. TRIMETRIC PROJECTION
 In general, the trimetric projection offers
more flexibility in orienting the object in
space.
 In a trimetric projection no two axes
make equal angles with the plane of
projection.
 The width and depth dimensions are at
arbitrary angles to the horizontal, and the
three angles at the upper front
corner of the cube are unequal.
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PTT 105/3: Engineering Graphics
 This makes the three sides of the cube each have a
different length as measured in the plane of the
drawing; hence the name tri-metric.
 In most CAD software, the trimetric projection fixes
one side along a horizontal line and tips the cube
forward.
 Generally, small manufactured objects are adequately
represented by isometric or trimetric views.
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PTT 105/3: Engineering Graphics
Axonometric Projections
Advantages and Disadvantages
 Lines are scaled (foreshortening) – can find scaling factor
but can’t measure distance directly.
 Parallel lines preserved but angles are not
 Can see three principal faces of box-like object
 Some optical illusions possible
- parallel lines appear to diverge
 Does not look real because far objects are scaled the
same as near objects
 Used in CAD applications
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PTT 105/3: Engineering Graphics
Oblique Projection
 An OBLIQUE projection is one in which the projectors are other
than perpendicular to the plane of projection.
 Figure below shows the same object in both orthographic and
oblique projections.
 The oblique projection:
- shows the front surface and the top surface, which includes
three dimensions: length, width, and height. Therefore, an
oblique projection is one way to show all three
dimensions of an object in a single view.
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PTT 105/3: Engineering Graphics
PERSPECTIVE PROJECTION
 A simply perspective (pictorial perspective)
projection is drawn so that parallel lines
converge towards a single point, unlike
isometric or trimetric projections where
parallel lines remain parallel.
 This has the effect that distant objects appear
smaller than nearer objects.
 A perspective projection is quite useful in
providing a realistic image of an object
when the object spans a long distance such as
the view of a bridge, railways or aircraft from
one end.
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PTT 105/3: Engineering Graphics
PERSPECTIVE PROJECTION
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PTT 105/3: Engineering Graphics
Differences between 3D and 2D
Criteria
1. Viewing Direction
3D
- Look at your
object from an
angle
2D
- Look straight down on the
drawing plane
2. Object Created
- have depth
- No depth
3. Command related
- 80 AutoCAD
commands related
primarily to 3D
-Yes
- however, are also useful in
2D
4. Constructing object
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PTT 105/3: Engineering Graphics
- No.
- Drawing picture from
different views
3D Term Frequently Used
• 3D objects made in AutoCAD called
models
• 2D work referred to as drawing/drafting
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PTT 105/3: Engineering Graphics
4 types of model used in 3D
Wireframe
Model
Surface Model
Model
Solid Model
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PTT 105/3: Engineering Graphics
Rendering
• 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
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PTT 105/3: Engineering Graphics
• Surface model often use wireframe models as
a frame for their surfaces
• Surface model: part wireframe + part
surface
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PTT 105/3: Engineering Graphics
• Wireframe, surface model & computercalculated mass;
• eg: volume, centre of gravity, mass moment
of inertia
• Solid models look like wireframe unless a
hidden line removal command is in effect
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PTT 105/3: Engineering Graphics
• Shaded, realistic-looking picture of a surface solid
model is called a rendering
• Two type:
• Grayscale rendering
• Fully capable of colour rendering
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PTT 105/3: Engineering Graphics
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.
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PTT 105/3: Engineering Graphics
3D Capabilities of AutoCAD
1. AutoCAD has complete 3D coordinate system for specifying
points and drawing objects anywhere in space
2. To assist in point input and for working in local area, AutoCAD has
a movable user coordinate system
3. It can set viewpoints from any location in space that can
look in any directions
4. The computer screen can be divided into multiple viewports
for simultaneously viewing 3D space from different viewpoints and
different direction
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PTT 105/3: Engineering Graphics
5. AutoCAD has a good assortment of surface entities
for making surface models that have a variety of shapes
6. Solid models of most objects typically manufactured
in machine shop can be made within AutoCAD
7. 3D models can be transformed into standard multiview, dimensioned production drawing
8. AutoCAD has a built-in renderer with lights and surface
materials, capable of making realistic-looking shaded
picture from 3D models
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PTT 105/3: Engineering Graphics
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EPT 112/3: Introduction to Engineering