ERT249 CAD FOR BIOSYSTEMS ENGINEERING2-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 • modeling and object hierarchy • algorithms for removing hidden edges and

surfaces, shading and coloring, 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

Multiview

orthographic

Axonometric

isometric

dimetric

trimetric

Oblique

Perspective

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 faceUsually form front, top, side views

isometric (not multiview orthographic view)

front

sidetop

in CAD and architecture, we often display three multiviews plus isometric

b. Axonometric projectionSame as perspective projection except that the projectors are parallel.

This means that there are no vanishing points.

• 1.Trimetric.• 2.Dimetric.• 3.Isometric.

Depending on the orientation of the object, Axonometric projection can be divided into three classes:

iso: means similar

di: means there are two sets of axes.

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 PerspectiveOn 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

• 3D objects made in AutoCAD called models

• 2D work referred to as drawing/drafting

Model

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

Good for verifying design as well as for use in presentation and documentation as

well.

Show design more clearly

Closer to representing real object than a 2D

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:

Symbols

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 (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

Unnatural position

Natural position

View Selection

Sectioning

PREPARED BY: SAMERA BINTI SAMSUDDIN SAHSCHOOL OF BIOPROCESS ENGINEERING

Outline

Cutting Plane

Section Lines

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 DrawingsDefinition: 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

An imaginary plane that

defines where the object is

cut

Shown in drawing

adjacent to the sectioned

drawing

Drawn with the

PHANTOM line type

Arrows at the end of the

cutting plane line indicate

the direction of view for

the sectioned drawing.

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…