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MET71 COMPUTER AIDED DESIGN
UNIT – I
INTRODUCTION TO CAD
Computer Aided Design (CAD) is assistance of computer in engineering processes such as
creation, optimization, analysis and modifications.
CAD involves creating computer models defined by geometrical parameters which can be readily
altered by changing relevant parameters. CAD systems enable designers to view objects under a
wide variety of representations and to test these objects by simulating realworld conditions.
!t is an integration of "echanical and Computer technology to aid in the design process li#e
"odelling, Assembly, Drafting, Die Design, $ool Design, %heet metal, analysis of products.
Design Process:
$he process of designing something is characterized as an interactive procedure, which consists of si& identifiable steps or phases'
. ecognition of need
*. Definition of problem
+. %ynthesis
. Analysis and optimization
-. valuation
/. 0resentation
. ecognition of need
• ecognition of need involves the realization by someone that a problem e&ists for
which some corrective action should be ta#en
• $his might be the identification of some defect in a current machine design by an
engineer or the perception of a new product mar#eting opportunity by a salesperson
*. Definition of problem
• Definition of the problem involves a thorough specification of the item to be designed
•
+. %ynthesis
. Analysis and optimization
-. valuation
/. 0resentation
• $here is no aspect of our lives which is not influenced by the wor# of engineers.
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• $he buildings and e1uipment we use, the vehicles we travel in and the roads and rails upon
which they travel are all direct products of engineering activities.
• $he food we eat is grown and processed with the assistance of engineering products, and
engineering design and construct the e1uipment which prints our boo#s, manufacture our
medicines and produce our television images.
• !f we compare today2s engineering products with those of 3 years ago we will find a
starling increase in performance, 1uality and sophistication. "any of the products are great
comple&ity, and this improvement has been achieved by organizing large teams of people
to collaborate in the products2 development and manufacture.
Product Deveo!"ent #nd M#nu$#cture:
"achines involved 4 Computers
$as#s 4 information processing
5se 4 assist in the definition and processing of information connected with design of products
Process invoved in %ringing t&e !roduct to M#r'et
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!n recent years there have been several attempts to provide a formal description of these
stages or elements of the design process. %ome variation in these descriptions, both in terminology
and in detail, but in general the agree that design progress in a step 4 by 4 step manner from some
statement of need through identification of the problem , a search for solution and development of
the chosen solution to manufacture, test and use. $hese descriptions of design are often called
"odes o$ t&e design !rocess(
$o illustrate these we will consider two models which give different but complementary
insights into the process.
!. %teps of the design process according to 0ahl and 6eitz(78)
!!. $he design process according to 9hsuga
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I( Ste!s o$ t&e design !rocess #ccording to P#& #nd )eit* +1,-./
!n this model the design process is described by a flow diagram comprising four main phases
which may be summarized as'
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Although it presents a straightforward se1uence of stages through the process, in practice
the main phase are not always so clearly defined, and there is invariable feedbac# to previous
stages and often iteration between stages.
II( T&e design !rocess #ccording to O&sug#0
• 9hsuga again describes design as a series of stages, in this case progressing from
re1uirements through conceptual design and preliminary design to detail design.
• !n this case however the various stages of design process are generalized into common
form in which models of design are developed through a process of analysis and evaluation
leading to modification and refinement of the model.
• !n the early stage the tentative solution is proposed by designer. !n this stage the design
refined and evolution and modification repeated at a greater level of detail.
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A!!ic#tion o$ design "odes:
• Application of design model is to the receiver of the communication and considers the sort
of actions that are ta#en with the design information that is received.
• $his may be divided into two main classification
i. valuating actions
ii. :enerative actions
• !n each case the actions involve the e&traction of information from the design
representation and the combination of this with further information to form a new model.
$his is shown diagrammatically in figure.
• A design analyst might use this for the following assessments'
A visual assessment
An assessment of the mass of the components, by using the CAD model
An evaluation of loads in the components, by considering them as parts of a
mechanism
An evaluation of stresses, for e&le using the finite element model.
• At the later stage, detailed drawings will e&ist of the components of the design, and from
these, manufacturing engineers will e&tract information for tooling and for the control of production machines.
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T!es o$ Design Modes:
• $he design process model gives as hint of variety of representation needed in design. $here
are phrases such as ;develop preliminary layouts2 and complete detail drawings2.
•
!n practice, the designer uses a host of different models depending on what !ro!ert of the
design is to be modeled, and who or what is the target, or receiver2 for any communication.
• $he engineering designer has, at various times, to modeled the $unction of a design, its
structure, the $or" or shape of the components parts and the "#teri#s2 sur$#ce
conditions #nd di"ensions that are re1uired.
•
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Concurrent engineering or %imultaneous ngineering is a methodology of restructuring the
product development activity in a manufacturing organization using a cross functional team
approach and is a techni1ue adopted to improve the efficiency of product design and reduce the
product development cycle time.
$his is also sometimes referred to as 0arallel ngineering. Concurrent ngineering brings
together a wide spectrum of people from several functional areas in the design and manufacture of
a product. epresentatives from ? D, engineering, manufacturing, materials management,
1uality assurance, mar#eting etc. develop the product as a team.
veryone interacts with each other from the start, and they perform their tas#s in parallel.
$he team reviews the design from the point of view of mar#eting, process, tool design and
procurement, operation, facility and capacity planning, design for manufacturability, assembly,
testing and maintenance, standardization, procurement of components and subassemblies, 1uality
assurance etc as the design is evolved.
ven the vendor development department is associated with the prototype development.
Any possible bottlenec# in the development process is thoroughly studied and rectified. All the
departments get a chance to review the design and identify delays and difficulties.
$he departments can start their own processes simultaneously. =or e&le, the tool
design, procurement of material and machinery and recruitment and training of manpower which
contributes to considerable delay can be ta#en up simultaneously as the design development is in
progress. !ssues are debated thoroughly and conflicts are resolved amicably.
Concurrent ngineering (C) gives mar#eting and other groups the opportunity to review
the design during the modeling, prototyping and soft tooling phases of development. CAD
systems especially +D modelers can play an important role in early product development phases.
!n fact, they can become the core of the C.
$hey offer a visual chec# when design changes cost the least. !ntensive teamwor# between
product development, production planning and manufacturing is essential for satisfactory
implementation of concurrent engineering.
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$he teamwor# also brings additional advantages @ the cooperation between various
specialists and systematic application of special methods such as =D (uality =unction
Deployment), D="A (Design for "anufacture and Assembly) and ="A (=ailure "ode and
ffect Analysis) ensures 1uic# optimization of design and early detection of possible faults in
product and production planning. $his additionally leads to reduction in lead time which reduces
cost of production and guarantees better 1uality.
Co"!#rison o$ Concurrent Engineering #nd Se4uenti# Engineering
A comparison of concurrent and se1uential engineering based on cost is attempted in this
section. $he distribution of the product development cost during the product development cycle is
shown in =ig. $his figure shows that though only about -B of the budget is spent at the time of
design completion, whereas the remaining 8-B is already committed.
$he decisions ta#en during the design stage have an important bearing on the cost of the
development of the product. $herefore the development cost and product cost can be reduced by
proper and careful design. C facilitates this. $he significantly large number of nonconformities
detected in the later stages of product development cycle in se1uential engineering results in large
time and cost overrun.
IMP5EMENTATION O6 CONCURRENT ENGINEERING
$he cycle of engineering design and manufacturing planning involves interrelated
activities in different engineering disciplines simultaneously, than se1uentially as shown in =ig.
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(A). !n addition, the activities necessary to complete a particular tas# within a specific engineering
discipline have to emerge wherever possible from their se1uential flow into a concurrent wor#flow
with a high degree of parallelism as illustrated in =ig. (6).
Concurrency implies that members of the multidisciplinary project team wor# in parallel.
$his also means that there is no strict demarcation of jobs among various departments. $he multi
disciplinary approach has the advantage of several inputs which can be focused effectively early in
the design process. 0resently engineering departments are practicing this approach but still with a
high degree of manual involvement and redundancy.
CAD sste" #rc&itecture:
#rd3#re: the computer and associated peripheral e1uipment
So$t3#re: the computer programs running on the hardware
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D#t#: the data structure created and manipulated by the software'
u"#n 8no3edge #nd #ctiv#tes
CAD systems are no more than computer programs, perhaps using specialized computing
hardware. $he software normally comprises a number of different elements or functions that
process the data stored in the database in different ways. $hese are represented diagrammatically
in figure.
• Mode de$inition: for e&le, to add geometric elements to a model of the $or" of a
component@
•
Mode "#ni!u#tion: to move, copy, delete, edit or otherwise modify elements in design
models@
• Picture gener#tion: to generate images of the design model on a computer screen or on
some hardcopy device@
• User inter#ction: to handle commands input by user and to present output to the user
about the operation of the system@
• D#t#%#se "#n#ge"ent: for the management of the files that ma#e up the database@
• A!!ic#tion: these elements of the software do not modify the design model, but use it to
generate information for evaluation, analysis or manufacture@
• Utiities: a ;catchall2 term for parts of the software that do not directly affect the design
model, but modify the operation of the system in some way (e.g to set the color to be used
for display, or the units to be used for construction of a part model).
$hese features may be provided by multiple programs operating on a common database or by
a single program encompassing all of these elements.
CAD #rd3#re
9or'st#tion 4 C05
M#ss stor#ge – "agnetic tape storage, "agnetic Disc %torage, "agnetic drum storage
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In!ut devices (#eyboard, light pen, thumb wheel, joy stic#, mouse, digitizer, $ouch %creen,
$rac# 6all) Out!ut devices (printers, plotters)
Dis!# Devices (storage tube 4 raster scan, vector refresh, plasma panel and CD)
CENTRA5 PROCESSING UNIT:
$he C05 is the
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capable of performing multifunction and division and even other comple& mathematical functions.
A52s with simple& circuits are capable of being programmed to perform these more complicated
operations, but more computing time is re1uired. $he more comple& arithmetic logic units are
faster, but these units are more costly.
Me"or
$he memory section consists of binary storage units, which are organised into bytes. $he
memory section stores all the instructions and data of a program. $herefore the C05 must transfer
these instructions and data. $wo types of memory
"ain memory (primary storage)
Au&iliary memory (%econdary storage)
M#ss stor#ge
$he most common device used for computer storage technologies are
• "agnetic tape storage
• "agnetic Disc %torage
• "agnetic drum storage
M#gnetic t#!e stor#ge
"agnetic storage is a good e&le of se1uential access storage technology. Data are
stored on magnetic tape, similar to that used in audio systems. $he major advantages of magnetic
tapes are that is relatively cheap when compared with other types of storage medium and that it
can easily hold large amount of data for its size. "agnetic tape unli#e punched paper tapes or
cards can be used again by simply overwriting previously stored data.
%ince data are stored se1uentially access time is relatively slow.
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M#gnetic Disc Stor#ge
"agnetic dis# storage is also #nown as a random access storage device. $he storage
medium is a magnetically coated dis#. $here are several types and sizes of dis#s each best suited
to a particular set of applications.
6o!! Disc
=loppy dis#s come in two standard sizes' the larger one is 8 inches in diameter and smaller
is - E inches and is referred to as mini floppy.
M#gnetic Dru" Stor#ge
$he magnetic drum is direct access storage device with high capacity and high access
rates. $he magnetic drum consists of a magnetically coated cylinder during operation. $he drum is
rotated at a constant speed and data are recorded in the form of magnetized spots. $he drum can be
read repeatedly without causing data loss.
In!ut devices
Feyboard
"ouse
ight pen
$humb wheel
Goy stic#
Digitizer
$ouch %creen
$rac# 6all
8e%o#rd
$he #eyboard interacts with the computer on a hardware and software level. $he #eyboard
contains a #eyboard controller (li#e 83* or 838) to chec# if any #ey is pressed or released. !f
any #ey remains closed for more than half a second the controller sends a repeat action at specific
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intervals. !t has limited diagnostic and error chec#ing capabilities. A buffer is normally available
to store a certain number of #ey actions if the computer is busy.
Mouse
"ouse is today one of the widely used input devices in graphics applications. "ouse can
be moved around by the operator on any flat surface to provide graphic input. !ts ability to rapidly
position the cursor on the screen is its most important advantage. "ouse is available as a
mechanical or optical graphic input device. !n the case of a mechanical mouse, the rolling ball at
the bottoms of the mouse causes two encoders to rotate. $he movement of the mouse is thus
converted into pulses which move the cursor in the H and I direction in proportion to the
movement of the mouse. "ouse can be operated in a limited space. %ince the mouse can be used
without loo#ing at it, the user can concentrate on the screen and hence design productivity can be
considerably increased.
5ig&t !en
• A light pen is a computer input device in the form of a lightsensitive wand used in
conjunction with a computerJs C$ display.
http://en.wikipedia.org/wiki/Computerhttp://en.wikipedia.org/wiki/Input_devicehttp://en.wikipedia.org/wiki/Cathode_ray_tubehttp://en.wikipedia.org/wiki/Computerhttp://en.wikipedia.org/wiki/Input_devicehttp://en.wikipedia.org/wiki/Cathode_ray_tube
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• !t allows the user to point to displayed objects or draw on the screen in a similar way to a
touch screen but with greater positional accuracy. !t was long thought that a light pen can
wor# with any C$based display, but not with CDs and other display technologies.
T&u"% 3&ee
$humb wheels are potentiometric devices. $wo of them are provided for H and I
movements of cursor. $hese also have the advantage that one can loo# at the screen and move the
cursor.
;o stic'
Goystic# is a potentiometric device that contains sets of variable resistors which feed
signals that indicates the device position to the computer. $hese devices rely on the operator2s
sense of touch and handeye coordination to control the position of the cursor on the screen.
Goystic# devices are normally set so that sidetoside movement produces change in H Co
ordinates and front to bac# movements produce change in I Coordinates.
http://en.wikipedia.org/wiki/Touchscreenhttp://en.wikipedia.org/wiki/Liquid_crystal_displayhttp://en.wikipedia.org/wiki/Display_technologyhttp://en.wikipedia.org/wiki/Touchscreenhttp://en.wikipedia.org/wiki/Liquid_crystal_displayhttp://en.wikipedia.org/wiki/Display_technology
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Digiti*er
Digitizer boards or tablets are electromechanical vector graphic input devices that
resemble a drafting board. $hese are used together with a movable stylus or reticule called a
cursor or a puc#. $hey are used to enter drawings into computer graphics systems by taping the
drawing to the surface of the digitizing board and placing the cursor over points whose co
ordinates are to be entered. =igure shows a digitizer.
Touc& Screen
$ouch screens are direct devices. $hey are used by simply touching C$ display with
one2s finger or a pointing device. $wo types of touch screens (mechanical and optical) are used in
CAD applications. "echanical type is a transparent screen overlay which detects the location of
the touch.
Tr#c' )#
$rac# ball has a ball and soc#et construction but the ball must be rolled with fingers or the
palm of the hand. $he cursor moves in the direction of the roll at a rate corresponding to rotational
speed. $he user must rely heavily on the tactile sense when using a trac#ball since there is no
correspondence between the position of the cursor and the ball. $he ball momentum provides a
tactile feedbac#.
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OUTPUT DE
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$he coordinate motion generated by the rotation of the drum and linear movement draws
the pictures on the paper. !n the third type, i.e. the pinch roller plotter, the paper is tightly held
between two sets of rollers. 9ne roller in each pair has a rough surface and the linear motion to the
paper in one direction is imparted by the rotation of the roller. $he movement in the other
direction is through a linear motion imparted to the pen holder. 0lotters can also classify as pen
plotters and electrostatic plotters. 0en plotters use , , 8 or more different color pens. $he
drawings thus can be made in several colors. 0encil plotters are also available. lectrostatic
plotters are faster but there is no color variety. $hey are also cheaper.
PRINTERS
%everal types of printers are available'
(i) I"!#ct !rinters' $hey use small hammers or print heads containing small pins to stri#e a
ribbon to form dot matri& images. Colors are introduced through the use of multiple ribbons or
single ribbons with different color bands. Color intensity is fi&ed and creating shades is almost
impossible. 6ecause of the low resolution, copy 1uality is poor. !mpact printers are suitable for
high speed, low cost, high volume hard copies.
+ii/ In'=et !rinter: !n#jet printers produce images by propelling fine droplets of in# on to the
medium to be printed. Droplets can be generated in continuous streams or pulses. %ome of the
droplets get charged and are returned to the reservoir, while uncharged droplets attach to the
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printing surface to form graphics. $he laser jet printers are capable of giving good 1uality color
prints with shading at reasonable cost.
+iii/ 5#ser !rinter: aser printer is one of the most widely used output devices. $his type
combines high speed with high resolution and the 1uality of output is very fine.
DISP5A> DE
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+. $he plasma display uses small neon bulbs arranged in a panel which provides a medium
resolution display.
$hus far, none of these display technologies has been able to displace the C$ as the dominant
graphics display device.
CATODE RA>S TU)E:
$he operation of C$ is based on the concept of energizing an electron beam that stri#es
the phosphor coating at very high speed. $he energy transfer from the electron to the phosphor due
to the impact causes it to illuminate and glow.
$he electrons are generated via the electron gun that contains the cathode and focused into
a beam via the focusing unit shown in figure. 6y controlling the beam direction and intensity in a
way related to the graphics information generated in the computer, meaningful and desired
graphics can be displayed on the screen.
$he graphics display can be divided into two types based on the scan technology used to
control the electron beam.
andom %can
aster %can
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In R#ndo" sc#n graphics can be generated by drawing vectors or line segments on the screen in
a random order which is controlled by the user input and the software. $he word L r#ndo"?
indicates that the screen is not scanned in a particular order.
R#ster Sc#n system, the screen is scanned from top to bottom, left to right all the time to generate
graphics. $his is similar to home television scan system, thus suggesting the name digit# sc#n.
$he three e&isting C$ display that are based on these techni1ues are
i. efresh display (calligraphic)
ii. Direct view storage tube
iii. aster display
Re$res& Dis!#:
$he refresh buffer stores the display file or program, which contains points, lines,
characters and other attributes of picture to drawn. $hese commands are interpreted and processed
by the display processor.
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$he electron beam accordingly e&cites the phosphor, which glows for a short period. $o
maintain a steady flic#er 4 free image, the screen must be refreshed or redrawn at least +3 to /3
times per second, that is, at a rate of +3 to /3
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without flic#er. At the end of 7/3s the DK%$ was introduced by $e#troni& as an alternative and
ine&pensive solution.
$he DK%$ eliminates refresh processors completely and conse1uently the refresh buffer
used with refreshes display.
!t also uses a special type of phosphor that has a long 4 lasting glowing effect. $he
phosphor is embedded in a storage tube. !n addition, the speed of the electron beam in the DK%$
is slower than in the refresh display due to elimination of refresh cycle.
!n the DK%$ the picture is stored as a charge in the phosphor mesh located behind the
screen2s surface. $herefore, comple& pictures could be drawn without flic#er at high resolution.
9nce displayed, the picture remains on the screen until it is e&plicitly erased. $his
is why the name @stor#ge tu%e? was suggested.
!n addition to the lac# of selective erasure, the DK%$ cannot provide colors, animation and
use of light pen as an input device.
R#ster Dis!#:
$he inability of the DK%$ to meet the increasing demands by various CADCA"
applications for colors, shaded images and animation motivated hardware designer to continue
searching for a solution.
During the late 7M3s raster display based on the standard television technology began to
emerge as a viable alternative. $he drop in memory price due to advances in solid states made
large enough refresh buffers available support high resolution display.
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A typical resolution of raster display is *83 & *3 with a possibility to reach 37/ &
37/ as the DK%$. aster displays are very popular and nearly al recent display research and
development focus on them.
!n raster display, the display screen area is divided horizontally and vertically into matri& of small
elements called picture element or pi&el. A pi&el is a small addressable area on the screen. An N &
" resolution defines on a screen with N rows and " Columns. ach row defines a scan line. A
rasterization process is needed in order to display either a shaded area or graphics entities.
!n this process the area or entities are converted into their corresponding pi&els whose
intensity and color are controlled by the i"#ge !rocessing sste".
9or'ing:
!mages are displayed by converting geometric information into pi&el values which then
converted into electron beam deflection through display processor and deflection system. !f the
display is monochrome, the pi&el value is used to control the intensity level or the gray level on
the screen. =or color displays, the value is used to control the color mapping into a color map.
$he creation of transfer format data from geometric information is #nown as scan
conversion or rasterization. A rasterizer that forms the magecreation system is mainly a set of
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scan conversion algorithms. Due to the universal need for these algorithms, the scan conversion or
rasterization process is implemented.
UNIT II
$AN%=9"A$!9N !N :A0
TRANS6ORMATION IN GRAPICS
:eometric transformations provide a means by which an image can be enlarged in size, or
reduced, rotated, or moved. $hese changes are brought about by changing the coordinates of the
picture to a new set of values depending upon the re1uirements.
COORDINATE S>STEMS USED IN GRAPICS AND 9INDO9ING
$ransformations can be carried out either in *dimensions or in +dimensions. $he theory
of twodimensional transformations is discussed first in this chapter. $his is then e&tended to three
dimensions. >hen a design pac#age is initiated, the display will have a set of coordinate values.
$hese are called default coordinates. A user coordinate system is one in which the designer can
specify his own coordinates for a specific design application. $hese screen independent
coordinates can have large or small numeric range, or even negative values, so that the model can
be represented in a natural way. !t may, however, happen that the picture is too crowded with
several features to be viewed clearly on the display screen. $herefore, the designer may want toview only a portion of the image, enclosed in a rectangular region called a window. Different parts
of the drawing can thus be selected for viewing by placing the windows. 0ortions inside the
window can be enlarged, reduced or edited depending upon the re1uirements. =igure shows the
use of windowing to enlarge the picture.
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!t may be sometimes desirable to display different portions or views of the drawing in
different regions of the screen. A portion of the screen where the contents of the window are
displayed is called a view port. et the screen size be H O 3 to *33 and I O 3 to +3. A view port
can be defined by the coordinates say H O /-, H* O +3, I O -3 and I* O 33. !f we use the
same window as in =ig., the definition of this view port will display the image in the right handtop 1uarter of the screen (=ig.) choosing different view ports multiple views can be placed on the
screen. =ig. shows four views of a component displayed using view port commands.
C5IPPING
Clipping is the process of determining the visible portions of a drawing lying within a
window. !n clipping each graphic element of the display is e&amined to determine whether or not
it is completely inside the window, completely outside the window or crosses a window boundary.
0ortions outside the boundary are not drawn. !f the element of a drawing crosses the boundary the
point of intersection is determined and only portions which lie inside are drawn. eaders are
advised to refer to boo#s on computer graphics for typical clipping algorithms li#e Cohen
%utherland clipping algorithm. =ig. shows an e&le of clipping.
IDDEN SUR6ACE REMO
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Correspondingly, surfaces */-, */M+ and -/M8 are not visible since the object is opa1ue. $he
actual representation of the cube must be as shown in =ig. (b).
$here are a number of algorithms available for removal of hidden lines and hidden surfaces. $able
gives a list of algorithms for hidden line removal and hidden surface removal.
T#%e Agorit&"s $or idden 5ine #nd idden Sur$#ce
$here are two popular approaches to hidden surface removal. $hese are scan line based systems
and Pbuffer based systems. 9ther important approaches are area subdivision and depth list
schemes.
BD TRANS6ORMATIONS
!n computer graphics, drawings are created by a series of primitives which are represented
by the coordinates of their end points. Certain changes in these drawings can be made by
performing some mathematical operations on these coordinates. $he basic transformations are
scaling, translation and rotation.
ROTATION
Another useful transformation is the rotation of a drawing about a pivot point. Consider =ig.. 0oint
0 (3, *3) can be seen being rotated about the origin through an angle, QO-R, in the anti
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cloc#wise direction to position 0*. $he coordinates of 0* can be obtained by multiplying the co
ordinates of 0 by the matri&'
SCA5ING
Changing the dimensions of window and view port, it is possible to alter the size of
drawings. $his techni1ue is not satisfactory in all cases. A drawing can be made bigger by
increasing the distance between the points of the drawing. !n general, this can be done by
multiplying the coordinates of the drawing by an enlargement or reduction factor called scalingfactor and the operation is called scaling. eferring to =ig., 0 (+3, *3) represents a point in the
HI plane. !n matri& form, 0 can be represented as'0 O S+3, *3T
!f we multiply this by a matri&
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An e&le of scaling in the case of a triangle is shown in =ig. =ig. (a) %hows the original picture
before scaling. =ig. (b) %hows the triangle after the coordinates are multiplied by the scaling
matri&.
TRANS5ATION
"oving drawing or model across the screen is called translation. $his is accomplished by adding
to the coordinates of each corner point the distance through which the drawing is to be moved
(translated). =ig. shows a rectangle (=ig.(a)) being moved to a new position (=ig.(b)) by adding 3
units to H coordinate values and +3 units to I coordinate values. !n general, in order to translate
drawing by ($H , $I ) every point H, I will be replaced by a point H , I where
H O H U $H
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I O I U $I
RE65ECTION
%hading is an important element in +D computer graphics, as it gives the necessary
realism to the representation of the object. =ig. shows what happens when light is incident on a
surface. ight gets partly reflected, partly scattered, partly absorbed and partly transmitted. $he
relative magnitudes of these are influenced by many factors li#e the opa1ueness of the solid,
surface te&ture etc. $he intensity and wave length of light reflected from a surface depends on the
incident angle, the surface roughness, incident wave length and the electrical properties of the
surface. !n computer graphics designer can model reflected light and transmitted light.
eflected light could be categorized into two types'
Di$$use re$ection: Diffuse light is scattered in all directions and is responsible for the color of
the object. $he light is reflected from a surface due to molecular interaction between incident light
and the surface material. A yellow object for e&le, absorbs white light and reflects yellow
component of the light. $his property is attributed to diffuse reflection. >hen light from a point
source is incident on a solid object, the diffuse reflection depends upon the angle of inclination of
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MET71 COMPUTER AIDED DESIGN
the surface with that of the incident beam. "ore important source of illumination of the objects is
ambient light, which is the result of multiple reflections from the walls and other objects in the
vicinity and is incident on a surface in all directions.
S!ecu#r re$ection: A perfectly matt surface scatters light in all directions. "ost of the surfaces
that we deal with, however, have different levels of glossiness. $he specular deflection deals withthe reflection of the surface due to glossiness. Consider =ig. which shows the reflection of light
on a surface. !f the surface is perfectly glossy the reflected light is in the direction of . !f the
surface becomes more and more matt, the reflection intensity varies as in a profile shown as the
shaded area of the figure.
A techni1ue to model reflection from an object based on specular reflection has been proposed by
0hong. $his model assumes that'
V ight sources are point sources.
V All geometry e&cept the surface normal is ignored.
V Diffuse and specular components are modeled as local components
V $he model to simulate the specular term is empirical.
V $he color of specular reflection is that of the light source
V $he ambient lighting is constant.
SEARING
A shearing transformation produces distortion of an object or an entire image. $here are two types
of shears' Hshear and Ishear. A Ishear transforms the point (H, I) to the point (H, I) by a
factor %h, where
H O H
I O %h. H U I
=ig. shows I shear applied to a drawing.
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OMOGENEOUS TRANS6ORMATIONS
ach of the above transformations with the e&ception of translation can be represented as a
row vector H, I and a * H * matri&.
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COM)INATION TRANS6ORMATIONS
%e1uences of transformations can be combined into a single transformation using the
concatenation process. =or e&le, consider the rotation of a line about an arbitrary point. ine
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A6 is to be rotated through -R in anticloc#wise direction about point A (=ig (a)). =ig. (b) %hows
an inverse translation of A6 to A6. A6 is then rotated through -R to A*6*. $he line A*6* is
then translated to A+6+
%ince matri& operations are not commutative, care must be ta#en to preserve the order in which
they are performed while combining the matrices.
DIMENSIONA5 TRANS6ORMATIONS
!t is often necessary to display objects in +D on the graphics screen. $he transformation matrices
developed for *dimensions can be e&tended to +D.
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PRO;ECTIONS
!n drawing practice, a +dimensional object is represented on a plane paper. %imilarly in
computer graphics a +dimensional object is viewed on a *dimensional display. A projection is a
transformation that performs this conversion. $hree types of projections are commonly used in
engineering practice' parallel, perspective and isometric.
PARA55E5 +ORTOGONA5/ PRO;ECTION
$his is the simplest of the projection methods. =ig. shows the projection of a cube on to a
projection plane. $he projectors, which are lines passing through the corners of the object are all
parallel to each other. !t is only necessary to project the end points of a line in +D and then join
these projected points. $his speeds up the transformation process.
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PERSPECTI
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$his projection is called orthographic. $he orthographic projection is a special form of the
parallel projection by which parallel lines of the threedimensional object are transformed into
parallel lines of its image.
ISOMETRIC PRO;ECTION
!n isometric projection the three orthogonal edges of an object are inclined e1ually to the
projection plane. 6ecause of the relative ease of projection and the ability to give +D perception,
isometric projection is widely used in computer aided design. !n computer aided design the co
ordinates of the drawing are available in their natural coordinate system. $hese are transformed
suitably to enable the viewer different views or rotate the object in such away that all the faces of
the object are made visible continuously.
$here are several uses for this techni1ue in product design.
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UNIT – III
GEOMETRIC MODE55ING
:eometric modeling techni1ues li#e wire frame, surface and solid modeling have totally
changed not only the drawing office practices but also have helped to integrate design with
analysis, simulation and optimization as well as to seamlessly integrate design with downstreammanufacturing applications. Data created in geometric models can thus be directly passed on to all
the application software pac#ages li#e finite element analysis, mechanism analysis, CNC
programming, inspection etc. :eometric modeling has therefore paved the way for C!". $he
salient features of the different modeling techni1ues are discussed in this chapter. $he starting
point of new product development is conceptual design. $he designer has to develop the shape of
the product which in turn has to accommodate the functional parts inside. >hether it is a
consumer durable li#e a camera, and an electric iron, a washing machine, an automobile, an
entertainment electronic item li#e television or a sports item li#e a golf club, shape design is a
critical activity in product design. $his chapter also discusses conceptual design techni1ues and
transfer of data to modeling software.
INTRODUCTION
0roduct development activity starts with the design of the product. As mentioned in
Chapter * this is a very critical activity which will influence the cost, performance, service life,
1uality, manufacturability, maintainability etc. $he challenges before the product designers today
are listed below'
V
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diminished. !n addition to production drawings of components, the design department has to
create layout drawings, assembly drawings, and tool drawings (Gigs, fi&tures, templates, special
tools, inspection fi&tures etc). $he number of drawings re1uired for a product varies with the
comple&ity of the product. !n the case of the development of a centre lathe, it may be necessary to
create about 33-33 drawings. =or an aircraft, the number of drawings will be of the order of +3,333 to /3,333. !n addition to component drawings, it is necessary to create hundreds of tool
drawings and jig and fi&ture drawings for manufacture, assembly and inspection. Considerable
manpower and time will be re1uired to create such a large volume of drawings and the time
re1uired for this tas# represents a significant portion of the lead time re1uired for product
development.
Computer aided design and drafting (CADD) is a powerful techni1ue to create the
drawings. $raditionally, the components and assemblies are represented in drawings with the help
of elevation, plan, and end views and cross sectional views. !n the early stages of development of
CADD, several software pac#ages were developed to create such drawings using computers.
=igure shows four views (plan, elevation, end view and isometric view) of a part. %ince any entity
in this type of representation re1uires only two coordinates (H and I) such software pac#ages
were called twodimensional (*D) drafting pac#ages. >ith the evolution of CAD, most of these
pac#ages have been upgraded to enable +D representation.
C5ASSI6ICATION O6 GEOMETRIC MODE5ING
Computer representation of the geometry of a component using software is called a
geometric model. :eometric modeling is done in three principal ways. $hey are'
i. >ire frame modeling
ii. %urface modeling
iii. %olid modeling
$hese modeling methods have distinct features and applications.
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9IRE 6RAME MODE5ING
!n wire frame modeling the object is represented by its edges. !n the initial stages of CAD,
wire frame models were in *D. %ubse1uently +D wire frame modeling software was introduced.
$he wire frame model of a bo& is shown in =ig. (a). $he object appears as if it is made out of thin
wires. =ig. (b), (c) and /.*(d) show three objects which can have the same wire frame model of the bo&. $hus in the case of comple& parts wire frame models can be confusing. %ome clarity can be
obtained through hidden line elimination. $hough this type of modeling may not provide
unambiguous understanding of the object, this has been the method traditionally used in the *D
representation of the object, where orthographic views li#e plan, elevation, end view etc are used
to describe the object graphically.
6ig( A"%iguit in 9ire 6r#"e Modeing
A comparison between *D and +D models is given below'
* D "odels +D >ire =rame "odels
nds (vertices) of lines are represented by their H
and I coordinates
Curved edges are represented by circles, ellipses,
splines etc. Additional views and sectional views
are necessary to represent a comple& object with
clarity.
+D image reconstruction is tedious.
5ses only one global coordinate system
nds of lines are represented by their H, I and P
coordinates.
Curved surfaces are represented by suitably
spaced generators.
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!n this approach, a component is represented by its surfaces which in turn are represented
by their vertices and edges. =or e&le, eight surfaces are put together to create a bo&, as shown
in =ig.. %urface modeling has been very popular in aerospace product design and automotive
design. %urface modeling has been particularly useful in the development of manufacturing codes
for automobile panels and the comple& doubly curved shapes of aerospace structures and dies andmoulds.
Apart from standard surface types available for surface modeling (bo&, pyramid, wedge,
dome, sphere, cone, torus, dish and mesh) techni1ues are available for interactive modeling and
editing of curved surface geometry. %urfaces can be created through an assembly of polygonal
meshes or using advanced curve and surface modeling techni1ues li#e 6splines or N56% (Non
5niform ational 6splines). %tandard primitives used in a typical surface modeling software are
shown in =ig.. $abulated surfaces, ruled surfaces and edge surfaces and revolved are simple ways
in which curved geometry could be created and edited. %urface modeling is discussed in detail
later in this chapter.
SO5ID MODE5ING
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$he representation of solid models uses the fundamental idea that a physical object divides
the +D uclidean space into two regions, one e&terior and one interior, separated by the boundary
of the solid. %olid models are'
V bounded
V
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A LunionX operation (A Q6) will combine the two to convert them into a new solid. (=ig.(c)) $he∪
difference operation (A 4 6) will create a bloc# with a hole (=ig. (D)). an intersection operation
(A WQ6) will yield the portion common to the two primitives. (=ig. ()).
)ound#r Re!resent#tion
6oundary representation is built on the concept that a physical object is enclosed by a set of faces
which themselves are closed and orient able surfaces. =ig. %hows a 6rep model of an object. !n
this model, face is bounded by edges and each edge is bounded by vertices. $he entities which
constitute a 6rep model are'
:eometric entities $opological entities
0oint Kerte&
Curve, line dge
%urface =ace
A solid model is a +D representation of an object. !t is an accurate geometric description
which includes not only the e&ternal surfaces of part, but also the part2s internal structure. A solid
model allows the designer to determine information li#e the object2s mass properties,
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MET71 COMPUTER AIDED DESIGN
interferences, and internal cross sections. %olid models differ from wire frame and surface models
in the #ind of geometric information they provide. >ire frame models only show the edge
geometry of an object. $hey say nothing about what is inside an object. %urface models provide
surface information, but they too lac# information about an object2s internal structure. %olid
models provide complete geometric descriptions of objects. ngineers use solid models indifferent ways at different stages of the design process. $hey can modify a design as they develop
it. %ince computerbased solid models are a lotA solid model is a +D representation of an object.
!t is an accurate geometric description which includes not only the e&ternal surfaces of part, but
also the part2s internal structure. A solid model allows the designer to determine information li#e
the object2s mass properties, interferences, and internal cross sections. %olid models differ from
wire frame and surface models in the #ind of geometric information they provide. >ire frame
models only show the edge geometry of an object. $hey say nothing about what is inside an
object. %urface models provide surface information, but they too lac# information about an
object2s internal structure. %olid models provide complete geometric descriptions of objects.
ngineers use solid models in different ways at different stages of the design process. $hey
can modify a design as they develop it. %ince computerbased solid models are a lot
SA5IENT 6EATURES O6 SO5ID MODE5ING
6EATURE)ASED DESIGN
$he most fundamental aspect in creating a solid model is the concept of featurebased
design. !n typical *D CAD applications, a designer draws a part by adding basic geometric
elements such as lines, arcs, circles and splines. $hen dimensions are added. !n solid modeling a
+D design is created by starting a base feature and then adding other features, one at a time, until
the accurate and complete representation of the part2s geometry is achieved.
A feature is a basic building bloc# that describes the design, li#e a #eyway on a shaft. ach
feature indicates how to add material (li#e a rib) or remove a portion of material (li#e a cut or a
hole). =eatures adjust automatically to changes in the design thereby allowing the capture of
design intent. $his also saves time when design changes are made. 6ecause features have the
ability to intelligently reference other features, the changes made will navigate through design,
updating the +D model in all affected areas. =igure shows a ribbed structure. !t consists of feature
li#e ribs and holes.
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%imilarly, if a flanged part shown in =ig. (A) is to be created, the one approach is to s#etch the
cross section as shown in =ig. (6) and then revolve through +/3R.
!n typical solid modeling software the designer can create a feature in two basic ways. 9ne
is to s#etch a section of the shape to be added and then e&trude, revolve, or sweep it to create the
shape. $hese are called s#etched features. Another type of feature is the pic#andplace feature.
hen a dimension is changed
the solid modeling software recalculates the geometry. Design of a part always begins with a base
feature. $his is a basic shape, such as a bloc# or a cylinder that appro&imates the shape of the part
one wants to design. $hen by adding familiar design features li#e protrusions, cuts, ribs, #eyways,
rounds, holes, and others the geometry of a part is created.
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$his process represents true design. 5nli#e many CAD applications in which designing
means drawing a picture of the part, wor#ing with the featurebased solid modeling method is
more li#e sculpting designs from solid material.
SUR6ACE MODE5ING
All physical objects are +dimensional. !n a number of cases, it is sufficient to describe the
boundary of a solid object in order to specify its shape without ambiguity. $his fact is illustrated in
=ig.. $he boundary is a collection of faces forming a closed surface. $he space is divided into two
parts by the boundary one part containing the points that lie inside and forming the object and the
other the environment in which the object is placed. $he boundary of a solid object may consist of
surfaces which are bounded by straight lines and curves, either singly or in combination.
=igure is typical of several components, one comes across in engineering. $he surface of this component can be produced by revolving a profile about an a&is of rotation. A surface model
is defined in terms of points, lines and faces. $his type of modeling is superior to wire frame
modeling discussed earlier in this chapter. A major advantage of surface modeling is its ability to
differentiate flat and curved surfaces. !n graphics, this helps to create shaded image of the product.
!n manufacture, surface model helps to generate the NC tool path for comple& shaped components
that are encountered in aerospace structures, dies and moulds and automobile body panels.
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A surface can be created in several ways'
i. Creating a plane surface by the linear sweep of a line or series of lines.
ii. evolving a straight line about an a&is. Cylindrical, conical surfaces etc. can be generated bythis techni1ue.
iii. evolving a curve about an a&is.
iv. Combination of plane surfaces.
v. Analytic surfaces' 0lanes, cylinders, cones, ellipsoid, parabolic hyperboloid etc can be defined
by mathematical e1uations in terms of H, I and P coordinates.
vi. %culptured surfaces' $hese are also called free form surfaces. $hese are created by spline
curves in one or both directions in a +D space. $hese surfaces are used in the manufacture of car
body panels, aircraft structures, mi&ed flow impellers, telephone instruments, plastic containers
and several consumer and engineering products.
"odeling of curves and surfaces is essential to describe objects that are encountered in several
areas of mechanical engineering design. Curves and surfaces are the basic building bloc#s in the
following designs'
i. 6ody panels of passenger cars
ii. Aircraft bul# heads and other fuselage structures, slats, flaps, wings etc.
iii. "arine structures
iv. Consumer products li#e plastic containers, telephones etc.
v. ngineering products li#e mi&ed flow impellers, foundry patterns etc A curve has one degree of
freedom while a surface has two degrees of freedom. $his means that a point on a curve can be
moved in only one independent direction while on surfaces it has two independent directions to
move. $his is shown in =ig.
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REPRESENTATION O6 CURhere &, y, z are coordinates of the points on the curve which are functions of some parameter u
and the parametric variable is constrained in the interval. =or e&le, a point (&, y) is located at
an angle from UH a&is on a circle with centre at (3, 3) and radius O can be described in
parametric form as'
& O Cos
y O %in
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>here is the parameter. %urfaces are described similarly for which &, y and z are
functions two independent parameters u and v. 0arametric design is very popular in computer
aided design for a variety of reasons, which are listed below'
V %eparation of variables
V ach variable is treated ali#eV "ore degrees of freedomcontrol
V 0arametric e1uations can be transformed directly
V !nfinite slopes can be handled without computational brea#down
V asy to e&press as vectors
V Amenable to plotting and digitizing
V !nherently bounded
DESIGN O6 CUR
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9ne of the popular methods of interpolation is to use the agrange polynomial, which is the
uni1ue polynomial of degree n passing through n U points.
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$he above e1uations can be solved to obtain the four e1uations given below'
a O *H(3) 4 *H() U H2(3) U H2()
b O 4+H(3) U +H() 4 *H2(3) 4 H2()
c O H2(3)
d O H(3)
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)EIER CUR
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$he advantages of 6ezier curve over cubic spline is that the direction of the curve at the
joints can be defined and changed simply by specifying the position of the second and third data points. Changing a control point not only affects the shape of the curve near the control point but
has an influence throughout the curve. $his lac# of local control is a major wea#ness of 6ezier
curve. =ig. shows 6ezier cubic segments for two sets of values of H.
Z SP5INES
$his form of cubic segments uses a third set of basis functions different from the types discussed
earlier. A cubic Zspline curve is a special case of spline curve. $he e1uation for this curve can be
written as'
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>hen the control points are distinct, this curve is continuous in slope and in curvature
between successive segments but it does not pass through any of the intermediate control points.
$he cubic Zspline has the advantage that the control points may be moved without affecting slope
and curvature continuity and only four spans of the overall curve will be affected by the change.
"oreover, by allowing two control points to coincide it is possible to create a curvature
discontinuity. A slope discontinuity, similarly, can be introduced by choosing three successive
control points to be coincident.
!t is possible to represent comple& curve shapes by considering composite curves constructed from
individual segments, in the case of cubic spline, 6ezier and 6spline techni1ues.
NUR)S AND SP5INES
$wo important surface representation schemes e&ist that e&tend the control of shape
beyond movement of control vertices. $hese are N56% (Non 5niform ational Z %plines) and
Z splines. !n the case of N56% a local verte& is e&tended to a four dimensional coordinate, the
e&tra parameter being a weight that allows a subtle form of control which is different in effect to
moving a control verte&. !n the simplest form of Z spline control two global parameters (bias and
tension) are introduced which affect the whole curve.
NUR)S
A nonuniform spline curve is defined on a #not vector where the interior #not spans
are not e1ual. A rational spline is defined by a set of four dimensional control points.
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>i associated with each control point is called a weight and can be viewed as an e&tra shape
parameter. >i affects the curve only locally and can be interpreted geometrically as a coupling
factor. $he curve is pulled towards a control point if > increases.
SP5INES
splines are obtained from splines by introducing two new degrees of freedom' bias and
tension. $hese can be applied uniformly or nonuniformly.
REPRESENTATION O6 SUR6ACES
A surface can be defined as the locus of points which satisfy a constraint e1uation in the form of
=(H, I, P) O 3. !n parametric form a surface may be represented as
DESIGN O6 SUR6ACES
$he design of surfaces may be based on 1uadrics li#e ellipsoid, hyperboloid, cone, hyperbolic
cylinder, parabolic cylinder, elliptic cylinder and elliptic paraboloid. A surface may be generated
by sweeping a pattern curve along a spline curve. $he swept surface may also be linear, conical
linear or circular swept surface.
PARAMETRIC DESIGN O6 SUR6ACES
0arametric surfaces may be defined in one of the following methods'i. !n terms of points of data (positions, tangents, normal2s)
ii. !n terms of data on a number of space curves lying in these surfaces.
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$he resulting surface will either interpolate or appro&imate the data. %urfaces are normally
designed in patches, each patch corresponding to a rectangular domain in uv space. A surface
patch defined in terms of point data will usually be based on a rectangular array of data points
which may be regarded as defining a series of curves in one parameter direction which in turn are
interpolated or appro&imated in the direction of the other parameter to generate the surface. =ig.shows the parameter curves on a surface patch defined by a rectangular array of data points.
)ICU)IC PO5>NOMIA5 SUR6ACE PATCES
A bicubic polynomial surface can be represented in the form'
)EIER )ICU)IC SUR6ACE PATCES
$he 6ezier bicubic surface patch uses the basis matri&'
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$he vector coefficients are given by a [ matri& of position vectors for si&teen points forming a
characteristic polyhedron. =ig. shows the characteristic polyhedron for a 6ezier surface. $he four
corner points (3,3), (+,3), (+,+) and (3,+) lie at the corners of the surface patch itself
whereas remaining points do not lie on the patch. $he four points along each edge of the
polyhedron define the four edge curves of the patch. $he four interior points determine the cross
derivatives at the corner and cross slopes along the nearest edges to them.
CU)IC )SP5INE SUR6ACES
$he basis function for a cubic 6spline surface is the same as that of cubic 6spline curve.
As in the case of 6spline curve, none of the control points forming the characteristic polyhedronlies on the surface. Composite surfaces can be obtained by combining several surface patches.
$able gives the properties of the surfaces generated by the common methods.
$he surfaces patches described above cover a rectangular domain in uv space. $here are also
methods proposed for interpolation on triangular and pentagonal domains.
SUR6ACE MODE5ING IN COMMERCIA5 DRA6TING AND MODE5ING
SO6T9ARE
%urface types available for geometric modeling range from simple planes to comple&
sculptured surfaces. $hese surfaces are usually represented on the wor#station terminals as a set of
ruled lines.
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SUR6ACE MODE5ING COMMANDS
$here are a number of commands to create a surface model
i. +D face' $he different faces of an object can be modeled using this command. $he H,I,P co
ordinates of each verte& are input one after another to model a face and each of the faces is
defined one after another in this manner.ii. 0 face' $he 0face command produces a general polygon mesh of a arbitrary topology. 5sing
this command, it is possible to avoid defining a single verte& several times as is done in +D face
command. $he user defines all vertices and then defines the faces in terms of the vertices.
iii. ulesurf' $his command creates a polygon representing the ruled surface between two curves.
=igure shows an e&le of ruled surfaces.
v. ev surf' A surface of revolution is created by rotating a path curve or profileabout an a&is. $he
rotation can be through +/3 degrees or part of it.
vi. dge surf' $his command constructs a Coon2s surface patch using four adjoining curved edges,
an e&le of edge surf commands is shown in =ig.
6EATURES O6 SUR6ACE MODE5ING PAC8AGE
Soid !ri"itive
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%olid primitives are predefined bloc#s that can be accessed from a dedicated toolbar or dragged
and dropped from a library or palette to create a model using 6oolean operations (eg. addition,
subtraction, and intersection). >hen inserted into a drawing, the user can enter values for length,
breadth, height, etc. %olid primitives are not created by drawing circles, rectangles, etc and then
e&truding this is defined as an ;object created through e&trusion2. $he most common solid primitives are bo&, cylinder, cone, sphere and torus, although there are others subject to the
software pac#age being used.
9&ere to $ind soid !ri"itives
ach software pac#age has its own way of using solid primitives and our verifiers have found that,
although various pac#ages are used in schools across the country, the most commonly used
pac#ages in N :raphic Communication are AutoCAD, 0ro Des#top
AutoCAD
$he solid primitives can be accessed from the "odeling toolbar as shown. ater versions of
AutoCAD have a Dashboard from which the primitives can be dragged.
Pro Des'to!
$he solid primitives can be accessed from a 0alette of 6ase %hapes that can be dragged into a
drawing and edited to create a model.
CSG:
Constructive soid geo"etr +CSG/ is a techni1ue used in solid modelling. Constructive solid
geometry allows a modeller to create a comple& surface or object by using 6oolean operators to
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combine objects. 9ften C%: presents a model or surface that appears visually comple&, but is
actually little more than cleverly combined or decombined objects.
!n +D computer graphics and CAD C%: is often used in procedural modelling. C%: can also be
performed on polygonal meshes, and may or may not be procedural andor parametric.
Workings of CSG
$he simplest solid objects used for the representation are called !ri"itives. $ypically they are the
objects of simple shape' cuboids, cylinders, prisms, pyramids, spheres, cones. $he set of allowable
primitives is limited by each software pac#age. %ome software pac#ages allow C%: on curved
objects while other pac#ages do not.
!t is said that an object is constructed from primitives by means of allowable o!er#tions, which
are typically 6oolean operations on sets' union, intersection and difference. A primitive can
typically be described by a procedure which accepts some number of parameters@ for e&le, a
sphere may be described by the coordinates of its center point, along with a radius value. $hese
primitives can be combined into compound objects using operations li#e these'
Union
"erger of two objects into oneDi$$erence: %ubtraction of one
object from another
Intersection: 0ortion common to
both objects
Combining these elementary operations, it is possible to build up objects with high comple&ity
starting from simple ones.
Applications of CSG
Constructive solid geometry has a number of practical uses. !t is used in cases where simple
geometric objects are desired, or where mathematical accuracy is important. $he ua#e engine
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and 5nreal engine both use this system, as does hen C%: is
procedural or parametric, the user can revise their comple& geometry by changing the position of
objects or by changing the 6oolean operation used to combine those objects.
9ne of the advantages of C%: is that it can easily assure that objects are \solid\ or watertight if
all of the primitive shapes are watertight. $his can be important for some manufacturing or
engineering computation applications. 6y comparison, when creating geometry based upon
boundary representations, additional topological data is re1uired, or consistency chec#s must be
performed to assure that the given boundary description specifies a valid solid object.
A convenient property of C%: shapes is that it is easy to classify arbitrary points as being either
inside or outside the shape created by C%:. $he point is simply classified against all the
underlying primitives and the resulting 6oolean e&pression is evaluated. $his is a desirable 1uality
for some applications such as collision detection.
)Re! "ode
• ] 6oundary representation ^
• "odel based on the representation of surfaces
• "odel of e&change (%$0 format) and definition
• $he LnaturalX set of operators is richer than for C%: &trusion, chamfer etc...
• Does not carry the history of construction of the model (whereas C%: usually does)
Consists of two type of information
1( Geo"etric
• :eometric information is used for defining the spatial position, the curvatures, etc...
$hatJs what we have seen until now 4 Nurbs curves and surfaces
B( To!oogic#
http://en.wikipedia.org/wiki/Unreal_enginehttp://en.wikipedia.org/wiki/Valve_Hammer_Editorhttp://en.wikipedia.org/wiki/Source_enginehttp://en.wikipedia.org/wiki/Torque_Game_Enginehttp://en.wikipedia.org/wiki/Torque_Game_Engine_Advancedhttp://en.wikipedia.org/wiki/Boundary_representationhttp://en.wikipedia.org/wiki/Collision_detectionhttp://en.wikipedia.org/wiki/Unreal_enginehttp://en.wikipedia.org/wiki/Valve_Hammer_Editorhttp://en.wikipedia.org/wiki/Source_enginehttp://en.wikipedia.org/wiki/Torque_Game_Enginehttp://en.wikipedia.org/wiki/Torque_Game_Engine_Advancedhttp://en.wikipedia.org/wiki/Boundary_representationhttp://en.wikipedia.org/wiki/Collision_detection
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• $his allows ma#ing lin#s between geometrical entities.
• $wo types of entities
o :eometric entities' surface, curve, point
o $opological entities ' volume, face, edge, verte&
• A topological entity Llies onX a geometric entity, which is its geometrical support
Co"!ete &ier#rc&ic# "ode
Descri!tion o$ ot&er "odeing tec&ni4ues:
0ure primitive instancing
Cell Decomposition
%patial occupancy enumeration
6oolean 9peration
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Creating +D operation from *D profile
Pure Pri"itive Inst#ncing
$his scheme is based on the notion of families of objects, each member of a family
distinguishable from the other by a few parameters. ach object family is called a generic
primitive, and individual objects within a family are called primitive instances. =or e&le a
family of bolts is a generic primitive, and a single bolt specified by a particular set of parameters
is a primitive instance. $he distinguishing characteristic of pure parameterized instancing schemes
is the lac# of means for combining instances to create new structures which represent new and
more comple& objects.
$he other main drawbac# of this scheme is the difficulty of writing algorithms for
computing properties of represented solids. A considerable amount of familyspecific information
must be built into the algorithms and therefore each generic primitive must be treated as a special
case, allowing no uniform overall treatment.
Ce Deco"!osing:
$his scheme follows from the combinatoric (algebraic topological) descriptions of solids
detailed above. A solid can be represented by its decomposition into several cells. %patial
occupancy enumeration schemes are a particular case of cell decompositions where all the cells
are cubical and lie in a regular grid. Cell decompositions provide convenient ways for computing
certain topological properties of solids such as its connectedness (number of pieces) and genus
(number of holes).
Cell decompositions in the form of triangulations are the representations used in +d finite
elements for the numerical solution of partial differential e1uations. 9ther cell decompositions
such as a >hitney regular stratification or "orse decompositions may be used for applications in
robot motion planning.
S!#ti# occu!#nc enu"er#tion:
$his scheme is essentially a list of spatial cells occupied by the solid. $he cells, also called
vo&els are cubes of a fi&ed size and are arranged in a fi&ed spatial grid (other polyhedral
http://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Topological_propertieshttp://en.wikipedia.org/wiki/Connected_spacehttp://en.wikipedia.org/wiki/Genus_(mathematics)http://en.wikipedia.org/wiki/Finite_elementshttp://en.wikipedia.org/wiki/Finite_elementshttp://en.wikipedia.org/wiki/Topologically_stratified_spacehttp://en.wikipedia.org/wiki/Voxelhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Topological_propertieshttp://en.wikipedia.org/wiki/Connected_spacehttp://en.wikipedia.org/wiki/Genus_(mathematics)http://en.wikipedia.org/wiki/Finite_elementshttp://en.wikipedia.org/wiki/Finite_elementshttp://en.wikipedia.org/wiki/Topologically_stratified_spacehttp://en.wikipedia.org/wiki/Voxel
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arrangements are also possible but cubes are the simplest). ach cell may be represented by the
coordinates of a single point, such as the cellJs centroid. 5sually a specific scanning order is
imposed and the corresponding ordered set of coordinates is called a spatial array.
%patial arrays are unambiguous and uni1ue solid representations but are too verbose for
use as JmasterJ or definitional representations. $hey can, however, represent coarse appro&imations
of parts and can be used to improve the performance of geometric algorithms, especially when
used in conjunction with other representations such as constructive solid geometry.
)ooe#n o!er#tions:
6oolean operations are used to ma#e more complicated shapes by combining simpler
shapes.
$hree types of operations are possible
5nion (;∪2) or join
!ntersection (;∩2)
Difference (;;) or subtract or cut
Union or ;oin:
$wo or more solids combined to form a single solid.
Intersection:
9btaining single composed from the common part of two or more solids.
Di$$erence or su%tr#ct or cut:
9btaining single solid composed by mathematical subtracting of the common part of two
or more solids.
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Union
"erger of two objects into one
Di$$erence: %ubtraction of one
object from another
Intersection: 0ortion common to
both objects
Cre#ting D o%=ects $ro" BD !ro$ies:
Creating Solids
"any +D solids can be created by e&truding, rotating or lofting *D profiles. 9ther basic
solids such as cylinders, bo&es, cones or pyramids can be defined by entering dimensions. Nearly
all mechanical parts are comprised of basic solids, which can be joined andor trimmed.
Combining and subtracting solids are called 6oolean operations, and resulting solids are called
L6oolean $rees.X Kari CAD provides tools to add solids and to use one solid to cut another, either
#eeping or deleting the cutting solid. Commonlyused 6oolean operations such as drilling holes,
creating grooves, and cutting by a large bo& are also available. 6lending functions are provided for
rounding and chamfering solid edges.
Cre#ting D Soids $ro" BD Pro$ies
5sing *D profiles to create solids enables you to model a wide range of objects. $he solid shape
can be edited by modifying the original *D profile.
De$ining # BD Pro$ie
>hen using a +D function that re1uires a *D profile as input, you will be optionally switched
to the *D drawing area. Iou can stay in +D and create the profile using *D drawing in +D. !n this
case, you can define a drawing plane'
• As an e&isting plane at a solid
• 0lane created by selected a&es at a selected solid
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• 0lane defined by + points
• 0lane created by selected a&es of +D space
!f you create a new profile used for e&trusion, rotation or other similar method of solid
creation, the created solid is preinserted according to the profile2s location in +D space.
!f you edit an e&isting profile of a solid, you will always stay in +D and the profile will be
edited with *D drawing methods in +D.
0rofiles are created by *D lines, arc segments or N56% *D curves. $here are two methods of
profile detection'
Detect 0rofile %egments (or press ) define the profile segment by segment
Detect 0rofile (or press =) select one segment and the entire chained profile is detected
Apart of automatic detection of profile2s segments, you can select objects with standard
methods of *D selection 4 see selecting *D 9bjects. 0ress nter or rightclic# to finish the profile
definition, when the solid is created, you return to +D space and define the object location, %ee
$ransforming and Copying %olids.
0rofiles used for +D solids must be continuous. !f multiple profiles are used, they cannot
intersect@ one profile must completely encompass the other profiles. 0rofiles used in a evolve
operation cannot intersect the revolving a&is.
ines, circles or circular arcs can be selected for all type of solid creations.
!f a profile contains gaps or intersections of segments, you can optionally highlight a
location of the error.
Soid Insertion Point
0rior to selecting a *D profile, most solid functions re1uire you to enter the solid height or
revolving angle. Along with these parameters, you can also identify the solid insertion point and
set the H a&is direction. !f you do not select an insertion point, the point at lower left point of
profile will be used. !f you do not set the H a&is, the default *D H a&is will be used. $he insertion
point and H a&is direction are used when inserting the solid into +D space.
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&le of !nsertion 0oints
un LC=:X command to set solid insertion point relative to its creation profile. Although this
setting can be done within the profile definition, not all functions offer this. !nsertion point setting
during profile definition is possible only when the solid height or rotation angle is defined. Iou
can use this function at any time, and it will set the insertion point for subse1uent solids. Iou can
also choose whether to define the insertion point and H a&is direction automatically.
Revoving2 Etruding2 #nd 5o$ting Pro$ies
Full Revolve - RSO
evolves one open or closed profile +/3 degrees about a revolving a&is. =or an open profile, the
a&is is defined by the profile endpoints. =or a closed profile, you must define the a&is. !f the
insertion point is defined automatically, it is located at the first defined point of the revolving a&is.
>hen selecting closed profiles, multiple profiles are allowed inside one outer profile this will
create holes in the solid.
&le of =ull evolve using an open profile
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Partial Revolve - RSOP
%imilar to =ull evolve, e&cept that you can enter a revolving angle less than +/3 degrees.
&le of 0artial evolve using closed profiles
UNIT – I<
INITIA5 GRAPICS ECANGE SPECI6ICATION +IGES/ GRAPICS STANDARD
$he !:% committee was established in the year 7M7. $he CADCA" !ntegrated
!nformation Networ# (C!!N) of 6oeing served as the preliminary basis of !:%. !:% version .3
was released in 783. !:% continues to undergo revisions. !:% is a popular data e&change
standard today. =igure shows a CAD model of a plate with a centre hole. $he wire frame model of
the component is shown in =ig. . $here are eight vertices (mar#ed as 0N$ 3 0N$ 8), * edges
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and two circles that form the entities of the model. $able shows the !:% output of the wire frame
model.
6ig( D Mode o$ # P#te
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!:% files can also be generated for'
i. %urfaces
ii. Datum curves and points
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PRODUCT DATA ECANGE SPECI6ICATION +PDES/
A li#ely alternative to !:% is the product data e&change specification (0D%) developed
by !:% organization. 0D% is aimed at defining a more conceptual model. 0arts will be based on
solids and defined in terms of features such as holes, flanges, or ribs. !nstead of dimensions 0D%
will define a tolerance envelope for the parts to be manufactured. 0D% will also contain non
geometric information such as materials used, manufacturing process and suppliers. 0D% will be
a complete computer model of the part.
OTER DATA ECANGE 6ORMATS
$here are several e&isting alternative data e&change formats. $hese include the %tandard
0roduct Data &change =ormat (%D=) of Kought Corporation (available for CADA", CADD%-,
0A$AN, and 0!" etc.) %tandard !nterchange =ormat (%!=) of !ntergraph Corporation
(available for Applicon, Autotrol, and Calma etc.), !CA" 0roduct Data Definition !nterface
(0DD!), and KDA sculptured surface !nterface (KDA=%), lectronic Design !nterchange =ormat
(D!=), $ransfer and Archiving of 0roduct Definition Data ($A0) etc. Another alternative to !:%
is the neutral format outlined in AN%! I.*/" standard. !t must be noted here that some of the
features of many of these alternatives are superior to that of !:%.
!ntroduction to %
STRUCTURED FUER> 5ANGUAGE SF5H
$he advent and successful implementation of relational databases has brought with it need
for a data base language that is user friendly enough for the common user while being convenient
and comfortable for the programmer and applications builder. $he structured 1uery language now
called % Spronounced Lse1uelXT, has emerged to fill this need. $he user can easily learn and
understand %. !t can be embedded in a procedural language such as C, C969, or 0l. %
helps user and programmer to understand the re1uirements of each other. $his fact is very
important in ma#ing the transition from paperfiles to computerized database systems smooth. %
is acronym