cad notes.doc

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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&ample 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&ample, 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&ample, 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&ample 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&ample 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&ample 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&ample, 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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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&ample, 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&ample, 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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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&ample, 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&ample 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&ample 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

http://en.wikipedia.org/wiki/Solid_modelinghttp://en.wikipedia.org/wiki/Boolean_data_typehttp://en.wikipedia.org/wiki/Operator_(programming)http://en.wikipedia.org/wiki/Solid_modelinghttp://en.wikipedia.org/wiki/Boolean_data_typehttp://en.wikipedia.org/wiki/Operator_(programming)


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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&ample, 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

http://en.wikipedia.org/wiki/3D_computer_graphicshttp://en.wikipedia.org/wiki/CADhttp://en.wikipedia.org/wiki/Polygon_meshhttp://en.wikipedia.org/wiki/Cuboidhttp://en.wikipedia.org/wiki/Cylinder_(geometry)http://en.wikipedia.org/wiki/Prism_(geometry)http://en.wikipedia.org/wiki/Pyramid_(geometry)http://en.wikipedia.org/wiki/Spherehttp://en.wikipedia.org/wiki/Cone_(geometry)http://en.wikipedia.org/wiki/Boolean_logichttp://en.wikipedia.org/wiki/Operation_(mathematics)http://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Union_(set_theory)http://en.wikipedia.org/wiki/Intersection_(set_theory)http://en.wikipedia.org/wiki/Complement_(set_theory)http://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Parameterhttp://en.wikipedia.org/wiki/Quake_enginehttp://en.wikipedia.org/wiki/File:Boolean_intersect.PNGhttp://en.wikipedia.org/wiki/File:Boolean_difference.PNGhttp://en.wikipedia.org/wiki/File:Boolean_union.PNGhttp://en.wikipedia.org/wiki/3D_computer_graphicshttp://en.wikipedia.org/wiki/CADhttp://en.wikipedia.org/wiki/Polygon_meshhttp://en.wikipedia.org/wiki/Cuboidhttp://en.wikipedia.org/wiki/Cylinder_(geometry)http://en.wikipedia.org/wiki/Prism_(geometry)http://en.wikipedia.org/wiki/Pyramid_(geometry)http://en.wikipedia.org/wiki/Spherehttp://en.wikipedia.org/wiki/Cone_(geometry)http://en.wikipedia.org/wiki/Boolean_logichttp://en.wikipedia.org/wiki/Operation_(mathematics)http://en.wikipedia.org/wiki/Set_theoryhttp://en.wikipedia.org/wiki/Union_(set_theory)http://en.wikipedia.org/wiki/Intersection_(set_theory)http://en.wikipedia.org/wiki/Complement_(set_theory)http://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Parameterhttp://en.wikipedia.org/wiki/Quake_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&ample 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.

http://en.wikipedia.org/wiki/Constructive_solid_geometryhttp://en.wikipedia.org/wiki/Constructive_solid_geometry


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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

http://en.wikipedia.org/wiki/File:Boolean_intersect.PNGhttp://en.wikipedia.org/wiki/File:Boolean_difference.PNGhttp://en.wikipedia.org/wiki/File:Boolean_union.PNG


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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.

http://www.varicad.com/userdata/files/manual/en/2D_Input.htm#JTag18http://www.varicad.com/userdata/files/manual/en/3D_Transformation.htm#JTag36http://www.varicad.com/userdata/files/manual/en/2D_Input.htm#JTag18http://www.varicad.com/userdata/files/manual/en/3D_Transformation.htm#JTag36


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&ample 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.

&ample 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.

&ample 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

Documents

cad notes.doc