cad unit2.pptx
TRANSCRIPT
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BRESENHAM’S LINE ALGORITHM
Bresenham’s algorithm enables the selection of optimum raster locations to represent a
straight line
Fig. a Location of Pixels Using Fig. Pixels fo! Line of
B!esen"a# Algo!it"# Slo$e% # & '.(
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Pse)*o co*e fo! B!esen"a#’s line+*!a,ing algo!it"#
Given a line from x1, y1 to x2, y2...
dx is the difference between the x components of end points
dy is the difference between the y components of end points
ix is the absolute value of dx
iy is the absolute value of dyinc is the larger of dx, dy
plotx is x1
ploty is y1 (the beginning of line
x starts at !
y starts at !
plot a pixel at plotx, ploty
increment x using ixincrement y using iy
plot is false
if x is greater than inc
plot is true
decrement x using inc
increment plotx if dx is positive
decrement plotx id dx is negative
if y is greater than inc
plot is true
decrement y using inc
increment ploty if dy is positive
decrement ploty if dy is negative
if plot is true, plot a pixel at plotx, plotyincrement i.
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" include #stdio. h$
" include #graphics. h$
" include #stdlb. h$
void draw line (int x1, int y1, int x2, int y2,void main (void
%
draw line (1!!, 1!!, &!, &! '
void draw line (int x1, int y1, int x2 m int y2
%
int dx, dy, inc, ix, iy, x, y, plot, plotx, ploty, i 'int gd, gm '
gd ) *++- '
initgraph (gd, gm, / / '
dx ) x1 0 x2 '
dy ) y1 0 y2 '
ix ) abs (dx '
iy ) abs (dy '
inc ) max (ix, iy '
x ) y ) ! '
plot x ) x1 '
plot y ) y1 '
for (i ) ! ' i #inc ' i
%
x ) ix '
y iy '
plot ) !
if (x $ inc
% plot ) 1 '
x 0 ) inc '
if (dx # !
plot x 0 ) 1 '
else
plotx ) 1 '
if (y $ inc
%
plot ) 1 '
y 0 ) inc '
if (dy
ploty 0 ) 1 '
else ploty ) 1 '
if (plot
putpixel (plotx, ploty, 1
else
getch ( 'closegraph ( '
P!og!a# in T)!o+- to *!a, a line
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BRESENHAM’S -IR-LE ALGORITHM
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GEOMETRI- MOELLING
wire frame, surface and solid modeling
-LASSIFI-ATION OF GEOMETRI- MOELING
-omputer representation of the geometry of a component using software is called
a geometric model. Geometric modeling is done in three principal ways. hey are
/. 0i!e f!a#e #o*eling
1. S)!face #o*eling
2. Soli* #o*eling
hese modeling methods have distinct features and applications.
UNIT + 2
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0IRE FRAME MOELING
3n wire frame modeling the ob4ect is represented by its edges
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2 5 * 6odels 75* 8ire 9rame 6odels
1. +nds (vertices of lines are represented
by their 3 an* 4 coordinates
2. -urved edges are represented by
circles, ellipses, splines etc.
A**itional 5ie,s an* sectional 5ie,s
are necessary to represent a complex
ob4ect with clarity.
7. 75* image reconstruction is te*io)s.
:. ;ses only one gloal coo!*inate
s6ste#
1. +nds of lines are represented by their
3% 4 an* 7 coordinates.
2. -urved surfaces are represented by
suitably spaced generators. Hi**en
line o! "i**en s)!face eli#ination is
a must to interpret complex
components correctly.
7. 25* views as well as various pictorial
views can be generated easil6.
:. 6ay re
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SURFA-E MOELING
3n this approach, a component is represented by its surfaces which in turn are
represented by their vertices and edges.
For example, eight surfaces are put together to create a box, as
shown in
>urface modeling has been very popular in
aerospace product design and automotive
design.
=part from standard surface types
available for surface modeling
(ox% $6!a#i*% ,e*ge% *o#e%
s$"e!e% cone% to!)s% *is" an*
#es" techni
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SOLI MOELING
he representation of solid models uses the fundamental idea that a physical
ob4ect divides the 75* +uclidean space into two regions, one exterior and one interior,
separated by the boundary of the solid. >olid models are
? bounded
? @omogeneously three dimensional
? 9inite
here are six common !e$!esentations in solid modeling.
i. S$atial En)#e!ation 3n this simplest form of 7* volumetric raster model, a
section of 7* space is described by a #at!ix of evenly spaced cubic volume
elements called 5oxels.
ii. -ell eco#$osition his is a hierarchical adaptation of spatial enumeration.
7* space is sub5divided into cells. -ells could be of different siAes. hese simple
cells are glued together to describe a solid ob4ect.
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iii. Bo)n*a!6 Re$!esentation he solid is represented by its boundary which
consists of a set of faces, a set of e*ges and a set of 5e!tices as well as their
topological relations.
iv. S,ee$ Met"o*s 3n this techni
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-onst!)cti5e Soli* Geo#et!6 9-SG:
• 3n a ->G model, physical ob4ects
are created by co#ining asic
ele#enta!6 s"a$es Cnown as
primitives liCe blocCs, cylinders,
cones, pyramids and spheres.
• he Boolean operations liCe )nion
(∪, *iffe!ence (0 and
inte!section E are used to carry out
this tasC. 9or example, let us
assume that we are using two
primitives, a blocC and a cylinder
which are located in space as
shown in 9ig.
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Bo)n*a!6 Re$!esentation
Boundary representation is built on
the concept that a physical ob4ect is
enclosed by a set of faces which
themselves are closed and orient able
surfaces. 9ig. >hows a B5rep model of
an ob4ect. 3n this model, face is bounded
by edges and each edge is bounded by
vertices. he entities which constitute a
B5rep model are
Geometric entities opological
entities
Point
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0o!=ings of -SG
-SG E l
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-SG Exa#$le
+ =
ADD
REMOVE INTERSEC
T
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SALIENT FEATURES OF SOLI MOELING
FEATURE+BASE ESIGN
• he most fundamental aspect in creating a solid model is the concept of feature5based
design.• 3n typical 25* -=* applications, a designer draws a part by adding basic geometric
elements such as lines% a!cs% ci!cles an* s$lines.
• 3n solid modeling a 75* design is created by starting a ase feat)!e and then a**ing other
feat)!es, one at a time, until the accurate and complete representation of the part’s
geometry is achieved.
• = feature is a basic building blocC that describes the design, liCe a =e6,a6 on a s"aft.
+ach feature indicates how to add material (liCe a !i or remove a portion of material
(liCe a c)t or a "ole.
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SURFA-E MOELING
• =ll physical ob4ects are 75dimensional.
• 3n a number of cases, it is sufficient to describe the boundary of a solid ob4ect in order
to specify its shape without ambiguity. his fact is illustrated in 9ig..
•
he boundary is a collection of faces forming a closed surface
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= surface can be created in several ways
i. -reating a plane surface by the linear s,ee$ of
a line or series of lines.
ii. Re5ol5ing a st!aig"t line about an axis.
-ylindrical, conical surfaces etc. can be generated
by this techni
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6odeling of curves and surfaces is essential to describe
ob4ects that are encountered in several areas of mechanical
engineering design. -urves and surfaces are the basic building
blocCs in the following designs
i. Bo*6 $anels of passenger cars
ii. Ai!c!aft bulC heads and other fuselage structures, slats,
flaps, wings etc.
iii. Ma!ine structures
iv. -onsumer products liCe $lastic containe!s, telephones etc.
v. +ngineering products liCe mixed flo, i#$elle!s, fo)n*!6 $atte!ns etc = 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 9ig.
A$$lication of S)!face #o*eling
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REPRESENTATION OF -UR
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REPRESENTATION OF -UR
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9or example, a point (x, y is located at an angle FFfrom axis on a circle with
centre at (!, ! and radius ) 1 can be described in parametric form as
x ) -os F
y ) >in F
where F is the parameter. >urfaces are described similarly for which x, y and A
are functions two independent parameters u and v.
arametric design is very popular in computer aided design for a variety of reasons,
which are listed below? >eparation of variables
? +ach variable is treated aliCe
? 6ore degrees of freedomHcontrol
? arametric e
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ESIGN OF -UR