Mod 2 Dda Line Drawing Algorithm

7/24/2019 Mod 2 Dda Line Drawing Algorithm

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Line Drawing Algorithms


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Rasterization-Process ofdetermining which pixels give thebest approximation to a desired lineon the screen.

Scan Conversion-Digitizing apictre definition given in anapplication program into a set of

pixel intensit! vales for storage inthe frame bffer.


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Points-Point plotting is accomplished b!

converting a single coordinate position in

an application program into appropriate

operations for the otpt device in se.

Line- Line drawing is accomplished b!calclating intermediate positions along the

line path between ( specified end point

positions. )he otpt device is directed tofill these positions between the end points.


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0 1 2 3 4

0

1

2

3

4

Scan Line

nmber

Pixel Colmn

nmber


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x* x(

!*

!(

Straight line segment with + sampling

positions along the x axis and ! axis


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)he Cartesian slope intercept e,n for

straight line is ! m x b

/x*0!*1 2 /x(0!(1be the two endpointsof the line0 then m/!(-!*1%/x(-x*1

b !*- mx*

i.e !* mx* b

!( mx( b/31 4/(1

/ !(-!*1 m /x( 4 x*1

m/!(-!*1%/x(-x*1 ie 5!% 5x

/(1

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/*1


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6or an! given x interval 5xalong a line0

compte the corresponding ! interval

5!as 5! m5x

Similarl! the x interval is obtained as

5x 5! %m

)he above e,ns form the basis for

determining deflection voltages.


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Lines with slope magnitde 7m7 8*0 5x is setproportional to a small horizontal deflectionvoltage and the corresponding verticaldeflection voltage 5! is 5! m5x

5x9 5!

Lines with slope magnitde 7m7 9*0 5!is setproportional to a small vertical deflectionvoltage and the corresponding horizontal

deflection voltage is 5x 5! %m

5!9 5x

P*

P(

P(


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Digital Differential Algorithm(DDA)

Scan conversion algorithm based on

calclating either 5x or 5!. Sample the line at nit intervals in one

coordinate and determine the corresponding

integer vales nearest the line path for the other

coordinate.

Case *

Line with positive slope less than or e,al to *0

we sample at nit x intervals /5x*1 anddetermine the sccessive ! vale as

:$* :$ m5!m 5x

:$*- :$ m 5x

:$*- :$ m /5x *1


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$ ta$es integer vales starting from *andincreases b! *ntil the final point is reached.

mcan be an! nmber between ;and *.

Calclated !vales mst be ronded off tothe nearest integer.

6or lines with positive slope greater than *0sample at nit ! intervals /5! *1 and

calclate each sccessive x vale asx$.* x$ *%m

)he above e,ns are based on the assmption

that lines are processed from left to right.


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Steps

P* / xa0!a1 and P( /xb0!b1are the two end points.

(. =orizontal and vertical differences between the

endpoint positions are compted 2 assigned to

two parameters namel! dxand d!.

3. )he difference with greater magnitde

determines the >vale?of increments to be done.

)hat means the nmber of times sampling has to

be done. )his vale is assigned to a parametercalled >steps?.


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@. Starting from the *stpixel 0we determine theoffset needed at each step to generate the

next pixel position along the line path. Callthe offset vale as xincrementand !increment.

)he starting points are xa and !a.

Assign x xa and !!a

x x xincr 2 ! ! !incr

+. Loop throgh the process steps times0 tillthe last point xb0 !b is reached.

P*

/xa0!a1

P(

/xb0!b1


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Step * Accept as inpt the ( end point

pixel position.

P*/xa0!a1 P( /xb0 !b1

Step ( =orizontal and vertical

differences between the endpoint

positions are compted 2 assigned totwo parameters namel! dx and d!.

dx xb 4 xa d! !b - !a

Steps for DDA Algorithm


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Step 3


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Advantages

DDA algorithm is a faster method forcalclating the pixel positions than the direct

se of line e,ation.

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Mod 2 Dda Line Drawing Algorithm