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11/10/20

DEC 2009

Derive the Bresenham’s Line drawing

Algorithm. What are its advantages ? 10M

Solution: -Hint( Here first we have to write

the concept behind Bresenham’s

algorithm in some steps(2 marks) and

then write the bresenham’s algorithm in

steps in points as given in the notes (4marks) and then an small example (2

marks) and then write four advantages (2

marks) )



11/10/20

Differentiate between Raster scan display

and Random scan display.(5Marks)

Solution (Hint:- Here for 5 marks we haveto write total 8 points its should contain

the diagram its very important if 8 points

then complete 5 marks .One important

thing is that write the difference in the

points and don’t make the paragraph)

Write a short note on Homogenous co-ordinate system.(5 marks)

Solution (Hint: - here we have to write

first what is a composite co-ordinate

system(1 mark) and then tell its

disadvantage and then write definition of

homogenous coordinates (2 marks) and

then give the homogenous coordinates

for Translation scaling and rotation(2

marks))



11/10/20

Solution: -(Hint: - Here explain what u mean by VR toolkit (2 marks) then list

its different types (1 mark) and then explain any one out of three either JAVA

3D, WTK or GHOST with all the steps given in the notes (7 marks) keep inmind diagrams are very important in this case. )

Solution: -(Hint : - here list all the types of the computing architecture as PC

Graphics Architectures, Work Station Based Architectures (The Sun

Blade 1000 Architecture, The SGI Infinite Reality Architecture) Distributed VR

Architectures ( Multipipeline Synchronization, Collocated rendering Pipelines,

Distributed Virtual Environments). (2 marks) And then explain any one that is

either workstation based or pc graphics architecture or Distributed VR

architecture in detail (8 marks) Diagram are important. )

Solution (Hint: -Here first define VR and list all 7 the application of VR (2Marks) and

then consider any one application and explain in detail with eg and diagrams as and

when required in that application (8 Mark ) )

Solution : -( Hint : -Here attempt any two if ur attempting first then explain first

what is warping in 2 lines then give its type (1 Mark) and Difference with

Diagram (4 mark) differnce 5-6 points enough

If ur attempting the second then first explain Morphing (1 Mark) then explain

what is 2D morphing and then 3D morphing (2 Marks) and then give the

advantage of 3D over today 2D (2 mark)

If ur attempting the third option then explain first what is warping (1 mark)

then explain what u mean by Thin Plate splin with diagram (4 marks) )



11/10/20

Solution : -(hint : - Here explain what is Brezier curve with diagram (2 Mark)

then give its mathematical derivation (4 Marks ) then write the properties of

the Brezier curve (4 marks) and then u can also include the other way ofdrawing Brezier curve which is optional (mid point method) )

Solution :- (hint : -Here first write what is give and then draw thewindows and line (1 mark) then write about the region codes and give

the region codes by using formula that is to set bit (2 marks) and then

start solving problem show all the steps and clip the line (5 marks) then

tabulate ur answer and also draw the final clipped diagram (2 Marks) )

Solution : -(Hint : - Here first tell what are problems in true curve

drawing 4 problems (1 mark) and then explain the Complete

Interpolation derivation with diagram (9 marks) )

Solution (Hint : - Here define projection and then draw that chart and explain in

brief different types (5 Marks) and then derive the matrix representation forperspective transformation in X-Y plane on Negative z- axis (5 marks) with

diagram.

Solution : - ( hint : -Here refer page 413-418 of hean and baker the

derivation is completely given there which is more than enough for

10 marks)



11/10/20

Perspective Projection

Most common computer graphics, art, visualsystem

Further objects are smaller (size, inverse

distance)

Parallel lines not parallel; converge to single

point

B

A’

B’

Center of projection

(camera/eye location)

A

Overhead View of Our Screen

Looks like we’ve got some nice similar triangles here?

x x d x x

z d z

* y y d y y

z d z

, , x y d , , x y z

d

0,0,0



11/10/20

In Matrices

Note negation of z coord (focal plane – d)

(Only) last row affected (no longer 0 0 0 1)

w coord will no longer = 1. Must divide at

end1 0 0 0

0 1 0 0

0 0 1 01

0 0 0

P

d

Verify

1 0 0 0

0 1 0 0

?0 0 1 0

110 0 0

x

y

z

d

*

*

1

1

d x x

z y

d y z

z d

d



11/10/20



11/10/20

•RGB is based on projecting. Red light plus Green light plus Blue light

all projected together create white. Black is encoded as the absence of

any color.

•CMYK is based on ink. Superimpose Cyan ink plus Magenta ink plus

Yellow ink, and you get black, although this format also encodes Black

(K) directly. White is encoded by the absence of any color.

•Prism uses RGB internally. Exporting in RGB will give you results very

close to what you see on screen.

•Even though it uses one more number to encode a color, the CMYK

scheme encodes a smaller "color space" than does RGB.

•When a color is converted from RGB to CMYK, the appearance may

change. Most noticeably, bright colors in RGB will look duller and darker

RGBRed, green, and blue are the primary stimuli for human colorperception and are the primary additive colors. Therelationship between the colors can be seen in thisillustration

The secondary colors of RGB, cyan, magenta, and yellow, areformed by the mixture of two of the primaries and theexclusion of the third. Red and green combine to makeyellow, green and blue make cyan, blue and red makemagenta.

The combination of red, green, and blue in full intensitymakes white. White light is created when all colors of the EMspectrum converge in full intensity.

The importance of RGB as a color model is that it relatesvery closely to the way we perceive color withthe r g b receptors in our retinas. RGB is the basic colormodel used in television or any other medium that projectsthe color. It is the basic color model on computers and isused for Web graphics, but it cannot be used for printproduction.



11/10/20

CMY(K)

Cyan, magenta, and yellow correspond roughly to the primary colors in art

production: red, blue, and yellow. In the illustration below, you can see the CMY

counterpart to the RGB model shown above

Just as the primary colors of CMY are the secondary colors of RGB, the primary

colors of RGB are the secondary colors of CMY. But as the illustrations show, the

colors created by the subtractive model of CMY don't look exactly like the colors

created in the additive model of RGB. Particularly, CMY cannot reproduce the

brightness of RGB colors. In addition, the CMY gamut is much smaller than the

RGB gamut (see below).

The CMY model used in printing lays down overlapping layers of varying

percentages of transparent cyan, magenta, and yellow inks. Light is transmitted

through the inks and reflects off the surface below them (called the substrate).The percentages of CMY ink (which are applied as screens of halftone dots),

subtract inverse percentages of RGB from the reflected light so that we see a

particular color

http://dba.med.sc.edu/price/irf/Adobe_tg/models/rgbcmy.html

http://dba.med.sc.edu/price/irf/Adobe_tg/models/rgbcmy.html



11/10/20

Fractals

Fractals are geometric objects.

Many real-world objects like ferns are

shaped like fractals.

Fractals are formed by iterations.

Fractals are self-similar. In computer graphics, we use fractal

functions to create complex objects.



11/10/20

Fractal Fern

Generator

Iteration 0 Iteration 1 Iteration 2 Iteration 3

Add Some Randomness

The fractals we’ve produced so far seem to be

very regular and “artificial”.

To create some realism and variability, simply

change the angles slightly sometimes based on a

random number generator.

For example, you can curve some of the fernsto one side.

For example, you can also vary the lengths of

the branches and the branching factor.



11/10/20

Fractal dimension D=fractal dimension

◦ Amount of variation in the structure

◦

Measure of roughness or fragmentation of the object Small d-less jagged

Large d-more jagged

Self similar objects◦ nsd=1 (Some books write this as ns-d=1)

s=scaling factor

n number of subparts in subdivision

d=ln(n)/ln(1/s) [d=ln(n)/ln(s) however s is the number of segments versus how much the

main segment was reduced

I.e. line divided into 3 segments. Instead of saying the line is 1/3, sayinstead there are 3 sements. Notice that 1/(1/3) = 3]

◦ If there are different scaling factors

Sk d=1

K=1

n

Figuring out scaling factorsI prefer: ns-d=1 :d=ln(n)/ln(s)

Dimension is a ratio ofthe (new size)/(old size)

◦ Divide line into n identicalsegments

n=s

◦ Divide lines on square intosmall squares by dividingeach line into n identicalsegments

n=s2 small squares

◦ Divide cube

Get n=s3 small cubes

Koch’s snowflake

◦ After division have 4 segments

n=4 (new segments)

s=3 (old segments)

Fractal Dimension

D=ln4/ln3 = 1.262

◦ For your reference: Book method

n=4

Number of new segments

s=1/3

segments reduced by 1/3

d=ln4/ln(1/(1/3))



11/10/20

Perspective Projection

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