IT- 601: Computer Graphics

Lecture-03Scan Conversion

Jesmin Akhter Lecturer,IIT

Jahangirnagar University, Savar, Dhaka,Bangladesh

04/21/23

Midpoint Ellipse Algorithm

• Implicit equation is: F(x,y) = b2x2 + a2y2 – a2b2 = 0• We have only 4-way symmetry• There exists two regions

– In Region 1 dx > dy• Increase x at each step• y may decrease

– In Region 2 dx < dy• Decrease y at each step• x may increase

Region 1

Region 2 S SE

E

SE

(x1,y1)(-x1,y1)

(x1,-y1)(-x1,-y1)

(-x2,y2)

(-x2,-y2)

(x2,y2)

(x2,-y2)

Midpoint Ellipse Algorithm

)22()32(

)()2(

),2(

SE tomove then 0 if

)32(

)()2(

),2(

),1(x),y(xE; tomove then 0 if

)()1(

),1(

22

222322

23

1

21

22221222

21

1

i1i1i

22221222

21

iiii

ii

iii

iii

ii

iii

ii

ii

iii

yaxbdd

bayaxb

yxFd

d

xbdd

bayaxb

yxFd

yd

bayaxb

yxFd

M

E

Pre

vio

us

Curr

ent

Next

),1( 21 ii yx ),2( 2

1 yx

SE

),2( 23 ii yx

Midpoint of the vertical line connecting E and SE is used to define the following decision parameter:

Decision Parameter (Region 1)Decision Parameter (Region 1)

),( ii yxp

iy

1iy

2iy

ix 1ix 2ix

Initial value with (0,b)

4/)2

1( 22222222

1 ababbababp

Midpoint Ellipse Algorithm

)32(

)2()(

)2,(

1)-y,(x)y,S(x tomove then 0 if

)32()22(

)2()(

)2,(

1)-y1,(x)y,SE(x tomove then 0 if

)1()(

)1,(

21

22222212

21

1

jj1j1j

221

22222232

23

1

jj1j1j

22222212

21

jjj

jj

jjj

j

jjjj

jj

jjj

j

jj

jjj

yadd

bayaxb

yxFd

d

yaxbdd

bayaxb

yxFd

d

bayaxb

yxFd

MS

Pre

vio

us

Curr

ent

Next

)1,( 21 jj yx

)2,( 21 jj yx

SE

)2,( 23 jj yx

)( jj yxp jx 1jx 2jx

jy

1jy

2jy

Decision Parameter (Region 2)Decision Parameter (Region 2)

Self Study

• Pseudo code for midpoint ellipse algorithm • Solved Problems:

3.1,3.2,3.6,3.7,3.10,3.11,3.12,3.20,3.21

Side Effects of Scan Conversion

The most common side effects when working with

raster devices are:

1. Aliasing

2. Unequal intensity

3. Overstrike

In computer graphics, a raster graphics image, or

bitmap, is a dot matrix data structure representing a

rectangular grid of pixels, or points of color, viewable

via a monitor, paper, or other display medium

1. AliasingJagged appearance of curves or diagonal lines on a display screen, which is caused by low screen resolution.

Refers to the plotting of a point in a location other than its true location in order to fit the point into the raster.

Consider equation y = mx + bFor m = 0.5, b = 1 and x = 3 : y = 2.5

So the point (3,2.5) is plotted at alias location (3,3)

RemedyApply anti-aliasing algorithms. Most of these algorithms introduce extra pixels and pixels are intensified proportional to the area of that pixel covered by the object.

2. Unequal IntensityHuman perception of light is dependent on Density and Intensity of light source.

Thus, on a raster display with perfect squareness, a diagonal line of pixels will appear dimmer that a horizontal or vertical line.

Remedy1. By increasing the number of pixels on diagonal

lines.

1.44

1

3. OverstrikeThe same pixel is written more than once.

This results in intensified pixels in case of photographic media.

RemedyCheck each pixel to see whether it has already been written to prior to writing a new point.

10

ExampleExample

i pi xi+1, yi+1 2ry2xi+1 2rx2yi+1

0 -332 (1, 6) 72 768

1 -224 (2, 6) 144 768

2 -44 (3, 6) 216 768

3 208 (4, 5) 288 640

4 -108 (5, 5) 360 640

5 288 (6, 4) 432 512

6 244 (7, 3) 504 384

rx = 8 , ry = 6

2ry2x = 0 (with increment 2ry

2 = 72)

2rx2y = 2rx

2ry (with increment -2rx2 = -128)

Region 1Region 1 (x0, y0) = (0, 6)

2 2 210 41 332y x y xp r r r r

Move out of region 1 since2ry

2x > 2rx2y

11

ExampleExample

6

5 4 3

2 1 0

0 1 2 3 4 5 6 7 8

i pi xi+1, yi+1 2ry2xi+1 2rx2yi+1

0 -151 (8, 2) 576 256

1 233 (8, 1) 576 128

2 745 (8, 0) - -

Region 2Region 2 (x0, y0) = (7, 3) (Last position in region 1)

10 22 (7 ,2) 151ellipsep f

Stop at y = 0

12

ExercisesExercises

• Draw the ellipse with rx = 6, ry = 8.

• Draw the ellipse with rx = 10, ry = 14.

• Draw the ellipse with rx = 14, ry = 10 and center at (15, 10).