TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Affiliated to Institution of G.G.S.IP.U, Delhi

Scan Conversion

Himja Sethi

Assistant Professor

Course BCA

Paper Title Computer Graphics

Paper Code BCA 303

Paper ID 20303

Quick Overview of Syllabus

Unit I Unit II

Applications of computer graphics

Video display technologies

Raster scan systems

Graphics related input and output

devices

Computer graphics related

software

Scan conversion of line, circle and

ellipse using algorithms, DDA,

Bresenham, mid-point

2D and 3D geometric transformations

(Translation, Rotation, Scaling,

Shearing, Reflection)

Composite transformations and its

practical application through numericals

Homogenous coordinates

Antialiasing

Window to viewpoint transformation

Clipping algorithms (Cohen Sutherland,

Cyrus Beck, Midpoint Subdivision)

Quick Overview of Syllabus

Unit III Unit IV

Parametric Cubic Curve Representation

Solid modelling

Types of surface representations Wireframe

Sweep

Spatial Partitioning

Boundary

Octree

Comparison amongst all of the above

User interfaces for solid modelling

3D objects and related concepts

Projection

Types of projection Parallel Orthographic

Oblique

Perspective

3D clipping Cohen Sutherland

Hidden surface removal Depth buffer / z-buffer algo Depth sorting algo

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Course BooksTEXT BOOKS:

Foley, Van Dam, Feiner, Hughes, Computer Graphics Principles & Practice, 2000, Pearson

Chennakesava R. Alavla “Computer Graphics”, PHI Learning Pvt. Limited

REFERENCES BOOKS:

D. Hearn & Baker: Computer Graphics with OpenGL, Pearson Education, Third Edition,2009.

Foley, J.D. & Van Dam, A: Fundamentals of Interactive Computer Graphics.

Rogers & Adams, “Mathematical Elements for Computer Graphics”, McGraw Hill, 1989.

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

How to Attempt a Question?

Introduction

Definition

Point-wise description

Examples, if any

Conclusion

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Marking Scheme

Internal

25 marks (10 marks I minor +10 marks II

minor + 5 marks internal assessment)

External

75 marks (Major semester exam)

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Affiliated to Institution of G.G.S.IP.U, Delhi

Lets begin with…

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Applications of Computer Graphics

around us

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Yes, that’s right…

Gaming

Animation Movies

3D object simulation for engineering, manufacturing etc

Virtual Reality Simulation for pilot training, surgical practice

etc

Computer Aided Design

And many more…

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Computer GraphicsTypes Of Computer Graphics

Raster Graphics

Primitive drawing using coordinate positions for each pixel

Vector graphics

Primitive drawing using pre-defined mathematical functions

Main focus of the course is Raster Graphics

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Raster Graphics

Definition : Raster graphics, also called bitmap

graphics, are digital images that are composed of

tiny rectangular pixels that are arranged in a grid

(or raster) of x and y coordinates in such a way

that it forms an image.

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Drawing a Line on the Computer

Screen

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Solution

Three approaches for solution are :

Equation of line , y = mx + c

DDA algorithm, step increments in x / y

Bresenham’ s algorithm, using a decision variable to

find the right pixel

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Equation of line

y= mx + c, where m = (y2 – y1) / x2 – x1)

Through an example we can see that ,it is

Quite expensive

Involves floating point multiplication for each and

every pixel

Requires large amount of memory space and

processing time.

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Scan Conversion Algorithms

Raster scan or scan conversion of a line involves finding the

right pixels to plot on the computer screen. Following

algorithms are used to achieve the solution

Digital Differential Analyzer Algorithm

Bresenham’s Algorithm

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

DDA Algorithm

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

DDA Pseudocode

m = (y2-y1)/(x2-x1)

dx = x2 – x1

dy = y2 – y1

Putpixel (x1, y1)

X = x1

Y = y1

If (dx > dy)

steps = dx

Else

steps = dy

While(x <= x2 || y <= y2)

xinc = x + dx/steps

yinc = y + dy/steps

putpixel (x,y)

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Analysis of DDA Algorithm

Advantages

Simple to understand

Easy to implement

Disadvantages

Expensive computation

Floating point division and addition

(i.e. slope m can be in decimal )

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Analysis of DDA Algorithm

Advantages

Simple to understand

Easy to implement

Disadvantages

Expensive computation

Floating point division and addition

(i.e. slope m can be in decimal )

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Bresenham’s Line Drawing Algorithm

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Bresenham’s Pseudocode (for slope

|m| <1)Dy = y2 – y1

Dx = x2 – x1

X = x1

Y=y1

Putpixel (x1, y1)

P = 2dy – dx // decision variable

While (x <= x2 || y <= y2)

x = x + 1

if (p< 0)

p = p + 2dy // plot east pixel

else

p = p + 2dy – 2dx

y = y +1 // plot north east pixel

Putpixel (x,y)

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Analysis of Bresenham’s Algo

Advantages

Only integer computation

Disadvantages

Lacks precision

Aliasing / staircasing

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Antialiasing

Removing the jaggies or staircase effect caused due to under-

sampling of information due to rounding off coordinate

values to pixel positions, is called anti-aliasing.

This can be achieved thorough super-sampling, area

sampling, higher resolution display systems and special

hardware configurations.

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Clipping

Identifying portions of a picture that are inside or outside a

specified region of space is referred as clipping.

Algorithms used for line clipping are:

Cohen-Sutherland clipping

Cyrus Beck clipping

Midpoint subdivision algorithm

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

2D Transformations

Translation – change of co-ordinate position along a straight

line

Rotation – repositioning along a circular path w.r.t. origin or

a specific point

Scaling – change in size of an object

Shearing – distorts shape of an object along an axis

Reflection – mirror image of an object

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

2D Transformations

Translation – change of co-ordinate position along a straight

line

Rotation – repositioning along a circular path w.r.t. origin or

a specific point

Scaling – change in size of an object

Shearing – distorts shape of an object along an axis

Reflection – mirror image of an object

TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75

Thank You