Download - Computer Graphics
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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
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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)
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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
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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.
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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
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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)
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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…
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TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75
Applications of Computer Graphics
around us
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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…
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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
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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.
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TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75
Drawing a Line on the Computer
Screen
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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
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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.
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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
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TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75
DDA Algorithm
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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)
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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 )
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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 )
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TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75
Bresenham’s Line Drawing Algorithm
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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)
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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
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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.
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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
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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
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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
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TRINITY INSTITUTE OF PROFESSIONAL STUDIESSector – 9, Dwarka Institutional Area, New Delhi-75
Thank You