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GNDU QUESTION PAPERS 2024
Bachelor of Computer Applicaon (BCA) 6th Semester
(Batch 2023-26) (CBGS)
PAPER-I: COMPUTER GRAPHICS
Time Allowed: 3 Hours Maximum Marks: 75
Note: Aempt Five quesons in all, selecng at least One queson from each secon. The
Fih queson may be aempted from any secon. All quesons carry equal marks.
SECTION-A
1. What is Computer Graphics? Which are the various applicaons of Computer Graphics?
2. (a) What is dierence between Raster scan and Random scan?
(b) Explain the pros and cons of LCD, LED and Plasma Panel display systems.
SECTION-B
3. Which are dierent Line Drawing methods? Write and Explain Bresenham's algorithm.
4. Which are 2-D transformaons? Explain any four. Also, give their matrix representaon.
SECTION-C
5. Explain the meaning of Windowing and Clipping. What is Line Clipping? Where it may be
required? Give any one Line Clipping algorithm.
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6. What is a viewport? What is Window-to-Viewport transformaon? What is its need?
SECTION-D
7. Explain any four 3-D transformaons. Give their matrix representaon.
8. What is Projecon? Explain the use and dierence between the parallel and perspecve
transformaon.
GNDU ANSWER PAPERS 2024
Bachelor of Computer Applicaon (BCA) 6th Semester
(Batch 2023-26) (CBGS)
PAPER-I: COMPUTER GRAPHICS
Time Allowed: 3 Hours Maximum Marks: 75
Note: Aempt Five quesons in all, selecng at least One queson from each secon. The
Fih queson may be aempted from any secon. All quesons carry equal marks.
SECTION-A
1. What is Computer Graphics? Which are the various applicaons of Computer Graphics?
Ans: Imagine you open your phone and watch a video, play a game, or even scroll through
Instagram. Everything you see—images, icons, animations, videos—is created using
Computer Graphics.
In simple words, Computer Graphics is the art and science of creating, storing, and
manipulating images and visual content using computers.
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It means using a computer to generate pictures, drawings, animations, and even realistic 3D
environments.
A Simple Example to Understand
Think about drawing on paper. You use a pencil to create shapes and colors.
Now imagine doing the same thing—but on a computer using software like Paint,
Photoshop, or any design tool.
That is Computer Graphics.
But it goes much further than simple drawing:
• It can create realistic movies
• Design video games
• Build 3D models of buildings
• Simulate medical operations
Types of Computer Graphics (Easy Idea)
To understand better, let’s look at two main types:
1. Raster Graphics (Pixel-Based)
• Made up of tiny dots called pixels
• Example: Photos taken from your mobile
• If you zoom too much → image becomes blurry
2. Vector Graphics (Shape-Based)
• Made using lines, curves, and shapes
• Example: Logos, icons
• Can be zoomed infinitely without losing quality
Applications of Computer Graphics
Computer Graphics is used almost everywhere in today’s world. Let’s explore its major
applications in a simple and interesting way.
1. Entertainment (Movies, Games, Animation)
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This is the most popular use of computer graphics.
Where it is used:
• Animated movies (like cartoons)
• Video games (PUBG, GTA, etc.)
• Visual effects (VFX) in films
Example:
In movies, dangerous scenes (like explosions or flying superheroes) are created using
graphics instead of real action.
Why important?
It makes content more realistic, exciting, and visually appealing.
2. Education and Training
Graphics help students understand difficult topics easily.
Examples:
• 3D models of the human body
• Science simulations (like solar system)
• Virtual labs
Why important?
It turns boring theory into interactive learning.
3. Business and Advertising
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Companies use graphics to attract customers.
Examples:
• Posters and banners
• Social media ads
• Product design visuals
• Logos and branding
Why important?
Good visuals = more attention = more sales.
4. Medical Field
Computer graphics play a huge role in healthcare.
Examples:
• X-ray, CT scan, MRI visualization
• Surgery simulations
• 3D models of organs
Why important?
Doctors can diagnose and treat patients better.
5. Engineering and Architecture
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Before building anything, engineers design it using graphics.
Examples:
• Building designs (houses, malls)
• Machine designs
• Interior layouts
Why important?
Helps visualize projects before actual construction.
6. User Interfaces (UI)
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Every app or website you use has graphics.
Examples:
• Buttons, icons, menus
• Mobile apps
• Websites
Why important?
Makes software easy and attractive to use.
7. Scientific Visualization
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Used to represent complex data visually.
Examples:
• Weather forecasting maps
• Space simulations
• Graphs and charts
Why important?
Helps scientists understand large data easily.
8. Virtual Reality (VR) and Augmented Reality (AR)
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This is the future of computer graphics.
Examples:
• VR games
• AR apps (placing furniture in your room virtually)
• Training simulations
Why important?
Creates immersive, real-like experiences.
Conclusion
Computer Graphics is not just about drawing images—it is about bringing imagination to
life using computers.
From movies to medicine, from education to engineering, it plays a vital role in almost every
field. It helps us:
• Understand complex ideas
• Create beautiful designs
• Improve communication
• Experience virtual worlds
In today’s digital world, computer graphics is everywhere—even if we don’t notice it.
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2. (a) What is dierence between Raster scan and Random scan?
(b) Explain the pros and cons of LCD, LED and Plasma Panel display systems.
Ans: 2. (a) Difference between Raster Scan and Random Scan
First, Imagine This…
Think of your computer screen like a canvas for painting.
Now, there are two different ways to draw on that canvas:
1. One method paints line by line (like filling a coloring book row by row)
2. The other draws only the required shapes directly (like sketching with a pencil)
These two methods are exactly what we call:
• Raster Scan
• Random Scan (Vector Scan)
What is Raster Scan?
In a Raster Scan, the screen is divided into tiny dots called pixels.
The system:
• Starts from the top-left corner
• Moves left to right
• Then goes to the next line
• Continues until the entire screen is filled
Just like reading a book: line by line.
Diagram of Raster Scan
→ → → → → → →
→ → → → → → →
→ → → → → → →
→ → → → → → →
Each arrow shows how the beam moves across the screen.
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Simple Example
Think of watching a movie or image on your phone:
• Every image is made of millions of pixels
• Each pixel has a color
• The screen refreshes many times per second
That’s Raster Scan working behind the scenes.
What is Random Scan (Vector Scan)?
In Random Scan, the system:
• Does not scan the entire screen
• It only draws the required shapes or lines
Like drawing a triangle:
Instead of coloring the whole page, it only draws the three lines of the triangle
Diagram of Random Scan
/\
/ \
/____\
The beam directly draws these lines instead of scanning the whole screen.
Simple Example
Imagine using a pen tool in drawing software:
• You click points
• Lines appear directly between them
That’s how Random Scan works.
Key Differences (Very Easy Table)
Feature
Raster Scan
Random Scan
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Drawing Method
Line by line (full screen)
Draws only required shapes
Speed
Slower (covers entire screen)
Faster for simple drawings
Image Type
Best for photos & videos
Best for line drawings
Memory Use
High (stores pixels)
Low (stores coordinates)
Quality
Can blur when zoomed
Very sharp lines
Example
TV, Mobile, LCD screens
Old vector displays, CAD systems
Final Understanding
• Raster Scan = Pixel-based (paint everything)
• Random Scan = Line-based (draw only what is needed)
2. (b) LCD, LED, and Plasma Display Systems
Now let’s move to the second part.
Imagine you are buying a TV. You see options like:
• LCD
• LED
• Plasma
But what do these actually mean?
Let’s simplify it.
1. LCD (Liquid Crystal Display)
What is LCD?
LCD uses liquid crystals that control light to produce images.
Important: LCD does not produce its own light
It needs a backlight (usually fluorescent light)
Basic Structure of LCD
[Backlight] → [Liquid Crystals] → [Screen]
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How It Works
• A light shines from behind
• Liquid crystals act like tiny shutters
• They control how much light passes
• This creates images on the screen
Advantages of LCD
✔ Thin and lightweight
✔ Uses less power than CRT
✔ Affordable
✔ Good for everyday use
Disadvantages of LCD
✖ Limited viewing angles
✖ Lower contrast (blacks look grayish)
✖ Slower response time (motion blur possible)
2. LED (Light Emitting Diode Display)
What is LED?
LED is actually an advanced version of LCD.
The only difference:
• Instead of fluorescent backlight, it uses LED lights
Structure of LED
[LED Backlight] → [Liquid Crystals] → [Screen]
Simple Explanation
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Think of LED as:
Better lighting for LCD
Because LEDs are:
• Brighter
• More efficient
• More controllable
Advantages of LED
✔ Better brightness
✔ Higher contrast (deeper blacks)
✔ Energy efficient
✔ Slim design
✔ Longer life
Disadvantages of LED
✖ Slightly expensive than LCD
✖ Still depends on backlight (not true black like OLED)
3. Plasma Display
What is Plasma?
Plasma displays use tiny gas cells filled with plasma.
Each cell:
• Emits light when electricity passes through it
Unlike LCD/LED, Plasma creates its own light
Structure of Plasma
[Gas Cells (Plasma)] → Emit Light → Form Image
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How It Works
• Each pixel contains gas
• When electricity flows → gas glows
• This creates colors and images
Advantages of Plasma
✔ Excellent color quality
✔ Deep blacks
✔ Wide viewing angles
✔ Smooth motion (great for sports)
Disadvantages of Plasma
✖ High power consumption
✖ Heavier and thicker
✖ Can suffer from screen burn-in
✖ Not commonly used now
Comparison Table (Very Easy)
Feature
LCD
LED
Plasma
Light Source
Fluorescent
LED
Self-light (gas)
Thickness
Thin
Very thin
Thick
Power Use
Medium
Low
High
Picture Quality
Good
Very good
Excellent
Black Levels
Weak
Better
Best
Price
Low
Medium
High (earlier)
Usage Today
Still used
Most popular
Almost discontinued
Final Summary
Raster vs Random Scan
• Raster = Full screen scanning (pixels)
• Random = Draw only shapes (lines)
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LCD vs LED vs Plasma
• LCD = Basic display (uses backlight)
• LED = Improved LCD (better lighting)
• Plasma = Self-light display (best quality but outdated)
Real-Life Analogy to Remember Everything
• Raster Scan = Coloring an entire notebook page
• Random Scan = Drawing only the picture lines
• LCD = Tube light behind screen
• LED = Smart, bright LED bulbs
• Plasma = Tiny glowing fireflies making images
SECTION-B
3. Which are dierent Line Drawing methods? Write and Explain Bresenham's algorithm.
Ans: Line Drawing Methods in Computer Graphics
When we draw a straight line on a computer screen, it may look simple—but internally, the
computer has to decide which pixels to turn ON to make that line look smooth and
continuous.
Since screens are made up of tiny square pixels, drawing a perfect straight line (which is
continuous in mathematics) becomes a discrete problem in computer graphics.
To solve this, different line drawing algorithms are used.
Different Line Drawing Methods
There are mainly three popular line drawing methods:
1. Direct (Equation-Based) Method
• Uses the equation of a line:
y = mx + c
• For every x, we calculate y.
• Simple but slow because it involves floating-point calculations.
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Problem: Computers prefer integers, and floating-point operations are expensive.
2. Digital Differential Analyzer (DDA) Algorithm
• Improves the direct method.
• Calculates small incremental changes in x and y.
• Uses floating-point arithmetic.
Advantage: Easy to understand
Disadvantage: Still uses decimal calculations → less efficient
3. Bresenham’s Line Drawing Algorithm (Most Important)
• Uses only integer calculations
• Very fast and efficient
• Widely used in computer graphics systems
This is the algorithm you are asked to explain in detail.
Understanding Bresenham’s Algorithm (In a Simple Way)
Let’s imagine:
You want to draw a line from point (x₁, y₁) to (x₂, y₂) on a pixel grid.
But the computer cannot draw a continuous line—it must choose which pixels best
approximate that line.
Basic Idea
At each step, the algorithm decides:
Should we move:
• Straight right (E pixel)
OR
• Right and up (NE pixel)
This decision is made using a decision parameter (p).
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Visual Idea
Think of it like climbing stairs:
• You either go right (→)
• Or right + up (↗)
The algorithm chooses the best step to stay closest to the actual line.
Assumptions (for simplicity)
We assume:
• Line slope is between 0 and 1
• Line moves from left to right
Steps of Bresenham’s Algorithm
Step 1: Input Points
Given:
• Starting point → (x₁, y₁)
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• Ending point → (x₂, y₂)
Step 2: Calculate Differences
• Δx = x₂ − x₁
• Δy = y₂ − y₁
Step 3: Initialize Decision Parameter
p₀ = 2Δy − Δx
Step 4: Start Plotting
Start from (x₁, y₁)
At each step:
• If p < 0 → choose E (x+1, y)
• If p ≥ 0 → choose NE (x+1, y+1)
Step 5: Update Decision Parameter
If E is chosen:
p = p + 2Δy
If NE is chosen:
p = p + 2Δy − 2Δx
Step 6: Repeat until x = x₂
Step-by-Step Example
Let’s draw a line from (0,0) to (5,3)
Calculate:
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• Δx = 5
• Δy = 3
• p₀ = 2(3) − 5 = 6 − 5 = 1
Iteration Table
Step
x
y
p
Decision
1
0
0
1
NE
2
1
1
-3
E
3
2
1
3
NE
4
3
2
-1
E
5
4
2
5
NE
6
5
3
—
End
Visual Representation
Each dot represents a pixel chosen by the algorithm.
Why Bresenham is Better?
Advantages
• Uses only integer calculations
• Faster than DDA
• No floating-point operations
• Efficient for hardware implementation
Limitations
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• Original version works best for slope between 0 and 1
• Needs modification for:
o Negative slopes
o Steep lines
Intuition (Very Important!)
Instead of calculating exact y-values (like DDA), Bresenham:
Tracks the error between the actual line and chosen pixel
• If error becomes large → move diagonally (NE)
• If error is small → move horizontally (E)
So basically:
It always tries to stay closest to the real line
Decision Concept Visualization
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The algorithm checks which pixel is closer to the real line using a midpoint test.
Pseudocode (Simple)
Input: (x1, y1), (x2, y2)
dx = x2 - x1
dy = y2 - y1
p = 2*dy - dx
x = x1
y = y1
Plot(x, y)
while x < x2:
x = x + 1
if p < 0:
p = p + 2*dy
else:
y = y + 1
p = p + 2*dy - 2*dx
Plot(x, y)
Final Conclusion
Line drawing in computer graphics is not as simple as drawing on paper. Since computers
work with pixels, they must approximate a straight line using discrete points.
We studied three main methods:
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• Direct Method (simple but slow)
• DDA Algorithm (better but uses decimals)
• Bresenham’s Algorithm (best and fastest)
Bresenham’s algorithm stands out because:
• It uses integer math
• It is fast and accurate
• It is widely used in graphics systems
4. Which are 2-D transformaons? Explain any four. Also, give their matrix representaon.
Ans: What are 2-D Transformations?
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Imagine you have a shape drawn on paper—like a triangle or square. Now, what if you
move it, rotate it, resize it, or flip it? These changes are called 2-D transformations.
The term 2-D (two-dimensional) means the shape exists on a flat surface (X and Y axes).
A transformation means changing the position, size, or orientation of the shape.
So, in simple words:
2-D transformations are operations that change a shape's position, size, or direction on a
2D plane.
Types of 2-D Transformations
There are mainly five types:
1. Translation (Shifting)
2. Rotation (Turning)
3. Scaling (Resizing)
4. Reflection (Flipping)
5. Shearing (Slanting)
In your question, you need to explain any four, so we’ll cover the most important ones
in detail.
1. Translation (Shifting)
Concept
Translation means moving the object from one place to another without changing its
shape, size, or orientation.
Think of sliding a book on a table—it doesn’t rotate or change size.
Formula
If a point is (x, y) and we move it by (tx, ty):
Matrix Representation
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Visual Understanding
The triangle simply shifts to a new position.
2. Rotation (Turning)
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Concept
Rotation means turning the object around a fixed point (usually the origin).
Example: Rotating a clock hand.
Formula (Anti-clockwise rotation by angle θ)
Matrix Representation
Visual Understanding
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The shape turns around the origin but keeps its size and shape.
3. Scaling (Resizing)
Concept
Scaling means changing the size of the object.
• If size increases → Enlargement
• If size decreases → Reduction
Formula
Where:
•
= scaling factor in x-direction
•
= scaling factor in y-direction
Matrix Representation
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Visual Understanding
The shape becomes bigger or smaller but keeps its form.
4. Reflection (Flipping)
Concept
Reflection means flipping the object like a mirror image.
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Example: Your image in a mirror.
Common Cases
1. Reflection about X-axis
2. Reflection about Y-axis
Matrix Representation
About X-axis:
About Y-axis:
Visual Understanding
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The object flips to the opposite side like a mirror.
Quick Summary Table
Transformation
What it does
Shape Change
Size Change
Translation
Moves object
No
No
Rotation
Turns object
No
No
Scaling
Resizes object
No
Yes
Reflection
Flips object
No
No
Why Are 2-D Transformations Important?
These transformations are widely used in:
• Computer Graphics (games, animation)
• Mobile apps & UI design
• Maps and GPS systems
• Robotics and simulations
Final Understanding
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2-D transformations are mathematical ways to move, rotate, resize, or flip shapes on a flat
surface using coordinates and matrices.
SECTION-C
5. Explain the meaning of Windowing and Clipping. What is Line Clipping? Where it may be
required? Give any one Line Clipping algorithm.
Ans: Understanding Windowing, Clipping, and Line Clipping
You are looking outside through a window of your house.
You can only see the part of the world that fits inside that window, right?
Anything outside the window is not visible, even though it exists.
This simple idea is exactly what Windowing and Clipping mean in computer graphics.
1. What is Windowing?
Meaning:
Windowing is the process of selecting a specific rectangular area of a larger scene that we
want to display.
Think of it as:
“Choosing what part of the scene you want to look at.”
Simple Example:
Suppose a computer screen has a big map, but you only want to zoom into a small region.
That selected region is called the Window.
Diagram (Windowing Concept)
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Key Points:
• Window defines what part of the world you want to see
• It is usually a rectangular area
• It works in world coordinates
2. What is Clipping?
Meaning:
Clipping is the process of removing the parts of objects that lie outside the window.
“Cutting off what you don’t want to show.”
Simple Example:
Imagine:
• A long line passes through your window
• Only the part inside the window is visible
• The rest is removed (clipped)
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Diagram (Clipping Concept)
Key Points:
• Clipping removes unwanted parts
• Only visible portion remains
• It improves performance and clarity
3. What is Line Clipping?
Meaning:
Line Clipping is a special type of clipping where we deal only with lines.
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It determines which part of a line lies inside the window and displays only that part.
Simple Understanding:
A line can be in 3 situations:
1. Completely inside → Show full line
2. Completely outside → Remove it
3. Partially inside → Show only visible part
Diagram (Line Clipping Cases)
Why is Line Clipping Important?
Line clipping is required in many real-life computer applications:
Where it is used:
• Computer graphics (games, animations)
• CAD software (AutoCAD)
• Map systems (Google Maps)
• UI design (screen rendering)
• Video games (only visible objects are drawn)
Why needed?
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Without clipping:
• The system would try to draw everything (even invisible parts)
• This wastes time and memory
With clipping:
• Only visible parts are processed
• Faster and efficient rendering
4. One Line Clipping Algorithm: Cohen–Sutherland Algorithm
Name:
Cohen–Sutherland Line Clipping Algorithm
6. What is a viewport? What is Window-to-Viewport transformaon? What is its need?
Ans: 1. What is a Viewport?
Imagine you are standing inside a room and looking outside through a window.
• You cannot see the entire outside world.
• You can only see a part of it through the window.
That visible area is exactly what we call a viewport in computer graphics.
Simple Definition:
A viewport is the rectangular area on the screen where the final image is displayed.
Diagram 1: Viewport Concept
Outside World (Scene)
---------------------------------
| |
| (Many objects) |
| |
| +---------------+ |
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| | Viewport | |
| | (What you see)| |
| +---------------+ |
| |
---------------------------------
Example:
• When you play a game , you don’t see the whole virtual world.
• You only see the part inside your screen → that is the viewport.
2. What is a Window?
Before understanding transformation, you must know what a window is.
A window is the part of the world coordinates that you choose to display.
In simple words:
• Window = what you want to see
• Viewport = where you show it on screen
Diagram 2: Window vs Viewport
World Coordinates (Big Area)
---------------------------------
| |
| +-------------+ |
| | Window | |
| | (Selected | |
| | area) | |
| +-------------+ |
| |
---------------------------------
Screen (Device Coordinates)
-------------------------
| Viewport |
| (Display area) |
-------------------------
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3. What is Window-to-Viewport Transformation?
Now comes the main concept.
Imagine:
• You select a small area (window) from a big world.
• You want to display it on your screen (viewport).
But the sizes may be different!
So what do we do?
We transform (convert) the coordinates from the window to the viewport.
Definition:
Window-to-Viewport Transformation is the process of mapping a selected part of the
world (window) onto a specific area of the screen (viewport).
Diagram 3: Transformation Process
WORLD (Window) SCREEN (Viewport)
+-------------+ +-------------+
| | | |
| Window | ---------> | Viewport |
| | | |
+-------------+ +-------------+
4. How Does the Transformation Work?
Don’t worry, we’ll keep it very simple.
The system rescales the selected area to fit the screen.
Think like this:
• A small map printed on paper
• Enlarged on a projector screen
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Same idea!
Diagram 4: Scaling Effect
Window (Small) Viewport (Large)
+-------+ +---------------+
| | | |
| * | -----------> | * |
| | | |
+-------+ +---------------+
The object stays the same, only its size and position change.
5. Simple Formula (Basic Idea)
You don’t need to memorize deeply, just understand:
The computer calculates new coordinates using scaling.
• X and Y positions are adjusted
• Proportions are maintained
So the image does not get distorted (if done correctly)
6. Why Do We Need Window-to-Viewport Transformation?
This is the most important part.
Let’s understand through real-life situations.
1. To Display Only Required Area
You don’t always want the whole world.
Example:
• Google Maps
• You zoom into your city, not the whole Earth
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Window = selected area
Viewport = your screen
2. To Zoom In and Zoom Out
• Zoom In → small window → large viewport
• Zoom Out → large window → same viewport
Diagram 5: Zoom Effect
Zoom In:
Window (Small) → Viewport (Same size) → Object looks bigger
Zoom Out:
Window (Large) → Viewport (Same size) → Object looks smaller
3. To Fit Different Screen Sizes
Devices have different screen sizes:
• Mobile
• Laptop
• TV
Transformation ensures the image fits properly everywhere.
4. Used in Games and Graphics
In games:
• The world is huge
• You only see a portion (viewport)
As you move, the window changes dynamically.
5. To Control Viewing Area
You can:
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• Focus on a specific region
• Ignore unnecessary parts
This improves performance and clarity.
7. Easy Analogy to Remember
Think of this:
Window = Camera lens
Viewport = Photo frame
• Camera captures a part of the world → Window
• Photo is displayed on frame → Viewport
8. Final Summary
Let’s quickly revise:
✔ Viewport
• Area on the screen where image is displayed
✔ Window
• Selected part of the world you want to see
✔ Window-to-Viewport Transformation
• Process of mapping window to viewport
• Includes scaling and coordinate conversion
Conclusion
In simple words, this whole concept is about:
“Selecting what to see and deciding how to show it.”
• Window → What you choose
• Viewport → Where you show
• Transformation → How you fit it
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This concept is very important in:
• Computer Graphics
• Games
• UI Design
• Simulation systems
SECTION-D
7. Explain any four 3-D transformaons. Give their matrix representaon.
Ans: Understanding 3-D transformations may sound complex at first, but if we relate them
to real-life movements, they become much easier and even interesting to learn. Imagine
you are holding a cube in your hand—you can move it, rotate it, resize it, or even flip it. All
these actions are examples of 3-D transformations.
In computer graphics and mathematics, a 3-D transformation is used to change the
position, size, or orientation of an object in 3D space (which has x, y, and z axes). These
transformations are represented using matrices so that computers can process them easily.
1. Translation (Moving an Object)
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Concept:
Translation means moving an object from one place to another without changing its shape
or size.
Think of it like:
• Sliding a book on a table
• Moving a chair from one corner to another
The object remains exactly the same—only its position changes.
Mathematical Idea:
If a point is given as:
After translation by
, the new point becomes:
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Matrix Representation (Homogeneous Form):
Simple Insight:
• No change in shape or size
• Only position changes
• Very useful in animations and games
2. Scaling (Changing Size)
Concept:
Scaling means changing the size of an object.
Think of it like:
• Zooming in (object becomes bigger)
• Zooming out (object becomes smaller)
Types:
1. Uniform Scaling → Same scale in all directions
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2. Non-uniform Scaling → Different scaling on x, y, z axes
Mathematical Idea:
If scaling factors are
, then:
Matrix Representation:
Simple Insight:
• Changes size but not shape (if uniform)
• Used in zoom effects and resizing objects
3. Rotation (Turning an Object)
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Concept:
Rotation means turning an object around an axis.
Imagine:
• Rotating a globe
• Spinning a toy
• Turning a Rubik’s cube
In 3D, rotation can happen around:
• X-axis
• Y-axis
• Z-axis
Example: Rotation about Z-axis
Matrix Representation (Rotation about Z-axis):
Simple Insight:
• Object spins but stays same size
• Important in 3D animation, robotics, gaming
4. Reflection (Mirror Effect)
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Concept:
Reflection means flipping an object like a mirror image.
Think of:
• Your reflection in a mirror
• Flipping a page upside down
Example: Reflection in XY-plane
(Z-coordinate changes sign)
Matrix Representation:
Simple Insight:
• Creates mirror image
• Used in graphics, symmetry, design
Final Summary (Easy to Remember)
Transformation
What it Does
Key Idea
Translation
Moves object
Position change
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Scaling
Resizes object
Size change
Rotation
Turns object
Orientation change
Reflection
Flips object
Mirror image
Final Understanding
If you imagine a 3D cube, you can:
• Move it → Translation
• Resize it → Scaling
• Spin it → Rotation
• Flip it → Reflection
That’s all 3-D transformations are!
8. What is Projecon? Explain the use and dierence between the parallel and perspecve
transformaon.
Ans: What is Projection?
Imagine you’re standing outside on a sunny day. You hold your hand up, and the sunlight
casts a shadow of your hand on the ground. That shadow is a projection of your hand. Your
hand is three-dimensional, but the shadow is two-dimensional. Projection is basically the
process of mapping 3D objects onto a 2D plane.
In computer graphics, engineering drawing, or even art, projection is used to represent 3D
objects on flat surfaces. Without projection, we couldn’t draw buildings, design cars, or even
play video games realistically.
Why Do We Use Projection?
• To visualize 3D objects on paper or screen.
• To communicate designs (architects, engineers, and designers rely on it).
• To make movies and games look real by simulating how our eyes see the world.
So, projection is the bridge between the real world (3D) and the way we represent it (2D).
Two Main Types of Projection
There are many kinds of projections, but the two most important ones are:
1. Parallel Projection
2. Perspective Projection
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Let’s explore both with simple analogies.
1. Parallel Projection
Think of parallel projection like looking at a building blueprint. In this method, the lines of
sight (the imaginary rays from your eyes to the object) are parallel to each other. That
means objects don’t shrink with distance—they look the same size no matter how far they
are.
Example: Imagine you’re looking at a long railway track from above in a drone shot. The
rails look parallel and never meet. That’s parallel projection.
Key Features:
• Preserves the true size and shape of objects.
• Good for technical drawings (engineering, architecture).
• Doesn’t look “realistic” because in real life, things appear smaller when farther away.
2. Perspective Projection
Now, perspective projection is how your eyes naturally see the world. Here, the lines of
sight converge at a single point (called the “vanishing point”). That’s why distant objects
look smaller.
Example: Stand on a railway track and look ahead. The rails seem to meet at a point in
the distance. That’s perspective projection.
Key Features:
• Mimics human vision.
• Objects farther away appear smaller.
• Perfect for art, movies, and games because it feels realistic.
Diagrams to Make It Clear
Here are some simple diagrams to help you visualize:
Diagram 1: Parallel Projection (Lines stay parallel)
Object -----> || || || (Projection rays are parallel)
Diagram 2: Perspective Projection (Lines converge at a point)
Object -----> \ | / (Projection rays meet at vanishing
point)
Diagram 3: Railway Track Example Parallel (Drone view): || || Perspective (Human view): \
/
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Diagram 4: Cube in Parallel Projection Looks like a neat box, all sides equal, no shrinking.
Diagram 5: Cube in Perspective Projection Front face looks bigger, back face looks smaller,
giving depth.
Differences Between Parallel and Perspective Projection
Feature
Parallel Projection
Perspective Projection
Rays
Parallel
Converge at a point
Realism
Less realistic
Very realistic
Size of distant objects
Same size
Smaller with distance
Use cases
Engineering, CAD
Art, movies, games
A Relatable Story
Imagine two friends, Arjun and Meera, both sketching a house.
• Arjun uses parallel projection. His drawing looks like a technical blueprint—accurate,
but flat. The windows at the back are the same size as the ones in front.
• Meera uses perspective projection. Her drawing looks like a painting—the front
door is big, the windows at the back look smaller, and the whole house feels like it
has depth.
Both are correct, but they serve different purposes. Arjun’s drawing is useful for builders,
while Meera’s is pleasing to the eye.
Everyday Examples
• Video Games: Use perspective projection to make worlds feel immersive.
• Engineering Drawings: Use parallel projection to ensure accurate measurements.
• Movies: Use perspective projection to mimic how our eyes see.
• Maps: Often use parallel projection so distances are consistent.
Wrapping It Up
Projection is simply the art of showing 3D objects on a 2D surface.
• Parallel projection is about accuracy and measurement.
• Perspective projection is about realism and how our eyes naturally perceive the
world.
Both are powerful tools, and understanding them helps us appreciate everything from
blueprints to blockbuster movies.
“This paper has been carefully prepared for educaonal purposes. If you noce any
mistakes or have suggesons, feel free to share your feedback.”
