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GNDU QUESTION PAPERS 2025
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 scope of Computer Graphics in Business and Industry?
2. Which are various display device technologies available? Explain the features of LCD and
Plasma display devices.
SECTION-B
3. Write and explain Bresenham's line generang Algorithm.
4. Which are various 2-d transformaons? Give their matrix representaon.
SECTION-C
5. What is Clipping? Write and explain Cohen-Sutherland Clipping Algorithm.
6. Explain following:
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(a) Windowing
(b) Clipping
(c) Window and Viewport.
SECTION-D
7. Explain translaon, scaling and rotaon as 3-D transformaons.
8. Explain dierent types of projecons.
GNDU ANSWER PAPERS 2025
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 scope of Computer Graphics in Business and Industry?
Ans: What is Computer Graphics?
Computer Graphics means using computers to create, edit, and display visual images like
pictures, designs, animations, charts, and videos. You see computer graphics everywhere—
on websites, advertisements, movies, games, and even in business reports.
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Now, let’s explore how computer graphics are used in business and industry.
1. Advertising and Marketing
One of the biggest uses of computer graphics is in advertising.
• Businesses use graphics to create eye-catching ads.
• Social media platforms like Instagram, Facebook, and YouTube depend heavily on
visuals.
• Logos, banners, posters, and videos are all created using computer graphics.
Example:
When a company launches a new product, it creates attractive posters and animations to
grab attention.
Impact:
Better visuals = More customer interest = More sales
2. Product Design and Manufacturing
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Industries use computer graphics for designing products before manufacturing them.
• Engineers use software like CAD (Computer-Aided Design).
• They create 3D models of machines, cars, buildings, and tools.
• Problems can be detected before actual production.
Example:
Car companies design complete car models on computers before building them.
Impact:
Saves time, reduces cost, improves accuracy
3. Business Presentations and Data Visualization
Businesses deal with a lot of data. Computer graphics help present this data clearly.
• Charts, graphs, and infographics make data easy to understand.
• Helps managers make better decisions.
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Example:
Sales reports shown using bar graphs instead of long tables.
Impact:
Quick understanding + Better decision-making
4. Training and Simulation
Industries use computer graphics to train employees.
• Simulators create real-life situations using graphics.
• Workers can learn without risk.
Example:
Pilots train using flight simulators instead of real planes.
Impact:
Safe learning + Reduced risk + Better skills
5. E-Commerce and Online Business
Online shopping depends heavily on visuals.
• Product images, 360° views, and animations help customers.
• Good graphics increase trust and buying decisions.
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Example:
Amazon shows multiple product images from different angles.
Impact:
Better customer experience = More online sales
6. Architecture and Construction
• Architects use graphics to design buildings.
• 3D models show how buildings will look before construction.
Example:
A house design can be visualized before it is built.
Impact:
Better planning + Fewer mistakes
7. Media, Entertainment, and Industry Promotion
• Used in movies, TV ads, and company presentations.
• Animation and visual effects attract audiences.
Example:
Company promotional videos with animation.
Impact:
Stronger brand image
Simple Diagram: How Computer Graphics Work in Business
Idea → Design (Graphics Software) → Visualization → Decision Making → Final
Product/Service
Another Diagram: Areas of Use
Computer Graphics
|
------------------------------------------------
| | | | | |
Marketing Design Data Viz Training E-Commerce
Architecture
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Conclusion
The scope of computer graphics in business and industry is very wide and continuously
growing.
From designing products to marketing them, from training employees to presenting data—
computer graphics play a crucial role everywhere.
In simple words:
Computer graphics make business more attractive, efficient, and understandable.
In today’s digital world, no business can succeed without using graphics effectively. Whether
it’s a small shop or a large industry, computer graphics help them grow and compete in the
market.
2. Which are various display device technologies available? Explain the features of LCD and
Plasma display devices.
Ans: . The Big Picture: Types of Display Technologies
Before diving into LCD and Plasma, let’s quickly list the main display technologies you might
encounter:
• CRT (Cathode Ray Tube): The old bulky TVs and monitors. Heavy, but once the king
of displays.
• LCD (Liquid Crystal Display): Slim, lightweight, and widely used in laptops, TVs, and
phones.
• LED (Light Emitting Diode): Often used as a backlight for LCDs, but also in modern
LED TVs.
• Plasma Display: Popular for large TVs in the 2000s, known for rich colors and deep
blacks.
• OLED (Organic LED): Found in high-end smartphones and TVs, offering stunning
contrast.
• MicroLED & QLED: Newer technologies pushing brightness, color, and efficiency
further.
Now, let’s zoom in on LCD and Plasma, since those are the stars of your question.
LCD (Liquid Crystal Display)
Think of LCDs like a sandwich. At the center are liquid crystals—tiny molecules that can
twist and turn when electricity passes through them. These crystals don’t glow by
themselves; they act more like shutters, controlling how much light passes through.
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How LCD Works:
1. Backlight: A lamp (often LEDs today) shines light from behind.
2. Liquid Crystals: These crystals rotate to block or allow light.
3. Color Filters: Red, green, and blue filters combine to make millions of colors.
4. Glass Layers: Everything is sealed between thin sheets of glass.
Features of LCD:
• Slim and Lightweight: Perfect for laptops and flat TVs.
• Energy Efficient: Uses less power compared to Plasma.
• Sharp Images: Great for text and graphics.
• Brightness: Works well even in bright rooms.
• Limitations: Blacks aren’t truly black (since backlight always leaks a little), and
viewing angles can be narrower.
Plasma Display
Plasma screens are like millions of tiny neon lights packed together. Each pixel is a small cell
filled with gas. When electricity excites the gas, it turns into plasma (hence the name) and
emits ultraviolet light. This UV light then hits phosphors (special chemicals) that glow in red,
green, or blue.
How Plasma Works:
1. Gas Cells: Each pixel has tiny cells filled with gas.
2. Plasma State: Electricity excites the gas into plasma.
3. Phosphors Glow: UV light makes phosphors emit visible colors.
4. Image Formation: Millions of glowing cells create the picture.
Features of Plasma:
• Deep Blacks: Since pixels can turn completely off, contrast is excellent.
• Wide Viewing Angles: Picture looks good even from the side.
• Smooth Motion: Great for fast-moving images like sports.
• Rich Colors: Very natural and vibrant.
• Limitations: Heavier, consumes more power, and can suffer from “burn-in” (static
images leaving a ghost mark).
Comparing LCD vs Plasma
Here’s a simple table to make the differences clear:
Feature
LCD
Plasma
Thickness/Weight
Slim, lightweight
Bulkier, heavier
Power Consumption
Lower
Higher
Brightness
Better in bright rooms
Best in darker rooms
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Contrast/Black Level
Moderate (backlight leakage)
Excellent (true blacks)
Viewing Angle
Narrower
Very wide
Motion Handling
Sometimes blur
Very smooth
Lifespan
Long, no burn-in
Risk of burn-in
Diagrams to Visualize
Here are some simple diagrams to help you picture the difference:
1. LCD Structure
[ Backlight ] → [ Liquid Crystals ] → [ Color Filters ] → [ Glass Screen ]
2. Plasma Pixel
[ Gas Cell ] → Electricity → Plasma → UV Light → Phosphor Glow (RGB)
3. LCD vs Plasma Light Emission
4. Viewing Angle Difference
LCD: Best straight on → fades at angles
Plasma: Looks good from any angle
Storytelling Example
Imagine you’re watching a movie at night. On an LCD TV, the dark scenes might look a little
gray because the backlight is still shining faintly. On a Plasma TV, those same scenes look
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truly black, like staring into space. But if you switch on the lights in the room, the Plasma
might look dimmer, while the LCD stays bright and clear.
Conclusion
So, in simple terms:
• LCDs are like shutters controlling a flashlight. They’re slim, efficient, and great for
everyday use.
• Plasma displays are like millions of tiny glowing candles. They give richer colors and
deeper blacks but are heavier and less energy-efficient.
Both were revolutionary in their time, but LCDs eventually won the market because they
were cheaper, lighter, and more practical. Plasma TVs, while beautiful, slowly faded away—
like a star that shone brightly but briefly.
SECTION-B
3. Write and explain Bresenham's line generang Algorithm.
Ans: Bresenham’s Line Generating Algorithm
When we draw a straight line on paper, it looks smooth and continuous. But on a computer
screen, things are different. A screen is made up of tiny square pixels arranged in a grid. So,
when we try to draw a line, the computer must decide which pixels to turn ON to make the
line look straight.
This is where Bresenham’s Line Algorithm comes in. It is one of the most efficient ways to
draw a straight line using only integer calculations (no complex decimals), which makes it
fast and suitable for computers.
What is Bresenham’s Algorithm?
Bresenham’s Line Algorithm is a method used in computer graphics to draw a straight line
between two points by selecting the best possible pixels.
It was developed by Jack Bresenham in 1962.
It avoids floating-point calculations and uses only integers → making it fast and
efficient.
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Basic Idea (In Simple Words)
Imagine you want to draw a line from point A(x₁, y₁) to point B(x₂, y₂).
At each step:
• You move one step in x-direction
• Then decide whether to:
o Stay at the same y, OR
o Move one step up (increase y)
The decision is made using a decision parameter (p).
Why Do We Need a Decision Parameter?
Because the real line may pass between two pixels, like this:
• One pixel is slightly below the line
• One is slightly above the line
The algorithm chooses the pixel closest to the actual line.
Diagram 1: Pixel Grid Representation of a Line
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This shows how a straight line becomes a “staircase” of pixels.
Steps of Bresenham’s Algorithm (For slope 0 < m < 1)
Let’s assume:
• Starting point = (x₁, y₁)
• Ending point = (x₂, y₂)
Step 1: Calculate differences
dx = x₂ - x₁
dy = y₂ - y₁
Step 2: Initialize decision parameter
p₀ = 2dy - dx
Step 3: Start from (x₁, y₁)
For each step:
• Increase x by 1
• Check value of p
Decision Making
Case 1: If p < 0
• Choose pixel (x+1, y)
• Update:
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p = p + 2dy
Case 2: If p ≥ 0
• Choose pixel (x+1, y+1)
• Update:
p = p + 2dy - 2dx
Diagram 2: Decision Between Two Pixels
This diagram shows how the algorithm chooses between two possible pixels.
Complete Algorithm (Step-by-Step)
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1. Input starting point (x₁, y₁) and ending point (x₂, y₂)
2. Compute dx and dy
3. Initialize decision parameter:
p = 2dy - dx
4. Set:
x = x₁, y = y₁
5. Plot the first point
6. Repeat until x = x₂:
o If p < 0:
▪ x = x + 1
▪ p = p + 2dy
o Else:
▪ x = x + 1
▪ y = y + 1
▪ p = p + 2dy - 2dx
o Plot (x, y)
Diagram 3: Step-by-Step Pixel Selection
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This helps you visualize how pixels are selected step-by-step.
Example (Easy Understanding)
Let’s draw a line from (2, 2) to (8, 5)
Step 1:
dx = 6
dy = 3
Step 2:
p₀ = 2×3 - 6 = 0
Step 3: Iteration
Step
x
y
p
Action
1
2
2
0
p≥0 → y+1
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2
3
3
-6
p<0 → y same
3
4
3
0
y+1
4
5
4
-6
y same
5
6
4
0
y+1
6
7
5
-6
y same
7
8
5
—
End
Diagram 4: Example Output Line
Advantages of Bresenham’s Algorithm
✔ Uses only integer calculations
✔ Faster than other methods (like DDA)
✔ Efficient for real-time graphics
✔ Easy to implement
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Limitations
• Basic version works best for slopes between 0 and 1
• Needs modification for:
o Steep lines (m > 1)
o Negative slopes
Real-Life Applications
• Computer graphics (drawing lines on screens)
• Games and animations
• CAD (Computer-Aided Design)
• Raster displays
Diagram 5: Real-world Application (Graphics Rendering)
Final Understanding (In One Line)
Bresenham’s Algorithm helps computers draw straight lines efficiently by choosing the
closest pixels using simple integer calculations.
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4. Which are various 2-d transformaons? Give their matrix representaon.
Ans: What Are 2D Transformations?
Imagine you have a simple shape, say a triangle, drawn on graph paper. A 2D
transformation is just a rule that changes the position or appearance of that triangle while
keeping it in the same 2D plane. It’s like giving instructions: “Move this shape to the right,”
or “Rotate it 90 degrees,” or “Flip it upside down.”
Mathematically, we use matrices to represent these transformations. Don’t worry if
matrices sound scary—they’re just grids of numbers that tell us how to move points around.
The Main Types of 2D Transformations
There are several key transformations you should know:
1. Translation (Shifting)
2. Scaling (Resizing)
3. Rotation (Turning)
4. Reflection (Flipping)
5. Shearing (Slanting)
Let’s explore each one step by step, with simple examples and their matrix forms.
Translation (Moving Shapes)
Translation is just moving a shape from one place to another without changing its size,
shape, or orientation. Imagine sliding a book across your desk—it’s the same book, just in a
new spot.
Matrix Representation:
If you want to move a point
by
units in the x-direction and
units in the y-direction,
the matrix looks like this (in homogeneous coordinates):
Scaling (Resizing Shapes)
Scaling makes a shape bigger or smaller. Imagine zooming in on a photo—that’s scaling.
Matrix Representation:
If you scale by
along the x-axis and
along the y-axis:
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• If
, it’s uniform scaling (shape grows evenly).
• If they’re different, the shape stretches more in one direction.
Rotation (Turning Shapes)
Rotation spins a shape around a fixed point (usually the origin). Imagine turning a steering
wheel—that’s rotation.
Matrix Representation:
For rotation by angle :
This rotates the shape counterclockwise around the origin.
Reflection (Flipping Shapes)
Reflection is like looking in a mirror. The shape flips across a line (axis).
Matrix Representation:
• Reflection across the x-axis:
• Reflection across the y-axis:
Shearing (Slanting Shapes)
Shearing slants a shape, like pushing the top of a rectangle sideways while keeping the
bottom fixed. It’s often used in computer graphics to create perspective effects.
Matrix Representation:
• Shear along x-axis:
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• Shear along y-axis:
Diagrams to Visualize
Here are some simple sketches to help you imagine:
1. Translation
Original: ▲
Moved: ▲ → shifted right
2. Scaling
Original: ▲
Scaled: ▲▲ (bigger)
3. Rotation
Original: ▲
Rotated: ◄ (turned 90°)
4. Reflection
Original: ▲
Reflected: ▼ (mirror image)
5. Shearing
Original: □
Sheared: (slanted)
Everyday Examples
• Translation: Dragging an icon on your desktop.
• Scaling: Zooming in/out on a photo.
• Rotation: Rotating a picture in your phone gallery.
• Reflection: Flipping a selfie horizontally.
• Shearing: Tilting text in a design app.
Why Matrices?
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You might wonder: why do we use matrices? Because they make it super easy to apply
multiple transformations at once. For example, if you want to rotate a shape and then move
it, you just multiply the matrices together. Computers love this because it’s fast and
efficient.
Conclusion
So, to sum it up:
• Translation moves shapes.
• Scaling resizes them.
• Rotation spins them.
• Reflection flips them.
• Shearing slants them.
All of these can be neatly represented using matrices, which act like “recipes” for how to
transform points in 2D space. Once you get the hang of these, you’ll see them everywhere—
in animations, video games, design software, and even in simple apps on your phone.
SECTION-C
5. What is Clipping? Write and explain Cohen-Sutherland Clipping Algorithm.
Ans: What is Clipping?
Imagine you are looking at a large painting through a small window. You can only see the
part of the painting that falls inside that window, while the rest is hidden. This idea is exactly
what clipping means in computer graphics.
Clipping is the process of removing the parts of an object (like lines, shapes, or images)
that lie outside a specified boundary called the clipping window.
In simple words:
Clipping = Showing only the visible part and removing the invisible part.
Why do we need Clipping?
When graphics are displayed on a screen, not everything fits perfectly inside the display
area. So we use clipping to:
• Show only the required portion
• Improve performance (avoid drawing unnecessary parts)
• Maintain clean and organized visuals
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Types of Clipping
There are different types of clipping in computer graphics:
1. Point Clipping
2. Line Clipping
3. Polygon Clipping
4. Text Clipping
In this question, we focus on Line Clipping, specifically the Cohen-Sutherland Algorithm.
Understanding Line Clipping
Suppose you draw a line that extends outside your screen. Some part is visible, and some is
outside. We need to cut the extra parts.
Diagram 1: Clipping Window Concept
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In the above idea:
• The rectangle is the clipping window
• The line may be:
o Fully inside → keep it
o Fully outside → remove it
o Partially inside → trim it
Cohen-Sutherland Line Clipping Algorithm
This is one of the most popular and efficient methods for clipping lines.
Instead of checking every point of the line, it uses a smart technique called Region Codes
(Outcodes).
Step 1: Divide the Screen into Regions
The entire area is divided into 9 regions:
• 1 central region (inside window)
• 8 surrounding regions (outside)
Diagram 2: Region Division
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Step 2: Assign Region Codes (Outcodes)
Each region is given a 4-bit binary code:
Position
Code
Top
1000
Bottom
0100
Right
0010
Left
0001
The inside region has code 0000
Diagram 3: Outcodes Explanation
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Working of the Algorithm
Now let’s understand the working step-by-step in a very simple way.
Step 3: Assign Codes to Line Endpoints
Suppose a line has two endpoints:
• P1 (x1, y1)
• P2 (x2, y2)
We calculate the region code for both points.
Step 4: Apply Three Conditions
Case 1: Line Completely Inside
• If both codes are 0000
• → Accept the line (no clipping needed)
Case 2: Line Completely Outside
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• If logical AND of both codes ≠ 0
(i.e., they share an outside region)
• → Reject the line
Case 3: Line Partially Inside
• Otherwise → Clip the line
Diagram 4: Cases of Line Clipping
Step 5: Clipping the Line
If the line is partially inside:
1. Choose one endpoint outside the window
2. Find intersection with window boundary
3. Replace the outside point with intersection point
4. Repeat until line becomes fully inside
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Diagram 5: Clipping Process
Important Formulas for Intersection
To find intersection points:
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• For vertical boundary:
x = constant
y = y1 + slope × (x - x1)
• For horizontal boundary:
y = constant
x = x1 + (1/slope) × (y - y1)
Simple Example (Easy to Understand)
Think of a line crossing a rectangle:
• One end is outside (top)
• One end is inside
Algorithm will:
• Detect "top" region using code (1000)
• Find where the line enters the rectangle
• Cut the extra part
• Keep only the visible portion
Advantages of Cohen-Sutherland Algorithm
✔ Very fast and efficient
✔ Uses simple binary operations
✔ Easy to implement
✔ Avoids unnecessary calculations
Limitations
Not ideal for complex shapes
Works mainly for rectangular clipping windows
Conclusion
The Cohen-Sutherland Clipping Algorithm is a smart and efficient way to handle line
clipping in computer graphics. Instead of checking every point, it uses region codes and
logical operations to quickly decide whether a line is:
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• Completely visible
• Completely invisible
• Or partially visible (needs clipping)
You can think of it like a security guard at a gate:
• If both points are inside → allow entry
• If both are outside in the same direction → reject
• If one is inside and one is outside → adjust and allow partially
6. Explain following:
(a) Windowing
(b) Clipping
(c) Window and Viewport.
Ans: Imagine you’re playing a video game or working on a design software. The world inside
the computer is huge—it might have thousands of objects, lines, and shapes. But your
screen is limited. You can’t see everything at once. So, how do computers decide what part
of the world to show, how to show it, and what to cut off?
That’s where windowing, clipping, and viewport come in. They are like the rules of
photography: choosing what to frame, what to crop, and how to fit the photo into a frame.
(a) Windowing
Think of a window as a rectangular area in the “world coordinate system.” The world
coordinate system is like the giant map where all objects exist. But you don’t want to see
the entire map—you just want to look at a portion of it.
Analogy:
Imagine standing in front of a huge mural on a wall. You hold a rectangular photo frame
against the mural. The part of the mural visible inside the frame is your window.
Features of Windowing:
• Selection of Area: Windowing selects which part of the world you want to display.
• World Coordinates: The window is defined in world coordinates (like x and y
positions on the giant map).
• Flexible: You can move the window around to see different parts of the world.
Diagram 1: Windowing
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World Coordinate System (big map)
Here, the rectangle inside is the window—the selected portion of the world.
(b) Clipping
Now, once you’ve chosen your window, you need to decide what happens to objects that lie
partly inside and partly outside the window. That’s where clipping comes in.
Analogy:
Think of taking a photo through your photo frame. If a tree is half inside the frame and half
outside, only the part inside the frame appears in your photo. The rest is “clipped away.”
Features of Clipping:
• Inside vs Outside: Anything inside the window is kept; anything outside is discarded.
• Partial Objects: If an object crosses the boundary, only the visible portion is kept.
• Efficiency: Clipping reduces unnecessary drawing of objects that won’t be visible.
Types of Clipping:
• Point Clipping: Decides if a point lies inside the window.
• Line Clipping: Cuts lines so only the visible segments remain.
• Polygon Clipping: Keeps only the part of a polygon inside the window.
• Text Clipping: Shows only the text portion inside the window.
Diagram 2: Clipping
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(c) Window and Viewport
Okay, now comes the final step. You’ve chosen your window (what part of the world to look
at), and you’ve clipped objects (decided what’s visible). But your computer screen has its
own coordinate system, called the device coordinate system.
The viewport is the rectangular area on your screen where the window’s contents will be
displayed.
Analogy:
Back to our mural example:
• The window is the part of the mural you framed.
• The viewport is the photo frame on your desk where you paste that selected
portion.
So, window = what you choose to see, viewport = where you display it.
Features of Window–Viewport Mapping:
• Window: Defined in world coordinates (big map).
• Viewport: Defined in device coordinates (screen pixels).
• Mapping: A mathematical transformation maps window coordinates to viewport
coordinates.
• Scaling: If the window is large and the viewport is small, the image shrinks. If the
window is small and the viewport is large, the image enlarges.
Diagram 3: Window–Viewport Mapping
Putting It All Together
Let’s walk through an example step by step:
1. Windowing: You select a rectangle in the world map (say, coordinates from x=10 to
x=50, y=20 to y=60).
2. Clipping: A line that runs from (5,25) to (55,25) is clipped so only the part between
(10,25) and (50,25) remains.
3. Viewport Mapping: That clipped line is then mapped to your screen coordinates, say
from (100,100) to (300,100).
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So, the giant world is reduced, cropped, and neatly displayed on your screen.
Why Are These Important?
• Efficiency: Computers don’t waste time drawing things you can’t see.
• Control: Designers and programmers can decide exactly what part of the world to
show.
• Flexibility: You can zoom in/out, pan across, or resize views easily.
• Applications: Used in CAD software, video games, simulations, and even simple
drawing apps.
Extra Diagrams for Clarity
Diagram 5: Clipping Example
Line before clipping: -------------------------
Window: [ ]
Line after clipping: -----
Everyday Example
Imagine Google Maps:
• The whole Earth is the world coordinate system.
• The part of the map you zoom into is the window.
• The phone screen area where the map is drawn is the viewport.
• If a road extends beyond your screen, only the visible portion is shown—that’s
clipping.
Conclusion
So, in simple terms:
• Windowing is choosing what part of the world to look at.
• Clipping is cropping objects so only the visible parts remain.
• Window–Viewport mapping is fitting that chosen portion into your screen space.
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Together, these three concepts make computer graphics practical, efficient, and visually
meaningful. Without them, your screen would either be overloaded with unnecessary
details or fail to show the right portion of the digital world.
SECTION-D
7. Explain translaon, scaling and rotaon as 3-D transformaons.
Ans: Understanding 3-D transformations like translation, scaling, and rotation may sound
difficult at first, but if we relate them to real-life movements of objects, they become very
easy and even interesting to learn.
Imagine you are holding a small toy cube in your hand. You can move it, resize it, or turn it
in different directions. These three actions are exactly what we call translation, scaling, and
rotation in 3D graphics or computer applications.
1. Translation (Moving an Object)
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What is Translation?
Translation means shifting an object from one position to another in 3D space without
changing its shape, size, or orientation.
Think of it like:
• Sliding your book across a table
• Moving your chair from one place to another
The object remains exactly the same — only its position changes.
How it works in 3D
In 3D space, we have three axes:
• X-axis → left and right
• Y-axis → up and down
• Z-axis → forward and backward
If a point is at:
P(x, y, z)
After translation, it becomes:
P′(x + Tx, y + Ty, z + Tz)
Where:
• Tx, Ty, Tz are the distances moved along each axis
Example
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If a point is at:
(2, 3, 4)
And we move it by:
(1, -2, 3)
New position:
(3, 1, 7)
Key Idea
✔ Shape stays same
✔ Size stays same
✔ Only position changes
2. Scaling (Resizing an Object)
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What is Scaling?
Scaling means changing the size of an object — making it bigger or smaller.
Think of it like:
• Zooming in/out of a photo
• Inflating or deflating a balloon
Types of Scaling
1. Uniform Scaling
o All dimensions increase/decrease equally
o Shape remains the same
2. Non-uniform Scaling
o Different scaling in different directions
o Shape may stretch or compress
How it works in 3D
If a point is:
P(x, y, z)
After scaling:
P′(x × Sx, y × Sy, z × Sz)
Where:
• Sx, Sy, Sz are scaling factors
Example
Point:
(2, 3, 4)
Scaling factors:
(2, 2, 2)
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New point:
(4, 6, 8)
Key Idea
✔ Changes size
✔ Can stretch or shrink
✔ Shape may or may not remain same
3. Rotation (Turning an Object)
What is Rotation?
Rotation means turning an object around an axis.
Think of it like:
• Rotating a globe
• Turning a steering wheel
• Spinning a top
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Axes of Rotation
In 3D, an object can rotate around:
• X-axis (left-right axis)
• Y-axis (vertical axis)
• Z-axis (depth axis)
How it works
Rotation involves angles (θ). The position of points changes using mathematical formulas
depending on the axis.
For example, rotation about Z-axis:
x′ = x cosθ − y sinθ
y′ = x sinθ + y cosθ
z′ = z
Example
If you rotate a cube:
• Around X-axis → it tilts forward/backward
• Around Y-axis → it spins left/right
• Around Z-axis → it rotates like a wheel
Key Idea
✔ Shape stays same
✔ Size stays same
✔ Orientation changes
Putting It All Together
Let’s combine all three with a simple real-life example:
Imagine a 3D model of a car in a video game:
1. Translation → Car moves forward on the road
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2. Scaling → Car becomes bigger when zoomed in
3. Rotation → Car turns left or right
Summary Table
Transformation
What it does
Changes
Position
Changes
Size
Changes
Orientation
Translation
Moves object
✔ Yes
No
No
Scaling
Resizes object
No
✔ Yes
No
Rotation
Rotates
object
No
No
✔ Yes
Final Understanding
If you remember just this:
• Translation = Move
• Scaling = Resize
• Rotation = Turn
Then you’ve already understood the core idea of 3D transformations.
8. Explain dierent types of projecons.
Ans: What Are Projections?
Imagine you’re standing outside on a sunny day. The sun casts your shadow on the ground.
That shadow is a projection of your 3D body onto a 2D surface (the ground).
In computer graphics, projections are used to represent 3D objects on a 2D screen. Since
our monitors are flat, we need a way to “project” the 3D world onto this flat surface.
Different projection methods give different effects—some look realistic, others look more
technical.
Types of Projections
There are two broad categories:
1. Parallel Projection
o Projection lines are parallel to each other.
o Used in engineering drawings, CAD, and places where accuracy matters more
than realism.
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2. Perspective Projection
o Projection lines converge at a point (like your eye or a camera lens).
o Used in movies, video games, and art because it looks realistic.
Let’s explore each in detail.
1. Parallel Projection
Here, imagine shining light on an object with rays that are all parallel. The shadow
(projection) doesn’t shrink with distance—it looks the same size no matter how far the
object is.
Types of Parallel Projection:
• Orthographic Projection
• Oblique Projection
Orthographic Projection
This is the simplest form. The projection lines are perpendicular to the screen. It’s like
looking straight at the front, top, or side of an object.
• Front View: Shows height and width.
• Top View: Shows width and depth.
• Side View: Shows height and depth.
This is widely used in engineering and architectural drawings.
Diagram 1: Orthographic Projection
Code
Cube → Front View: □
Top View: □
Side View: □
Oblique Projection
Here, the projection lines are not perpendicular but slanted. It’s like tilting the object so you
can see more than one face at once.
• Cavalier Projection: Depth is drawn at full scale.
• Cabinet Projection: Depth is drawn at half scale (looks more natural).
Diagram 2: Oblique Projection
Cube → Appears slanted, showing front + side together
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2. Perspective Projection
This is the projection we’re most familiar with in real life. Objects farther away look smaller,
and parallel lines seem to meet at a point (vanishing point). It mimics how our eyes see the
world.
Types of Perspective Projection:
• One-Point Perspective
• Two-Point Perspective
• Three-Point Perspective
One-Point Perspective
All depth lines converge at a single vanishing point. Imagine looking straight down a long
road—the sides of the road seem to meet at the horizon.
Diagram 3: One-Point Perspective
Road → || → converges at one point on horizon
Two-Point Perspective
Here, lines converge at two vanishing points. Imagine standing at the corner of a building—
you see two sides, each shrinking toward its own vanishing point.
Diagram 4: Two-Point Perspective
Building corner → edges vanish left and right
Three-Point Perspective
This adds a third vanishing point, usually above or below. Imagine looking up at a
skyscraper—the vertical edges also converge at a point in the sky.
Diagram 5: Three-Point Perspective
Skyscraper → edges vanish left, right, and upward
Comparison of Projection Types
Projection Type
Realism
Use Case
Orthographic
Low
Engineering, CAD
Oblique
Medium
Technical illustrations
One-Point Perspective
High
Simple realistic scenes
Two-Point Perspective
Higher
Architecture, 3D drawings
Three-Point Perspective
Very High
Dramatic views, tall structures
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Everyday Examples
• Parallel Projection: Blueprints of a house, mechanical part drawings.
• Perspective Projection: A photo taken with your phone, video game graphics, movie
scenes.
Why Projections Matter
Without projections, we couldn’t represent 3D worlds on 2D screens. They allow:
• Engineers to design machines accurately.
• Architects to visualize buildings.
• Artists and game developers to create realistic worlds.
Conclusion
So, to sum it up:
• Parallel Projection keeps sizes consistent, great for technical accuracy.
• Perspective Projection mimics human vision, great for realism.
Together, these projection techniques bridge the gap between the 3D world we live in and
the 2D screens we use every day.
“This paper has been carefully prepared for educaonal purposes. If you noce any
mistakes or have suggesons, feel free to share your feedback.”
