Question Bank for Computer Graphics and Multimedia

Short question

1. What do you mean by raster scan display?

A raster scan display is a type of video display device where the screen is composed of a grid of pixels
(picture elements), and the image is built up by scanning the display area line by line, from top to
bottom. This method is commonly used in televisions, computer monitors, and other display devices.

2. Define parallel projection.

Parallel projection is a method of projecting three-dimensional objects onto a two-dimensional plane

(such as a computer screen) where the projection lines are parallel to each other. This type of projection
is often used in engineering and architectural drawings because it preserves the true dimensions of the
object, making it easier to measure and interpret.

3. Define perspective projection

Perspective projection is a technique used in graphics to create a realistic depiction of three-

dimensional (3D) objects on a two-dimensional (2D) plane, such as a computer screen or paper. This
method mimics how the human eye perceives the world, where objects appear smaller as they get
further away (foreshortening), and parallel lines seem to converge at a point in the distance (vanishing
point).

4. Write properties of Bezier curve

Bezier curves are used to create smooth, flowing shapes in computer graphics and animations.

o Control Points: The curve is defined by points called control points. For example, a cubic Bezier
curve has four control points.
o Starts and Ends at Control Points: The curve always starts at the first control point and ends at
the last control point.
 o Smoothness: The curve is smooth and continuous, without sharp corners, because it smoothly
transitions through the control points.
o Local Control: Moving a control point changes the shape of the curve in that area, allowing for
easy shaping.
o Contained within Convex Hull: The curve lies within the smallest polygon (convex hull) that can
enclose all control points.
o Symmetry: The curve behaves symmetrically with respect to its control points. Reversing the
order of control points gives the same curve in the opposite direction.
o Endpoint Interpolation: The curve always passes through the first and last control points.

5. What is Frame Buffer Memory?

Frame Buffer Memory is a dedicated block of memory in a computer or graphics system, used to store
image data that is displayed on the screen. It serves as a temporary storage area where the information
about each pixel on the screen (color, brightness, transparency, etc.) is kept before being sent to the
display.

6. What is multimedia?

Multimedia refers to the integration of multiple forms of media to convey information or provide
entertainment. It combines text, audio, images, animations, video, and interactive content to create a
rich and engaging experience for the audience.

7. Define translation in 2D.

It is the straight-line movement of an object from one position to another is called Translation. Here the
object is positioned from one coordinate location to another.

x1 = x + Tx y1 = y + Ty [The translation pair (Tx, Ty) is called as shift vector]

8. Define scaling in 2D.

Scaling in 2D is a geometric transformation that changes the size of an object by increasing or

decreasing its dimensions along the x-axis, y-axis, or both. It is performed by multiplying the
coordinates of each point of the object by scaling factors Sx (for the x-axis) and Sy (for the y-axis).

Sx: Scaling factor in the x-direction. Sy: Scaling factor in the y-direction.

9. Define rotation in 2D. What is scaling?

It is a process of changing the angle of the object. Rotation can be clockwise or anticlockwise. For
rotation, we have to specify the angle of rotation and rotation point. Rotation point is also called a pivot
point. It is print about which object is rotated.

10. Give the matrix to shear in 2D.

Shearing -- It is transformation which changes the shape of object. The sliding of layers of object
occurs. The shear can be in one direction or in two directions.

11. What is a composite transformation?

A number of transformations or sequence of transformations can be combined into single one called as
composition. The resulting matrix is called as composite matrix. The process of combining is called as
concatenation.
12. What are drawback of Cohen-Sutherland line clipping algorithm?
o Limited to Rectangular Windows: The Cohen-Sutherland algorithm is specifically designed
for rectangular clipping regions. It cannot be directly applied to clipping regions of arbitrary
shapes (e.g., circular or polygonal regions).
 o Complex for Non-Rectangular Regions: For non-rectangular clipping windows, additional
transformations or algorithms are required, making it less versatile in such cases compared
to algorithms designed for general polygons.

o Inefficient for Complex Scenes: Multiple clipping stages: In cases where lines are clipped
multiple times or the scene has a large number of lines, the algorithm might require several
iterations of testing and clipping, making it less efficient for complex or large-scale scenes.

o Overhead in Outcode Calculation: The need to calculate the outcodes for each endpoint of
the line adds some computational overhead, particularly in scenes with many lines or
complex window shapes. Although the calculations are relatively simple, the process can still
be time-consuming when there are many lines to clip.

o Not Suitable for Other Types of Clipping (Curves, Polygons): The algorithm is designed for
line clipping and cannot be directly applied to other types of geometric entities like curves,
circles, or polygons without significant modifications or the use of additional algorithms.

13. Discuss the conditions for clipping a point against a given rectangular window.

14. What are drawbacks of DDA line drawing algorithm?

o It involves floating point additions rounding off is done. Accumulations of round off error cause
accumulation of error.
 o Rounding off operations and floating point operations consumes a lot of time.
o It is more suitable for generating line using the software. But it is less suited for hardware
implementation.

15. Derive the component matrix of translation.

To represent translation in a 2D homogeneous coordinate system, we augment the original 2D
point (x, y) into a 3D vector by introducing a third coordinate (usually set to 1). The original point
(x, y) becomes:
16. Show that the composition of two rotation is additive.

17. What is aspect ratio?

Aspect ratio is the ratio of the width to the height of an image, screen, or display. It is typically
expressed as two numbers separated by a colon (e.g., 16:9 or 4:3).

Aspect Ratio = Height/Width

18. What is initial decision parameter value for Bresenham’s circle drawing algorithm?
19. Name two essential features of graphics software.

Graphics software comes packed with a variety of essential features that empower artists,
designers, and creators to bring their visions to life. Here are a few key ones:

 Layer Management: Organize different parts of your artwork on separate layers, making it easier
to edit and manipulate each component individually.
 Vector and Raster Support: Work with both scalable vector graphics for sharp lines and raster
images for detailed, pixel-based artwork.
 Brush Tools: Use customizable brushes to create freehand drawings and intricate designs,
simulating various types of brushes and pens.
 Color Management: Ensure color consistency across different devices and outputs with tools for
color correction, grading, and profiling.
 Text Tools: Add, format, and style text within your designs, often with extensive font options
and text effects.
 Selection Tools: Select specific areas of your image for editing, using tools like lasso, magic
wand, and marquee to make precise adjustments.
 Filters and Effects: Apply various filters and effects to enhance or transform your images, such
as blurring, sharpening, and stylizing.
  Undo/Redo Functionality: Easily revert and reapply changes to your work, giving you the
flexibility to experiment without fear of making mistakes.

20. What are the applications of computer graphics?

 Entertainment: Movies, video games, and virtual reality.

 Design: Architecture, engineering, and product design.
 Education: Interactive simulations and visual aids.
 Medical Imaging: MRI, CT scans, and 3D ultrasounds.
 Scientific Visualization: Data visualization for research.

21. What is reference point and reference axis of transformation?

Reference Point: This is a specific point in the coordinate system relative to which
transformations like translations, rotations, and scaling are performed. For instance, if you're
rotating an object, the reference point would be the center of rotation.

Reference Axis: This is the axis around which transformations like rotations and reflections are
carried out. In 2D transformations, it could be the x-axis or y-axis, and in 3D transformations, it
could be the x, y, or z-axis.

22. What is pixel?

A pixel is the smallest unit of a digital image, acting like a tiny dot or square. When many pixels are
combined, they form a complete image. The quality and detail of an image depend on the number of
pixels it contains.

23. What is control point?

A control point in computer graphics and geometric modeling is a specific point used to define the shape
of a curve or surface. Control points influence the curvature and the overall form of the object.

24. What do you understand by resolution?

Resolution refers to the amount of detail an image holds, measured in pixels. Higher resolution
means more pixels and finer detail. For screens, it's expressed as width x height (e.g.,
1920x1080), while in print, it's measured in dots per inch (DPI).
25. What is shearing?
Refer Q10
26. Derive the component matrix of rotation.

27. What is scan conversion?

Scan conversion is the process of converting geometric data (like lines, circles, and polygons)
into a raster image, which is composed of pixels that can be displayed on a screen. This is a
fundamental technique in computer graphics that allows the rendering of vector graphics into a
format suitable for display on raster devices, such as monitors and printers.

28. What is boundary fill algorithm?

This algorithm uses the recursive method. First of all, a starting pixel called as the seed is considered.
The algorithm checks boundary pixel or adjacent pixels are colored or not. If the adjacent pixel is already
filled or colored then leave it, otherwise fill it. The filling is done using four connected or eight connected
approaches.

1. Four connected approaches: In this approach, left, right, above, below pixels are tested.
2. Eight connected approaches: In this approach, left, right, above, below and four diagonals are
selected.

Boundary can be checked by seeing pixels from left and right first. Then pixels are checked by seeing
pixels from top to bottom. The algorithm takes time and memory because some recursive calls are
needed.

29. What is morphing?

Morphing is a computer graphics technique that transforms one image into another through a seamless
transition. It's widely used in animation and film to create visual effects where an object's shape changes
smoothly into another shape.

30. Why are hypertexts used for information representation in multimedia packages?

Hypertexts are used in multimedia packages because they:

1. Enable Interactivity: Users can click on links to navigate information easily.

2. Organize Efficiently: Present large amounts of information in an accessible way.
3. Integrate Multimedia: Combine text, images, audio, and video seamlessly.
4. Personalize Experience: Users can explore topics based on their interests.

31. How the image is drawn in CRT monitor?

On a CRT (Cathode Ray Tube) monitor, the image is drawn using the following process:

1. Electron Gun: The CRT has an electron gun that shoots a stream of electrons toward the screen.

2. Magnetic Coils: Magnetic coils are used to steer the electron beam in a precise pattern across
the screen. This process is called scanning.

3. Phosphor Coating: The inner side of the screen is coated with phosphor dots. When the electron
beam hits these dots, they emit light, creating visible images.

4. Raster Scan: The electron beam scans the screen from left to right and top to bottom in a series
of horizontal lines, known as raster lines. This process repeats rapidly to refresh the image on
the screen.

32. Write full form of

 i) MIDI - Musical Instrument Digital Interface
ii)JPEG - Joint Photographic Experts Group

Long Question
1. Scale the square ABCD (0,0)(3,0),(3,3),(0,3) three unit in X-direction and three unit in Y-
direction with respect to origin.
 2. What is Computer Graphics? Explain the different Application of Computer Graphics in several
fields.

Computer Graphics involves the creation, manipulation, and representation of visual images using
computers. It encompasses a wide range of techniques for rendering images, animations, and visual
effects. Here are some key applications of computer graphics across various fields:

Applications of Computer Graphics:

1. Entertainment and Media:

o Movies and Animation: Used to create visual effects, 3D animations, and realistic
scenes in films and TV shows.

o Video Games: Essential for designing game environments, characters, and interactive
experiences.

2. Design and Engineering:

o CAD (Computer-Aided Design): Used in architecture, automotive, and aerospace

industries for designing and modeling products and structures.

o Simulation and Visualization: Helps engineers visualize complex systems, perform

simulations, and analyze data in a visual format.
3. Medical Imaging:

o MRI and CT Scans: Used to create detailed images of the human body, aiding in
diagnosis and treatment planning.

o Surgical Simulations: Provides 3D models for pre-operative planning and virtual surgery
practice.

4. Education and Training:

o E-Learning: Interactive graphics enhance learning experiences through simulations and

visual demonstrations.

o Virtual Reality (VR) and Augmented Reality (AR): Used for immersive training and
educational simulations.

5. Geographical Information Systems (GIS):

o Mapping and Navigation: Helps in creating detailed maps, analyzing geographical data,
and providing navigation aids.

6. Scientific Visualization:

o Data Analysis: Transforms complex scientific data into visual representations, making it
easier to understand and interpret.

o Research: Used to visualize molecular structures, astronomical phenomena, and other

scientific models.

7. Art and Design:

o Digital Art: Enables artists to create digital paintings, illustrations, and sculptures.

o Graphic Design: Essential for creating visual content for advertising, marketing, and
branding.

3. Triangle ABC is (0,0),(4,0)and (0,4 ) Find shearing Transformation with a=2 and b=2.
 4. What is Cathode Ray Tube (CRT) . Explain functioning of CRT with proper diagram.

A Cathode Ray Tube (CRT) is a technology used in traditional television sets and computer
monitors to display images. It operates by directing electron beams onto a phosphorescent
screen.

Functioning of CRT

1. Electron Gun:
o The CRT contains one or more electron guns which emit a stream of electrons.
These guns are located at the back of the tube.
2. Control Grid:
o The control grid modulates the intensity of the electron beam, allowing it to vary
the brightness of the image displayed on the screen.
3. Deflection System:
o The deflection system, which includes magnetic or electrostatic deflection coils,
directs the electron beam to different parts of the screen. This system can steer the
beam horizontally and vertically.
4. Phosphor-Coated Screen:
o The inner surface of the front screen is coated with phosphor dots or stripes.
When the electron beam strikes these phosphor dots, they emit light, creating the
visible image.
o Different phosphors emit different colors (red, green, or blue), and combining
these allows for color images.
5. Raster Scan:
o The electron beam sweeps across the screen in a series of horizontal lines from
top to bottom, creating a raster scan. This process is repeated rapidly to create a
stable image.
6. Anode:
o The anode in the CRT helps to accelerate the electrons towards the screen.
Components of CRT:

1. Electron Gun: Electron gun consisting of a series of elements, primarily a heating filament
(heater) and a cathode. The electron gun creates a source of electrons which are focused into a
narrow beam directed at the face of the CRT.

2. Control Electrode: It is used to turn the electron beam on and off.

3. Focusing system: It is used to create a clear picture by focusing the electrons into a narrow
beam.

4. Deflection Yoke: It is used to control the direction of the electron beam. It creates an electric
or magnetic field which will bend the electron beam as it passes through the area. In a
conventional CRT, the yoke is linked to a sweep or scan generator. The deflection yoke which is
connected to the sweep generator creates a fluctuating electric or magnetic potential.

5. Phosphorus-coated screen: The inside front surface of every CRT is coated with phosphors.
Phosphors glow when a high-energy electron beam hits them. Phosphorescence is the term used
to characterize the light given off by a phosphor after it has been exposed to an electron beam.

5. Prove that the multiplication of transformation matrices for two successive rotations is
commutative.
6. Magnify the triangle with vertices A(0,0),B(1,1),C(5,2) to twice its size while keeping C(5,2)
fixed.

7. Prove that 2D rotation and scaling commute if S x=Sy or Ɵ= nΠ for integer n and otherwise they
donot. Here Sx and Sy are the scaling along the X and Y axis respectively and Ɵ is angle of
rotation
 8. Discuss boundary fill and flood fill algorithm.

9. Discuss Sutherland hodgman polygon clipping algorithm.

The Sutherland-Hodgman Polygon Clipping Algorithm is used for clipping polygons by a

rectangular clipping window. It is particularly useful in computer graphics to determine which
portions of a polygon are within a given viewport.

Steps of the Algorithm

1. Input:
oA polygon defined by a set of vertices.
oA rectangular clipping window defined by its minimum and maximum
coordinates (xmin,ymin)(x_{\text{min}}, y_{\text{min}}) and
(xmax,ymax)(x_{\text{max}}, y_{\text{max}}).
2. Process Each Edge of the Clipping Window:
o The algorithm processes each edge of the clipping window one by one.
o For each edge, it traverses the vertices of the polygon and generates a new set of
vertices for the portion of the polygon that lies within the clipping edge.
3. Check Each Vertex Against the Clipping Edge:
o For each vertex of the polygon, determine if it is inside or outside the clipping
edge.
o Depending on whether the vertices are inside or outside, it performs various
actions (add, discard, or compute intersection points).
4. Output:
o The result after processing all edges of the clipping window is the clipped
polygon.
Detailed Algorithm

1. Initialize:
o Start with the original list of vertices of the polygon.
2. Process Left Edge:
o Iterate through each edge of the polygon and:
 If the start vertex is inside the left boundary and the end vertex is also
inside, keep the end vertex.
 If the start vertex is inside and the end vertex is outside, compute the
intersection point and keep it.
 If the start vertex is outside and the end vertex is inside, compute the
intersection point, keep it, and then keep the end vertex.
 If both vertices are outside, discard the end vertex.
3. Process Right Edge:
o Repeat similar steps for the right edge, using the output vertices from the previous
step as input.
4. Process Bottom Edge:
o Repeat the same process for the bottom edge.
5. Process Top Edge:
o Finally, repeat the process for the top edge.
 10. Perform a 45° rotation of a triangle A(1,1),B(5,1),C(3,5) about an arbitrary point P (3,3) ,about
origin

11. Explain the importance of homogeneous co-ordinate system.

The homogeneous coordinate system is an extension of the Cartesian coordinate system used in
computer graphics and other fields. It is especially important in the context of geometric
transformations (such as translation, scaling, rotation, and perspective projections) and in the
representation of points and vectors in a consistent way. Here’s why the homogeneous coordinate
system is so significant:
Importance of Homogeneous Coordinate System
1. Unified Representation of Transformations:
o In a homogeneous coordinate system, all affine transformations (translation, scaling,
rotation, and shearing) can be represented as matrix multiplications. This unified
approach simplifies the computation and application of multiple transformations in
sequence.
2. Inclusion of Translation in Matrix Form:
o Traditional Cartesian coordinates represent translation separately from other
transformations. In homogeneous coordinates, translation can be represented within
the same matrix multiplication framework as other transformations, making it easier to
combine different transformations into a single matrix.
3. Simplified Composition of Transformations:
o Homogeneous coordinates allow for the straightforward combination of multiple
transformations by matrix multiplication. This makes it possible to concatenate
 transformations efficiently, improving performance and simplifying the overall process
of applying complex transformations.
4. Handling Perspective Projections:
o Homogeneous coordinates are essential for representing perspective transformations,
which are non-linear in Cartesian coordinates. They enable the use of linear algebra
techniques to handle perspective projections, making calculations more manageable.
5. Representation of Points at Infinity:
o Homogeneous coordinates can represent points at infinity, which is useful in computer
graphics for handling parallel lines and vanishing points in perspective projections. This
capability enhances the realism of graphical representations.
6. Consistency in Computation:
o By using homogeneous coordinates, points and vectors can be treated uniformly, which
simplifies the implementation of various algorithms and ensures consistency in the
computation of geometric transformations.

12.Derive the relationship between window port and view port.

 13. Write a short note on Bezier curve.

Bezier curve is discovered by the French engineer Pierre Bézier. These curves can be generated
under the control of other points. Approximate tangents by using control points are used to
generate curve. The Bezier curve can be represented mathematically as −
 14. The eight-way symmetry of a circle can be used to design an efficient circle drawing
algorithm-justify the statement with suitable algorithm.

The eight-way symmetry of a circle can be leveraged to design an efficient circle-drawing

algorithm by reducing the computation needed to plot points. Instead of calculating the points for
the entire circle, you only need to calculate the points for one-eighth of the circle and then mirror
these points across the other seven sections.

One widely used algorithm that utilizes this principle is the Midpoint Circle Algorithm, also
known as Bresenham's Circle Algorithm. Here's a brief overview of how it works:

Midpoint Circle Algorithm

1. Initialization: Start with the circle center at the origin (0, 0) and a radius r. Initialize the
first point (x0, y0) as (0, r).
2. Decision Parameter: Calculate the initial decision parameter P0 = 1 - r.
3. Plot Points Using Symmetry: For each point (x, y) in one-eighth of the circle, plot the
symmetric points in all eight octants:

(x, y)
(y, x)
(-x, y)
(-y, x)
(-x, -y)
(-y, -x)
(x, -y)
(y, -x)

4. Update Coordinates: Update the coordinates and the decision parameter using the
following rules:

o If P < 0:

x = x + 1P = P + 2x + 1

o If P ≥ 0:
x = x + 1y = y − 1P = P + 2x − 2y + 1

5. Loop: Continue the loop until x ≥ y.

Example

Let's say we want to draw a circle with a radius of 10. Here are the steps in action:

1. Initialize: x = 0, y = 10, P = -9
 2. Plot (0, 10) and its symmetrical points.
3. Update:
o x = 1, P = -7 (since P < 0, only x changes)
o Plot (1, 10) and its symmetrical points.
4. Repeat the process until x ≥ yx.

This algorithm is efficient because it reduces the number of calculations needed by utilizing the
symmetry of the circle, leading to a faster rendering process.

15. Derive a general transformation matrix for 3D rotation about x axis, y axis, z axis.
16. What can be concluded about the visibility of line segment in Cohen-Sutherland line clipping
algorithm.

In the Cohen-Sutherland line clipping algorithm, the visibility of a line segment is determined based
on its position relative to the clipping window (viewport). Here's what can be concluded about the
visibility:
1. Completely Visible: If both endpoints of the line segment lie within the clipping window, the line
segment is entirely visible and doesn't need clipping.
2. Completely Invisible: If the line segment lies entirely outside one of the boundaries of the
clipping window and doesn't intersect the window, it is completely invisible and can be
discarded.
3. Partially Visible: If the line segment intersects the clipping window, it is partially visible. The
algorithm then calculates the intersection points with the clipping boundaries to determine the
visible portion of the line segment.

The Cohen-Sutherland algorithm uses region codes (outcodes) to categorize the endpoints of the
line segment relative to the clipping window. These codes help in quickly determining the visibility
and guiding the clipping process.

17. Use DDA line generation algorithm to draw a line from (2,2) to (6,6)
18. Distinguish between random scan display and raster scan display.

19. Find the rotation transformation matrix form about an arbitrary line y=mx+b.

1. Translate the Line to the Origin:

o Translate the line y = mx + b to the x-axis by moving the line down by bb.
o Translation matrix T for moving down by b:

2. Rotate to Align with the X-Axis:

o Rotate the line to align with the x-axis. The angle of rotation θ is the angle
between the line y = mx and the x-axis, which is tan^{-1}(m).
o Rotation matrix R for angle θ:

3. Apply the Rotation:

o Perform the rotation about the origin by an angle ϕ.
4. Reverse the Rotation:
 oReverse the initial rotation by θ.
5. Reverse the Translation:
o Translate back by b units in the y-direction.

Combined Transformation Matrix

The combined transformation matrix M is the product of these matrices:

 T is the translation matrix.

 R is the initial rotation matrix.
 R′ is the rotation matrix for angle ϕ.
 R^{-1} is the inverse of the initial rotation matrix.
 T^{-1} is the inverse of the translation matrix.

20.Consider the rectangle defined by (100,10),(160,10),(160,40),(100,40). Discuss clipping

situation of straight line PQ using Cohen-Sutherland line clipping algorithm where P(50,0) and
Q(70,80)
Final Results

 The visible portion of the line is from (110,40)(110, 40) to (60,40)(60, 40).
 The clipped line segment is inside the clipping window after processing.

21. Derive midpoint line drawing algorithm.

Steps to Derive Midpoint Line Drawing Algorithm

1. Initial Setup:
o Consider a line segment between points (x0, y0) and (x1, y1).
o Calculate the differences: Δx = x1 − x0 and Δy = y1 − y0.
o Assume the line has a positive slope less than 1 (0 ≤ m ≤ 1).
2. Decision Parameter:
o The midpoint decision parameter helps determine which pixel to choose next.
o Initialize the decision parameter dd:

d = 2Δy − Δx

3. Iteration:
o Start at the initial point (x0, y0).
o For each xk from x0 to x1:
 If d ≥ 0:
 Choose the pixel (xk+1, yk+1).
 Update d:

d = d + 2(Δy−Δx)
  If d < 0:
o Choose the pixel (xk + 1, yk).
o Update d:

d = d + 2Δy

Algorithm in Steps:

1. Initialize:

x = x0, y = y0
Δx = x1 − x0, Δy = y1 − y0
d = 2Δy − Δx

2. Loop:
o For x from x0 to x1:
 Plot the pixel (x, y).
 If d ≥ 0:
 Increment y: y = y + 1.
 Update dd: d = d + 2(Δy − Δx).
 If d < 0:
 Update d: d = d + 2Δy.

Example:

To draw a line from (2, 2) to (8, 5):

1. Initialize:

x0 = 2, y0 = 2, x1 = 8, y1 = 5x
Δx = 6, Δy = 3
d=2×3−6=0

2. Plot the points using the algorithm:

o (2, 2)
o Increment x to 3.
o Since d ≥ 0, increment y to 3, update d: d = 0 + 2(3 - 6) = -6.
o Plot (3, 3).
o Repeat until (8, 5).

This method ensures an efficient and accurate line drawing on raster devices.

22. What are the advantages of Bresenham’s line drawing algorithm over DDA line drawing
algorithm?
23. Clip a line A (3,20), B(13.3) against a rectangular window whose left-bottom ,top-corner are at
the point (5,5), (25,15) respectively..
24. Discuss point clipping algorithm.
 25.”translation does not depend on reference point”- justify

Translation in computer graphics involves moving every point of an object by the same distance
in a specified direction. This process does not depend on a reference point because translation
uniformly displaces all points of the object. Here’s why:

1. Uniform Displacement: Translation applies the same displacement vector (dx, dy) to
every point (x, y) of the object. The new coordinates are calculated as:

(x', y') = (x + dx, y + dy)

This formula shows that the shift depends only on the displacement vector, not on any specific
reference point.

2. Relative Position Maintained: The relative positions of all points in the object remain
unchanged after translation. The entire object moves as a unit without altering its shape,
size, or orientation.
3. Independence from Initial Position: The initial position of the object or its points does
not influence the translation operation. The displacement vector determines the new
position regardless of where the object starts.

Example

Consider a square with vertices (1, 1), (1, 2), (2, 1), and (2, 2). If we apply a translation vector (3,
4):

 The new vertices will be (4, 5), (4, 6), (5, 5), and (5, 6).

Each vertex moves by the same amount, demonstrating that the translation effect is consistent
and does not depend on any specific reference point.

26.Discuss Cohen-Sutherland line clipping algorithm.

The Cohen-Sutherland Line Clipping Algorithm is a popular computer graphics algorithm used for line
clipping, which determines the portion of a line segment that lies within a rectangular clipping window.
Steps of the Algorithm:
1. Define the Clipping Window:
o The rectangular window is defined by its minimum and maximum coordinates (xmin,
ymin) and (xmax, ymax).
2. Assign Region Codes:
o Each endpoint of the line segment is assigned a region code based on its position
relative to the clipping window.
o The window is divided into nine regions, and each region is assigned a 4-bit code
(Outcode) representing the position:
 Bit 1: Above
 Bit 2: Below
 Bit 3: Right
 Bit 4: Left
For example:
o Region code for a point above and to the left of the window: 1001
3. Trivial Acceptance or Rejection:
o If both endpoints of the line segment have a region code of 0000, the line segment is
trivially accepted (completely inside the window).
o If the bitwise AND of the region codes of both endpoints is not 0000, the line segment is
trivially rejected (completely outside the window).
4. Clipping:
o For lines that are neither trivially accepted nor rejected, the algorithm iteratively clips
the line segment.
o The endpoint outside the window is moved to the intersection point with the clipping
boundary corresponding to its region code.
o The region code of the new endpoint is recalculated and the process is repeated until
the line segment is either trivially accepted or rejected.
Example:
Let's consider a line segment with endpoints P(5, 20) and Q(15, -5) and a clipping window with
boundaries (xmin=0, ymin=0) and (xmax=10, ymax=10):
1. Assign region codes:
o P(5, 20): Above (0100)
o Q(15, -5): Right-Below (1001)
2. Initial check:
o Both endpoints are outside, and not trivially accepted or rejected.
3. Clip endpoint PP:
o Intersect P with the top boundary: y = 10

o Calculate new x:
o New point(10, 10)
4. Clip endpoint Q:
 o Intersect Q with the right boundary: x = 10

o Calculate new y:
o New point (10, -2.5)
Advantages:
1. Efficiency: The algorithm can quickly determine line segment visibility.
2. Trivial Acceptance/Rejection: Quickly handles cases where line segments are entirely inside or
outside the clipping window.
27. Derive and write midpoint circle drawing algorithm.
28. Compare parallel and perspective projections with reference to practical use only.

29.Derive a general transformation matrix for 3D translation and scaling.