Question 1: What are the two focusing methods in CRT?
Answer:
Two focusing methods are:
- Electrostatic Focusing
The electron beam passes through a positively charged metal cylinder which acts like an electrostatic lens and focuses the beam on the screen. - Magnetic Focusing
A magnetic field created by a coil around the CRT focuses the electron beam on the screen.
Question 2: What is the relation between triads and shadow mask method?
Answer:
In the shadow mask method, each pixel is made of three phosphor dots called triads.
These triads produce different colors on the screen.
Question 3: Discuss the pixel drawing methods.
Answer:
Three pixel drawing methods are:
- BIOS routines – Built into VGA cards but very slow.
- Direct memory access – Faster because pixels are written directly to memory.
- Library functions – Easier and faster because they are optimized.
Question 4: What are the steps in Boundary Fill Algorithm?
Answer:
Steps:
- Check the pixel for boundary color
- Check the pixel for fill color
- Set the pixel with fill color
- Repeat the process for neighboring pix
Question 5: How can the locality of a point be defined with respect to a plane?
Answer:
A point can be classified in three ways:
- In front of the plane
- Behind the plane
- On the plane (coplanar)
Question 6: In which quadrant does the point (-2, 3) lie?
Answer:
The point (-2, 3) lies in the Second Quadrant.
Question 7: Compute A · (B × C) and (A × B) · C
A = [9,8,7]
B = [4,7,3]
C = [2,9,6]
Answer:
B × C = [15, -18, 22]
A · (B × C) = 145
A × B = [-25, 1, 31]
(A × B) · C = 145
Question 8: Difference between Orthographic and Oblique Projection
Orthographic Projection
Projection lines are perpendicular to the projection plane.
Oblique Projection
Projection lines are not perpendicular to the projection plane.
Question 9: Scaling with respect to a fixed point
Answer:
Steps:
- Translate the fixed point to the origin
- Scale the object
- Translate the point back to its original position
Question 10: Composite transformation operations
Operations order:
- Reflection about Y-axis
- Rotation 30°
- Reflection about X-axis
The final transformation matrix is obtained by multiplying the matrices of these transformations in the same order.
Question 11: Why is Bresenham’s algorithm more efficient than DDA?
Answer:
Bresenham’s algorithm is more efficient because it uses only integer calculations, while DDA uses floating-point calculations.
Right Hand Rule
Answer:
In the Right-Hand Rule, hold the axis with your right hand.
Your thumb points in the positive direction, and your fingers curl in the direction of positive rotation.
Question 12: What is Viewing Frustum?
Answer:
A viewing frustum is the 3D region visible to the camera.
Only objects inside this region appear on the screen.
Question 13: Homogeneous Translation Matrix (2D)
Answer:
Translation formula:
P’ = P + T
Question 14: What is Trivial Accept?
Answer:
Trivial Accept occurs when both endpoints of a line lie inside the clipping window, so the line is accepted without clipping.
Question 15: What is Rendering?
Answer:
Rendering is the process of creating a 2D image from a 3D scene using computer graphics algorithms.
Question 16: Two techniques of Triangle Rasterization
Answer:
- Smooth Shaded Triangle Rasterization
- Texture Mapped Triangle Rasterization
Question 17: Can a 2D polygon be translated?
Answer:
Yes.
A polygon can be translated by applying the formula:
P’ = P + T
to each vertex.
Question 18: Transformation formulas
Translation
P’ = P + T
Scaling
P’ = S × P
Rotation
x’ = x cosθ − y sinθ
y’ = x sinθ + y cosθ
Question 19: Define rotation in 2D
Answer:
Rotation in 2D means moving an object along a circular path around a fixed point in the XY plane.
Question 20: Formula to find length of vector
Answer:
|V| = √(x² + y² + z²)
Question 21: Which algorithm finds closest integer coordinates to a line?
Answer:
Bresenham Line Drawing Algorithm
It finds the closest pixel positions using integer calculations.
Question 22: Scaling with respect to fixed point
Answer:
Steps:
- Translate the point to origin
- Scale the object
- Translate back to original position
Question 23: Polygon types
Concave Polygon
A line between two points inside the polygon may pass outside the polygon.
Convex Polygon
A line between any two points inside the polygon always stays inside.
Complex Polygon
Edges intersect each other.
Filled Polygon
Interior area is colored.
Unfilled Polygon
Only boundary lines are drawn.
Question 24
a) How to check if a point lies inside a polygon?
Draw a line from the point to outside the polygon.
- Odd intersections → Point is inside
- Even intersections → Point is outside
b) When Boundary Fill algorithm may fail?
Boundary fill may fail for complex polygons or when boundary color is not properly defined.