**Q1 Answer the following questions: Short answer type**

**a) What is a light pen? List some of its important applications.**

Ans: A light pen pencil-shaped device is used to select screen positions by detecting the light coming from points on the CRT screen.

It allows the user to point to displayed objects or draw on the screen in a similar way to a touchscreen but with greater positional accuracy.

**b) Suppose an RGB raster system is to be designed using an 8 inch by 10-inch screen with a resolution of 100 pixels per inch in each direction. If we want to store 6 bits per pixel in the buffer, how much storage (in bytes) do we need for the frame buffer?**

Ans: Storage needed for the frame buffer is:

(8 inch x 100 pixels/inch) × (10 inch x 100 pixels/inch) × 6 bits ÷ 8 bits per byte ≈ 486 KB

**c) What is fractal dimension? How is it calculated?**

Ans: The detail variation in a fractal object can be described with a number D, called the fractal dimension, which is a measure of the roughness, or fragmentation, of the object

**d) Consider the line from (5,5) to (13,9). Use the Bresenham’s algorithm to rasterize the line.**

Ans: As per Bresenham’s algorithm we have:

**step 1 :-** x1 = 5 , y1 = 5 and x2 = 13 , y2 = 9

**step 2 :-** Δx = | 13 – 5| =8 Δy = | 9 – 5 | = 4

**step 3 :-** x = 5 , y = 5

**step 4 :-** e = 2 * Δy – Δx = 2 * 4 – 8 = 0

Tabulating the results of each iteration in the step 5 through 10.

The results are plotted as shown below:

**e) Prove that 2-D rotation and scaling are commutative if scaling factors Sx = Sy or Q = nn where n is any positive integer.**

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**f) State the limitations of Cohen -Sutherland line clipping algorithm.**

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g) Write 3-D composite transformation matrix using homogenous coordinates to scale a line AB with A(10,15,20) and B(45, 60,30) by 3.5 in z-direction while keeping point A fixed.

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h) What is back face removal algorithm and why it is used?

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i) Discuss the convex hull property of Bezier curves? How it is satisfied?

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j) Find the transformation matrix for perspective projection by assuming view plane normal to z-axis at z=d and center of projection at the origin.

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