**[Total Time: 3hrs.]**

**[Total Marks: 80]**

**Please check whether you have got the right question paper.**

**N.B.: 1) Question No. 1 is compulsory**

** 2) Attempt any three of the remaining five questions.**

** 3) Assumer any suitable data if necessary and justify the same.**

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Q. 1) a) Explain CSG method for solid modeling.** (5M)**

b) What is aliasing and Explain any one antialiasing method. ** (5M)**

c) Compare Raster Scan and Random Scan displays. ** (5M)**

d) Prove that two successive rotations are additive i.e R1(Θ_{1}) * R2 (Θ_{2})=(Θ_{1}+Θ_{2}) ** (5M)**

Q. 2) a) Explain the Bresenham line drawing algorithm with proper mathematical analysis and identify the pixel positions along a line between A (10,10) and B (18,16) using it. ** (10M)**

b) Explain the steps for 2D rotation about arbitrary points and provide a composite transformation for the same. **(10M)**

Q. 3) a) Explain Liang Barsky’s line clipping algorithm. Apply the algorithm to clip the line with coordinates (30, 60) and (60,20) against window (xmin, ymin)=(10,10) AND (xmax, ymax) =(50,50) **(10M)**

b) Explain Sutherland Hodgman’s polygon clipping algorithm with a suitable example and comment on its shortcoming. **(10M)**

Q. 4) a) What is window and viewport? Derive the window to viewport transformation and also identify the geometric transformation involved. **(10M)**

b) Explain what is meant by the Bezier curve? state the various properties of the Bezier curve. **(10M)**

Q. 5) a) What is meant by parallel and perspective projection? Derive matrix for oblique projection. **(10M)**

b) Explain z Buffer algorithm for hidden surface removal. **(10M)**

Q. 6) Write short notes on (any two) **(20M)**

a) Koch curve

b) Sweep representation and Octree representation

c) Gouraud and Phong shading.

d) Halftoning and Dithering.

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