Discuss the Taxonomy of Projection in computer graphics, with suitable diagram. Compare and contrast Parallel & Perspective projection, in detail (i.e. with suitable examples, equations, expressions etc.). What is isometric projection? What do you understand by the term vanishing point in context of projections, in computer graphics. Obtain a Projection matrix for perspective projection of a point P(x,y,z) onto z= 5 plane, provided the center of projection is at (0,0,-10), can we find the vanishing point(s) for this projection? Justify.

Write the Pseudocode for Bresenham's circle generation algorithm. Use this algorithm to produce a circle of radius (r) equal to four units, in the first quadrant from x = 0 to x = y.

Write and discuss Z-Buffer algorithm with suitable example. What are the maximum number of objects that can be handled by the Z-buffer algorithm? What will happen if Z-buffer algorithm is used and it is found that two polygons have same Z-value?

a) Windowing Transformations
b) Scan Line Polygon Fill Algorithm
c) Area Sub-Division Algorithm
d) Simulating Accelerations in Computer Animations
e) Shading and its types
f) Authoring Tools
g) Animation and its types
h) Video File Formats and its types

What are Geometric continuities ? How do Geometric continuities differ from Parametric continuities ? Discuss each type of Geometric continuity and Parametric continuity with suitable diagram.

Ray tracing and Ray casting

What are the uses of Bezier Curves and Bezier Surfaces? Explain the Mathematical expression of Bezier Curves. Write the properties of the Bezier curves, prove all properties. Discuss the Parametric Continuities and Geometric Continuities of Bezier Curves, with suitable expressions, equations and examples. Explain the purpose of control points in Bezier, a Cubic Bezier curve has control points P0 (0, 0); P1 (5, 40); P2 (40, 5); P3 (50, 15). Determine 2 more points on the same Bezier curve. Draw a rough sketch of the curve and show coordinates of various points on it?

Computer Graphics and Animation