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?

Ray tracing and Ray casting

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

Shading and its types

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.

Compare Cohen Sutherland and Cyrus beck line clipping algorithms, with suitable example of each. In Cyrus Beck line clipping algorithm, How will you determine whether the point of intersection between line segment and clipping window is Potentially Entering (PE) or Potentially Leaving (PL). Derive the expression for the parameter (t) with respect to ith edge and the line segment PQ (line to be clipped) in the context of Cyber Beck line clipping algorithm.

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?

Simulating Accelerations in Computer Animations