problem 1:

a) List out the properties of B-splines.

b) prepare about phong shading model.

problem 2:

a) What is the general form of quadric surface? Describe the terms in it.

b) Describe the algorithm for the generation of Bezier curve.

problem 3:

a) Show that the Bezier curve always touches the starting point (for u = 0) and the ending point (for u = 1).

b) Use a quadratic B-spline curve with five control points to prove that B-spline blending functions sum to unity.

problem 4:

a) Give a detailed note on Hermite interpolation.

b) List different polygon rendering methods. Compare their advantages and disadvantages.

problem 5:

a) What are the steps included in rotating a 3-D object about an arbitrary axis in 3-D space. Describe about the effects at each intermediate phase of the processing.

b) Define view volume. Describe about it in brief.

problem 6:

a) Derive the matrix form for the rotation regarding z- axis in 3-D space.

b) Categorize the projections and give a short note about the projection transforms.

problem 7:

a) List out the three fundamental rotation matrices for rotation about the three Principle axes. Describe about their nature of operation.

b) Give a short note about the approaches followed for clipping in 3-D space.

problem 8:

a) Apply an appropriate 3D transformation matrix to a line joining (1, 1, 1) and (2, 3, 4) to align it to the positive z axis and so that it originates from the origin.

b) How a point can be translated from one position to the other position with the help of matrix operations in 3D?