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Cohen sutherland line clipping algorithm

**Question 1**:

a) Prove the commutative property of two successive rotations in 2-D graphics.

b) Describe in brief about the transformations between coordinate systems.

**Question 2**:

a) Give the transformation matrix to rotate a point about an arbitrary point.

b) Show that the transformation matrix for a reflection about the line y = - x is equivalent to a reflection relative to the y-axis followed by a counterclockwise rotation of 90^{0}.

**Question 3**:

a) Prove that a uniform scaling (sx = sy) and a rotation form a commutative pair of operations, but that, in general, scaling and rotation are not commutative.

b) Derive the transformation matrix for rotation about origin.

**Question 4**: Show that the transformation matrix for a reaction about the line y = x is equivalent to a reflection relative to the x - axis followed by a counter clockwise rotation of 90^{0}.

**Question 5**:

a) Find out the normalization transformation that uses a circle of radius five units and center at (1,1) as a window and a circle with radius and center at (1/2; 1/2) as a view port.

b) Draw a flowchart corresponding to Cohen-Sutherland line clipping algorithm.

**Question 6**: With an illustration describe Cohen Sutherland line clipping algorithm.

**Question 7**: Describe cyrus-beck line clipping algorithm.

**Question 8**: Describe Sutherland-Hodgeman algorithm for polygon clipping with an illustration.

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## Q : Implementing displacement mapping on a sphere

Implement displacement mapping and bump mapping on a sphere. The displacement can be whatever your choice. The bump map can be whatever your choice as well.