Computer Graphics

a) In Section 3.2 we discussed scaling with reference to the origin O, that is, with O as a fixed point. It is also possible to use a different fixed point, say C(xc, yc), but, for such a scaling in two-dimensional space, we need a 3 x 3matrix M (and homogenous coordinates), writing Using scale factors sx and Sy for x and y again, find this matrix M. Hint: You can perform a translation from C to O, followed by a scaling as discussed in Section 3.2, but described by a 3 x 3 matrix, followed by a translation back from O to C. Alternatively, you can start with the following system of equations, which shows very clearly what actually happens: b) Describe scaling in three-dimensional space with reference to a point C and three scale factors sx, Sy and sz. Find the 4 x 4 matrix (similar to matrix M of Exercise 3.1) for this transformation