Computer Graphics

Remember, you must attempt the tutorial problems before the tutorial.

Question 1

Calculate the transformation matrix for rotation about (0,2) by 60°. Hint: You can do it as a product of a translation, then a rotation about the origin, and then a translation.

Question 2

Show that the order in which transformations is important by first sketching the result when triangle A(1,0), B(1,1), C(0,1) is rotating by 45° about the origin and then translated by (1,0), and then sketch the result when it is first translated and then rotated.

Question 3

A shear transformation maps the unit square A(0,0), B(1,0), C(1,1), D(0,1) to A‘(0,0), B‘(1,0), C‘(1+h,1), D‘(h,1).

Find the transformation matrix for this transformation. (Hint: Let

and solve for a,b,c,d,e,f.)

Question 4

Prove that we can transform a line by transforming its endpoints and then constructing a new line between the transformed endpoints. Can you do the same thing for circles by transforming the centre and a point on the circle?

Question 5

Complete the solution to finding the window to viewport transformation started in lectures.

This entry was posted on Thursday, August 7th, 2008 at 9:21 am and is filed under Tutorial Questions. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.