Computer Graphics- Homework 2

The mapping from a point in object or world coordinates to one in screen coordinates is well defined. It is not invertible because we go from three dimensions to two dimensions. Suppose, however, that we are working with a two-dimensional application. Is the mapping invertible? What problem can arise if you use a two-dimensional mapping to return to position in object or world coordinates by a locator device?
How does this apply to the picking operation?
Write out (as the product of exact matrices) the transformation matrix that results from a rotation of 45 degrees about the Y axis, followed by a translation by the vector [1,2,2,0]', followed by a rotation of 30 degrees around the Z-axis.
In Section 4.8, we showed that an arbitrary rotation matrix could be composed from successive rotations about the three axes. How many ways can we compose a given rotation if we can do only three simple rotations? Are all three of the simple rotation matrices necessary?
We defined an instance transformation as the product of a translation, a rotation, and a scaling. Can we accomplish the same effect by applying these three types of transformations in a different order?
In principle, an object-oriented system could provide scalars, vectors, and points as basic types, none of the popular APIs does so. Why do you think this is the case?

Paul Farrell