These are for the exercise classes. Questions that have a * besides them are more difficult and should be considered at some time, but not necessarily now.
1. Consider the canonical viewing space with COP = (0,0,-1), and the usual clipping planes x = -(z+1), x = (z+1), y = -(z+1), y = (z+1), z = 0, z = 1 (assuming that the front and back clipping planes are normalised to 0 and 1). The view plane is the XY plane.
(a) We have a line segment from p0 = (1,1,-4) to p1 = (2,4,4). What is the projection of this line onto the view plane?
(b) Find the intersection between this line and the z = 0 plane.
(c) Suppose there is a third point p2 = (3,1,6). Find the polygon formed by clipping the polygon p0,p1,p2 against the z = 0 plane.
2. In WC there is a line from (0,0,0) to (1,1,1). Find camera setups to achieve each of the following results:
(a) The display shows is a single point in the centre.
(b) The display shows a horizontal line all the way across and half way between the bottom and top of the display.
(c) The display shows a vertical line from top to bottom and half way across.
(d) The line is not visible at all.
3. Under what conditions will clipping in Projection Space lead to the same result as clipping in canonical viewing space?
4. (a) The point (1,1) is on the view plane in PS, and belongs to the polygon that has plane equation
x - y + z = 0.5. What is the z-depth corresponding to this point on that polygon?
(b) Suppose that there is another polygon, with plane equation 2x + y - z = 2.6, which of the two polygons is visible at the point (1,1) on the view plane?