Tutorial
Geometric Transformations 3
(The tutorial solutions are also available)
- Derive the projection matrix for an oblique projection and view
volume of the type shown below. It should map the given view
volume into the same NDC coordinate system used in class and in OpenGL,
namely one which is bounded by the cube -1<=x<=1, -1<=y<=1, -1<=z<=1.
Assume that the view volume is not oblique when viewed from above.
-
Come up with an estimate of the number of multiplications,
divisions, and additions necessary to do all the geometric transoformation work
for a triangle. Suppose that floating point multiplications and additions
take the same amount of time and that divisions take five times longer. How
many triangles per second could be drawn if a 1 Mflop processor is used
to do all the geometric transformations? Assume that the
scan conversion of the polygon is not a bottleneck.
- Suppose we are drawing a surface which is constructed using a mesh
of connected triangles. Is there a way to take advantage of the connectivity
to speed up the necessary transformations?