Schedule Syllabus Resources

Homework1

A reminder: you are free to collaborate, but you must understand and write up the final answers by yourself!

1. Show that the following sequences commute:
   1. A rotation and a uniform scaling
   2. Two rotations about the same axis
   3. Two translations

   General proof for any inputs	0: No general cases	1: Any inputs
   Show single commute permutation	0: No transformations	2: Single way commutes
   Show commute permutations are equal	0: Single commutativity	2: Show both commutes

2. Show that any sequence of rotations and translations can be replaced by a single rotation about the origin followed by a translation.
   

   Prove basic finite R T cases	0: No transform cases	4: Proves basic cases
   Prove basic infinite R T cases	0: No transform cases	4: Proves infinite cases
   Prove complex infinite R T cases	0: No infinite cases	5: Proves infinite cases
   General proof for any inputs	0: No general cases	2: Any inputs

3. Three vertices determine a triangle if they do not lie in the same line. Devise a test for collinearity of three vertices.
   

   Collinear test method	0: No method	3: Algorithm without justification	6: Algorithm by example	8: Justified algorithm
   Correct algorithm	0: Does not work at all	2: Correct for many inputs	5: Correct for all inputs
   General proof for any inputs	0: No general cases	2: Any inputs