CSCE 620: Computational Geometry
Homework Assignment #2

Due: Tuesday October 6, 2009 at the beginning of class

General Guidelines for Homework

• Be clear and precise. Write neatly and legibly (you will lose points for sloppy and illegible handwriting). Justify all answers, even if not specified in the question. Use good judgement concerning how detailed to make your answer.
• If the question is not fully specified, you may need to make some assumptions. In this case, you must state any assumptions you make, and justify why they are reasonable.
• Everyone must turn in their own copy of the assignment. You may consult outside material or work with others (this is encouraged), but you must reference your sources (people, texts, solutions, etc.). These must be listed on the cover sheet mentioned below.
• All assignments in this course must include a completed and signed cover sheet available on the course homepage. Any assignment turned in without a fully completed and signed coverpage will receive ZERO POINTS.

Do the following problems.

1. Prove that computing the convex hull of a set of points in the plane requires Omega(nlogn) time in the worst case. Hint: Reduce sorting to computing a convex hull. That is, describe a transformation that can be applied to map a set of real numbers to a set of points in the plane so that that the convex hull of the points will also identify the sorted order of the original input points.

2. Problem 2.1 in the text.

3. Problem 2.11 in the text.