1. Convex Hull ● Jarvis' March O(hn) – Find lowest point O(n) – Repeatedly Find next least-counterclockwise point O(hn) ● Grahm's Scan O(n log n) – Find lowest point O(n) – Sort points by counterclockwise-ness from lowest point O(n log n) – Visit points in order, popping verticies off the stack when turning right O(n)

2. Which is better? Depends whether h > log n

3. Data Set

4. Time

5. Size of Hull

6. Divergence 500,000 points

7. Time comparison

8. Time over n

9. h vs n

10. Conclusions ● Jarvis march slower, but implementation is correct ● JM and GS have similar complexity with this data set ● What about 3 dimensions? – applications in ray tracing