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.

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Presentation transcript:

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)

Which is better? Depends whether h > log n

Data Set

Time

Size of Hull

Divergence 500,000 points

Time comparison

Time over n

h vs n

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