UNIONS OF ONIONS Maarten L offler Wolfgang Mulzer Universiteit - PowerPoint PPT Presentation
UNIONS OF ONIONS Maarten L offler Wolfgang Mulzer Universiteit Utrecht Freie Universit at Berlin 1 CHAPTER I THE PROBLEM 2 PREPROCESSING PARADIGM 3 PREPROCESSING PARADIGM Once upon a time, we were given R . 3 PREPROCESSING
RECONSTRUCTION ALGORITHM First, locate P in R and T . Remove any empty leaves of T . Then, recursively unite the onions. P 8
RECONSTRUCTION ALGORITHM First, locate P in R and T . Remove any empty leaves of T . Then, recursively unite the onions. P 8
RECONSTRUCTION ALGORITHM First, locate P in R and T . Remove any empty leaves of T . Then, recursively unite the onions. Done! P 8
BUT! 9
BUT! ...how do you unite two onions? 9
BUT! ...how do you unite two onions? 9
BUT! ...how do you unite two onions? OBSERVATION: We can find the convex hull of two onions in O (log n ) time. 9
BUT! ...how do you unite two onions? OBSERVATION: We can find the convex hull of two onions in O (log n ) time. 9
BUT! ...how do you unite two onions? OBSERVATION: We can find the convex hull of two onions in O (log n ) time. Let’s remove it and recurse. 9
BUT! ...how do you unite two onions? OBSERVATION: We can find the convex hull of two onions in O (log n ) time. Let’s remove it and recurse. 9
BUT! ...how do you unite two onions? OBSERVATION: We can find the convex hull of two onions in O (log n ) time. Let’s remove it and recurse. Unfortunately, what is left are no longer proper onions... 9
ONION RESTAURATION & UNIFICATION 10
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. 10
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. 10
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. 10
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. 10
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. 10
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. 10
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. 10
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. 10
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. Etc... 11
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. Etc... 11
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. Etc... 11
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. Etc... 11
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. Etc... 11
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. Etc... 11
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. Etc... 11
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. Etc... 11
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. Etc... 11
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. Etc... 11
ONION RESTAURATION & UNIFICATION Compute convex hulls of the individual onions. Recurse once again. Etc... 11
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