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CS1114-lec12
Course: CS 100, Fall 2008School: Cornell
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CS1114 Polygonsandtheconvexhull Prof.NoahSnavely http://cs1114.cs.cornell.edu Administrivium Assignment3duethisFridayby5pm PleasesignupforslotsonCMS Thelastproblemhasyoucontrollingtherobots withthecamera;youllneedtousethe robotGetFrame function 2 Fishandgraphs Havetofindahomefornfish Someofthefishwouldeachotherfish Howdoweknowhowmanytankstoorder? 3 Fishandgraphs:Solution1...
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CS1114 Polygonsandtheconvexhull
Prof.NoahSnavely http://cs1114.cs.cornell.edu
Administrivium
Assignment3duethisFridayby5pm
PleasesignupforslotsonCMS Thelastproblemhasyoucontrollingtherobots withthecamera;youllneedtousethe robotGetFrame function
2
Fishandgraphs
Havetofindahomefornfish Someofthefishwouldeachotherfish Howdoweknowhowmanytankstoorder?
3
Fishandgraphs:Solution1
Everyfishisavertex,eachpairofconflictingfish isanedge
Tuna Tiger shark
Gupp y
Walley e
Acoloringofthegraphgivesyouavalid assignmentoffishtotanks
4
Fishandgraphs:Solution2
Everyfishisavertex,eachpairofcompatible fishisanedge
Tuna Tiger shark The complement of the previous graph
Gupp y
Walley e
Acliqueinthegraphcanbeassignedtothe sametank
5
Cliques
Asetofnodesinagraphthatareallconnected
6
Doesitmakesense?
tofindthemedianateachstageofquicksort? Yesandno: Foreachsubarray(ofsizen),wealreadydoO(n)workto partitionthatsubarray.
WecanfindthemedianinO(n)time(expected) FindingthemediandoesntincreasethebigOrunningtimefrom O(nlogn)
Usuallyslowsthingsdowninpractice
7
Doesitmakesense?
FromWikipedia:
8
O(n)vs.O(n2)
AlgorithmXisO(n),algorithmYisO(n2) XwilleventuallycatchuptoY butwedontknowwhen n=1,000,000,000mightnotbelargeenough
(seebubblesort)
(butusuallywillbe)
9
Introspectionsort
function S = introsort(A) n = length(A); if n < 2000 S = bubblesort(A); else S= quicksort(A); end
10
Findingthelightstickcenter
1. 2. 3. 4. Thresholdtheimage Findblobs(connectedcomponents) FindthelargestblobB ComputethemedianvectorofB
11
Findingthelightstickcenter
Butwealsowanttocontroltherobotbasedon theorientationofthelightstick
12
Findingthelightstickcenter
Sofarweveonlybuiltfunctionsthattakeasetof pointsandreturnanotherpoint
Withoneexception
Howcanweexpresstheshapeofthelightstick?
13
Findingthelightstickcenter
Welltrytocomeupwith asimplepolygonto describethelightstick
Simplestpolygon:the boundingbox
14
Boundingbox
Notasinformativeaswemightlike Letscomeupwithapolygonthatfitsbetter
15
Detour:convexpolygons
ApolygonPisconvexif,foranytwopointsA,B insideP,allpointsonalineconnectingAandB Whichpolygonsareconvex?
2 arealsoinsideP
B
A
16
Convexpolygons
1 4
17
3
Testingconvexity
HowcanwetestifapolygonPisconvex?
Considerthesmallestconvexpolygoncontaining P
CalledtheCONVEXHULL WhatistheconvexhullifPisconvex?
18
Convexhull
Canalsodefineforsetsof2Dpoints:the smallestconvexshapecontainingasetof2D points
from http://en.wikipedia.org/wiki/Convex_hull
19
Convexhullofpointsets
Wecanusethistofindasimpledescriptionof thelightsticksshape
http://www.cs.princeton.edu/~ah/alg_anim/version1/ConvexHull.html
Howcanwecomputetheconvexhull?
20
Computingconvexhulls
Idea:twopointsareanedgeintheconvexhullif ___________________
21
Computingconvexhull
Whichtwohorizontallinestouchpointsontheconvex hull?
Whichtwoverticallines? Itiseasytoidentifyatleastfourpointsthatarepartof theconvexhull
22
Giftwrappingalgorithm
1. Startatlowestpoint 2. Rotatethelineuntilwehit anotherpoint
Allotherpointswilllieonone sideofthisline Lookforthepointthatgives youthelargestanglewiththe currentline
3. Repeat 4. Youredonewhenyouget backtothestartingpoint
Figurecredit:CraigGotsman
23
Thedetails...
1. Startatlowestpoint 2. Rotatethelineuntilwehit anotherpoint
Allotherpointswilllieonone sideofthisline Lookforthepointthatgives youthelargestanglewiththe curre...
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