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I need to make a 2D convex hull function for a class assignment and I want a more robust test cases than the assignment provides. Does anyone known of a largish test cases (25 < n < 100) with the solution?

MvanGeest
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BCS
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2 Answers2

4

Here's some more test data:

Here's some test data:

Test 1

8 7 7 7 -7 -7 -7 -7 7 9 0 -9 0 0 9 0 -9

Test 2

16 7 7 7 -7 -7 -7 -7 7 9 0 -9 0 0 9 0 -9 0 0 1 2 -2 1 -1 -1 3 4 4 3 -5 4 6 5

Test 3

72 0 0 1 2 -2 1 -1 -1 3 4 4 3 -5 4 6 5 7 7 7 -7 -7 -7 -7 7 9 0 -9 0 0 9 0 -9 -8 0 8 0 -7 0 7 0 -6 0 6 0 -5 0 5 0 -4 0 4 0 -3 0 3 0 -2 0 2 0 -1 0 1 0 0 -8 0 8 0 -7 0 7 0 -6 0 6 0 -5 0 5 0 -4 0 4 0 -3 0 3 0 -2 0 2 0 -1 0 1 1 1 2 2 3 3 4 4 5 5 6 6 1 -1 2 -2 3 -3 4 -4 5 -5 6 -6 -1 1 -2 2 -3 3 -4 4 -5 5 -6 6 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6

All answers are the same: 8 (0, -9) (7, -7) (9, 0) (7, 7) (0, 9) (-7, 7) (-9, 0) (-7, -7)

Irwin
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3

The Qhull package, including qhull, qconvex, and rbox should do the trick (I've used them for this exact purpose myself). For example, the qconvex examples page gives the following (tweaked for a larger test case):

rbox 100 D3 | qconvex s o TO result

The above computes the 3-d convex hull of 100 random points, writes a summary to the console, and writes the points and facets to 'result'.

Here's a sample test case for finding the 3-d convex hull of 40 points. The points are:

0.3215426810286406 0.1678336189760208 -0.2203710966001927 
0.2229772524190855 -0.4213242506806965 -0.1966818060695024 
0.3688830163971363 -0.1831502133823468 -0.2056387967482571 
-0.1712592515826777 -0.3542439228428937 0.2223876390814666 
-0.3309556113844324 -0.370961861099081 0.2439994981922204  
-0.1004397059794885 -0.09014152417903909 -0.008600084584765189 
0.458374538420117 -0.09914027349943322 -0.2505798421339875     
-0.4954086979808367 -0.3339869997780649 -0.3195065691317492    
0.053091190339151 0.3036317017894533 0.1380056861210668
0.4615616439483703 0.4665423151725366 0.1766835406205464
-0.4797380864431505 0.0419809916447671 -0.4254776681079321
-0.003168473023146823 -0.2525299883005488 -0.27151530400991
-0.3577162826971303 -0.1375644040643837 -0.04494194644032229
-0.3392973838740004 0.4288679723896719 -0.01599531622230571
0.1667164640191164 0.003605551555385444 -0.4014989499947977
0.00714666676441833 0.1140243407469469 0.407090128778564
-0.03621271768232132 0.3728502838619522 0.4947140370446388
-0.3411871756810576 -0.3328629143842151 -0.4270033635450559
0.3544683273457627 -0.450828987127942 -0.0827870439577727
-0.4018510635028137 0.08917494033386464 -0.2367824197158054
0.3978697768392692 -0.002667689232777493 0.1641431727112673
-0.245701439441835 0.495905311308713 -0.3194406286994373
0.161352035739787 -0.1563404972258401 0.3852604361113724
0.07214279572678994 -0.4960366976410492 0.1112227161519441
0.3201855824516951 0.359077846965825 0.02136723140381946
0.1190541238701475 -0.05734495917087884 0.2032677509852384
0.3210853052521919 0.4807189479290684 0.4433501688235907
0.3862800354941562 0.2085496142586224 0.09336129957191763
0.1233572616459404 0.265491605052251 0.117400122450106
0.1438531872293476 -0.2594872752758556 -0.2026374435076839
0.2724846394476338 -0.3506708492996831 0.2750346518820475
-0.4926118841325975 -0.3279366743079728 0.3683135596740186
0.2459906458351674 0.3647787136629026 -0.1641662355178652
-0.141922976953837 -0.2994764654892278 -0.3009570467294725
-0.1850859398814719 0.2606059478228967 0.004159106876849283
-0.09789466634196664 -0.3156603563722785 -0.303610991503681
0.2100642609503719 -0.4499717643018549 0.3245569875692548
-0.1707163766685095 -0.2301452446078371 -0.05112823569320907
-0.312260808713977 -0.1674135249735914 0.2808831662692904
-0.1966306233747216 0.2291105671125563 -0.3387042454804333

The convex hull is composed of the following points:

0.3215426810286406 0.1678336189760208 -0.2203710966001927 
0.2229772524190855 -0.4213242506806965 -0.1966818060695024 
0.458374538420117 -0.09914027349943322 -0.2505798421339875 
-0.4954086979808367 -0.3339869997780649 -0.3195065691317492 
0.4615616439483703 0.4665423151725366 0.1766835406205464 
-0.4797380864431505 0.0419809916447671 -0.4254776681079321 
-0.3392973838740004 0.4288679723896719 -0.01599531622230571 
0.1667164640191164 0.003605551555385444 -0.4014989499947977 
-0.03621271768232132 0.3728502838619522 0.4947140370446388 
-0.3411871756810576 -0.3328629143842151 -0.4270033635450559 
0.3544683273457627 -0.450828987127942 -0.0827870439577727 
0.3978697768392692 -0.002667689232777493 0.1641431727112673 
-0.245701439441835 0.495905311308713 -0.3194406286994373 
0.161352035739787 -0.1563404972258401 0.3852604361113724 
0.07214279572678994 -0.4960366976410492 0.1112227161519441 
0.3210853052521919 0.4807189479290684 0.4433501688235907 
0.2724846394476338 -0.3506708492996831 0.2750346518820475 
-0.4926118841325975 -0.3279366743079728 0.3683135596740186 
0.2459906458351674 0.3647787136629026 -0.1641662355178652 
0.2100642609503719 -0.4499717643018549 0.3245569875692548

Here's a 2D test case. Points:

0.3215348546593775 0.03629583077160248 
0.02402358131857918 -0.2356728797179394 
0.04590851212470659 -0.4156409924995536 
0.3218384001607433 0.1379850698988746   
0.11506479756447 -0.1059521474930943    
0.2622539999543261 -0.29702873322836    
-0.161920957418085 -0.4055339716426413  
0.1905378631228002 0.3698601009043493   
0.2387090918968516 -0.01629827079949742
0.07495888748668034 -0.1659825110491202
0.3319341836794598 -0.1821814101954749
0.07703635755650362 -0.2499430638271785
0.2069242999022122 -0.2232970760420869
0.04604079532068295 -0.1923573186549892
0.05054295812784038 0.4754929463150845
-0.3900589168910486 0.2797829520700341
0.3120693385713448 -0.0506329867529059
0.01138812723698857 0.4002504701728471
0.009645149586391732 0.1060251100976254
-0.03597933197019559 0.2953639456959105
0.1818290866742182 0.001454397571696298
0.444056063372694 0.2502497166863175
-0.05301752458607545 -0.06553921621808712
0.4823896228171788 -0.4776170002088109
-0.3089226845734964 -0.06356112199235814
-0.271780741188471 0.1810810595574612
0.4293626522918815 0.2980897964891882
-0.004796652127799228 0.382663812844701
0.430695573269106 -0.2995073500084759
0.1799668387323309 -0.2973467472915973
0.4932166845474547 0.4928094162538735
-0.3521487911717489 0.4352656197131292
-0.4907368011686362 0.1865826865533206
-0.1047924716070224 -0.247073392148198
0.4374961861758457 -0.001606279519951237
0.003256207800708899 -0.2729194320486108
0.04310378203457577 0.4452604050238248
0.4916198379282093 -0.345391701297268
0.001675087028811806 0.1531837672490476
-0.4404289572876217 -0.2894855991839297

Hull:

-0.161920957418085 -0.4055339716426413 
0.05054295812784038 0.4754929463150845 
0.4823896228171788 -0.4776170002088109 
0.4932166845474547 0.4928094162538735 
-0.3521487911717489 0.4352656197131292 
-0.4907368011686362 0.1865826865533206 
0.4916198379282093 -0.345391701297268 
-0.4404289572876217 -0.2894855991839297
Matt J
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  • I'm doing 2D (will edit Q) Any way I can talk you into generating a set and dumping to a pastebin? – BCS Jan 27 '09 at 04:10
  • I'll answer again with a 2d test case – Matt J Jan 27 '09 at 04:16
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    I just need to do a sanity check here: These points (for the 2D hull) aren't necessarily in order, are they? Because I get the exact same points, but in CCW orderf or my algorithm (which fails one test case on a puzzle site). – Christofer Ohlsson Jul 13 '15 at 13:54
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    @ChristoferOhlsson you're right, the 2D hull in this answer seems to be randomly shuffled. For the record, I found that if you save the points to a file in that exact format, you can visualize them using gnuplot, with the command `plot 'filename' with lines` – aditsu quit because SE is EVIL May 06 '16 at 15:23