Problem with PlanarGraphPlot And ConvexHull

ksaranat · April 26, 2014, 5:00pm

I’m getting a lot of strange errors when using PlanarGraphPlot with a simple list of 11 points

<< ComputationalGeometry`;
x = {{184978.59580704456`, 77909.66948289984`}, {184978.27815712072`, 
    77909.76595227784`}, {184978.27082673783`, 
    77909.74177736834`}, {184977.5543690799`, 
    77909.95958192856`}, {184977.65873976916`, 
    77910.2913545858`}, {184977.87393886593`, 
    77910.32174601014`}, {184978.3127146399`, 
    77911.75682671613`}, {184979.13720817852`, 
    77911.37094455786`}, {184979.40459261995`, 
    77911.34308556134`}, {184979.6157774594`, 
    77912.04232488069`}, {184980.40222282038`, 77911.69604330455`}};
PlanarGraphPlot[x]

Errors I get are

Mod::indet: Indeterminate expression Mod[-1,0] encountered. >>

Part::partw: Part 1 of {} does not exist. >>

Part::pspec: Part specification Indeterminate is neither a machine-sized integer nor a list of machine-sized integers. >>

Part::pspec: Part specification {{4,2},{1,4,6},{6},{7,2,1},{6,6},{2,5,6,3,5},{11,10,9,4},{},{7,10},{9,7,11},{10,7}}[[8,1]] is neither a machine-sized integer nor a list of machine-sized integers. >>

Part::pspec: Part specification {{4,2},{1,4,6},{6},{7,2,1},{6,6},{2,5,6,3,5},{11,10,9,4},{},{7,10},{9,7,11},{10,7}}[[8,1]] is neither a machine-sized integer nor a list of machine-sized integers. >>

General::stop: Further output of Part::pspec will be suppressed during this calculation. >>

Part::partw: Part 1 of {} does not exist. >>

Set::shape: Lists {ComputationalGeometry`Private`merge$30945[[ComputationalGeometry`Private`l0$30945]],ComputationalGeometry`Private`merge$30945[[ComputationalGeometry`Private`r0$30945]]} and ComputationalGeometry`Private`insert[{{4,2},{1,4,6},{6},{7,2,1},{6,6},{2,5,6,3,5},{11,10,9,4},{},{7,10},{9,7,11},{10,7}}[[{6,{{4,2},{1,4,6},{6},{7,2,1},{6,6},{2,5,6,3,5},{11,10,9,4},{},{7,10},{9,7,11},{10,7}}[[8,1]]}]],6,{{4,2},{1,4,6},{6},{7,2,1},{6,6},{2,<<3>>,5},<<1>>,{},{7,10},{9,7,11},{10,7}}[[<<1>>]],2,3] are not the same shape. >>

Mod::indet: Indeterminate expression Mod[-1,0] encountered. >>

Part::partw: Part 1 of {} does not exist. >>

General::stop: Further output of Part::partw will be suppressed during this calculation. >>

Set::shape: Lists {ComputationalGeometry`Private`merge$33935[[ComputationalGeometry`Private`l0$33935]],ComputationalGeometry`Private`merge$33935[[ComputationalGeometry`Private`r0$33935]]} and ComputationalGeometry`Private`insert[{{4,2},{1,4,6},{6},{7,2,1},{6,6},{2,5,6,3,5},{11,10,9,4},{},{7,10},{9,7,11},{10,7}}[[{6,{{4,2},{1,4,6},{6},{7,2,1},{6,6},{2,5,6,3,5},{11,10,9,4},{},{7,10},{9,7,11},{10,7}}[[8,1]]}]],6,{{4,2},{1,4,6},{6},{7,2,1},{6,6},{2,<<3>>,5},<<1>>,{},{7,10},{9,7,11},{10,7}}[[<<1>>]],2,3] are not the same shape. >>

Mod::indet: Indeterminate expression Mod[-1,0] encountered. >>

General::stop: Further output of Mod::indet will be suppressed during this calculation. >>

Set::shape: Lists {ComputationalGeometry`Private`merge$35305[[ComputationalGeometry`Private`l0$35305]],ComputationalGeometry`Private`merge$35305[[ComputationalGeometry`Private`r0$35305]]} and ComputationalGeometry`Private`insert[{{4,2},{1,4,6},{6},{7,2,1},{6,6},{2,5,6,3,5},{11,10,9,4},{},{7,10},{9,7,11},{10,7}}[[{6,{{4,2},{1,4,6},{6},{7,2,1},{6,6},{2,5,6,3,5},{11,10,9,4},{},{7,10},{9,7,11},{10,7}}[[8,1]]}]],6,{{4,2},{1,4,6},{6},{7,2,1},{6,6},{2,<<3>>,5},<<1>>,{},{7,10},{9,7,11},{10,7}}[[<<1>>]],2,3] are not the same shape. >>

General::stop: Further output of Set::shape will be suppressed during this calculation. >>

When I drop the last point I get the expected plot

PlanarGraphPlot@Drop[x, -1]

I’ve attached a file with the code. My Mathematica version is 9.0.1 on Mac OS X

Thanks

sukrause · April 26, 2014, 5:15pm

Me too, the error disappears after commenting any point out, not just the last one. This works (Windows 7 64 Bit Mma 9.0.1) with all points

PlanarGraphPlot[Sort[x]]

ksaranat · April 26, 2014, 10:42pm

Also this set of points fails to give proper ConvexHull. It fails silently without errors or warnings. Using Mma 9.0.1 64-bit on Mac OSX

y = {{1.8497859580704457`, 0.7790966948289985`}, {1.8497827815712071`,
    0.7790976595227784`}, {1.8497827082673783`, 
   0.7790974177736835`}, {1.849775543690799`, 
   0.7790995958192857`}, {1.8497765873976917`, 
   0.779102913545858`}, {1.8497787393886593`, 
   0.7791032174601015`}, {1.849783127146399`, 
   0.7791175682671613`}, {1.8497913720817853`, 
   0.7791137094455786`}, {1.8497940459261994`, 
   0.7791134308556135`}, {1.849796157774594`, 
   0.7791204232488069`}, {1.849804022228204`, 
   0.7791169604330455`}, {1.849803552734635`, 
   0.7791159289575218`}, {1.8498057134522492`, 
   0.7791151852825192`}, {1.8498006729413692`, 
   0.7790991813917657`}, {1.8498002121744468`, 
   0.7790984699581178`}, {1.8497995890919037`, 
   0.7790977401058187`}, {1.8497986151981813`, 
   0.7790973602143807`}, {1.8497975924352397`, 
   0.7790973993547065`}, {1.8497955957785752`, 
   0.77909842160827`}, {1.8497951821355425`, 
   0.7790997823117062`}, {1.8497944840038416`, 
   0.779101624213374`}, {1.8497934996381435`, 
   0.7791037516125543`}, {1.8497920021456453`, 
   0.779106194441444`}, {1.849792775326504`, 
   0.7791094914607818`}, {1.8497897908134828`, 
   0.7791098506337076`}}
Graphics@Point@y[[ ConvexHull[y] ]]

Thanks for trying on windows Udo. Sorting doesn’t help on Mac OS X.

sukrause · April 27, 2014, 7:47am

Sorting doesn’t help on Mac OS X.

To clarify, please: Sort[] under Windows does help under the following circumstances only

load the ComputationalGeometry package
read in data set x
comment any data point from the set out and save the notebook
run PlanarGraphPlot with that reduced set x
reactivate the data point, thus restoring the set x to its original content
run PlanarGraphPlot[Sort], it works

If one loads ComputationalGeometry package, reads in the set x and runs directly PlanarGraphPlot[Sort] under Windows, it fails too, like under Mac. I’ve searched for hidden content in the notebook, but did not find some.

sukrause · April 27, 2014, 8:22am

To clarify even more: there is a problem with pseudo collinearity within the set x, pointed out by

PlanarGraphPlot[Normalize/@x]

DelaunayTriangulation::collin: Points {{0.921589,0.388168},{0.921589,0.388167},{0.92159,0.388165},<<5>>,{0.921592,0.388159},{0.921592,0.388159},{0.921593,0.388158}} are collinear. >>

Knowing that one has to go to the last resort

PlanarGraphPlot[MapIndexed[Rationalize[#, 0] &, x, {2}]]

and that works without any special fiddling by the user.

sukrause · April 27, 2014, 8:27am

The set y seems to have a similiar problem you might investigate further, again Rationalize[] works

ksaranat · April 27, 2014, 7:27pm

It was due to floating point precision. See discussion here

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Problem with PlanarGraphPlot And ConvexHull

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