Skip to main content

computational geometry - RegionIntersection puzzle


I am using RegionIntersection[] to intersect two rectangles, phrased as Polygon[]s:



BugRegInt

RegionIntersection[] returns an incorrect result (the green region above; detail below), and issues a series of error messages:

Errors


Here is the region returned as the intersection, which is not correct (it should be a quadrilateral):
Polygon[{{0.407273, 0.650444}, {0.509656, -0.0200315}, {0.998507, 
   0.0546171}, {0.640904, 0.767621}, {0.998507, 0.0546171}}]

Here it is as a line drawing:



PentQuad

Here is the originating call that produces the incorrect intersection:


RegionIntersection[

 Polygon[{{0.5096555454081809`, -0.02003146973392257`}, \
{0.9985073695269602`, 0.05461714932464575`}, {0.6966031018052412`, 
    2.0316992956026936`}, {0.2077512776864619`, 
    1.9570506765441251`}}] , 
 Polygon[{{0.9985073695269602`, 
    0.05461714932464575`}, {0.6409040075686694`, 
    0.767621034809768`}, {-1.1468443539373534`, \
-0.12901478643123643`}, {-0.7892409919790626`, -0.8420186719163586`}}]
 ]


Can anyone see what's going on?



Answer



This is a bug that has been fixed in the development version. For a possible workaround, use exact coordinates, for example


sp = Function[p, SetPrecision[p, Infinity]];

ri = RegionIntersection[
 sp@Polygon[{{0.5096555454081809`, -0.02003146973392257`}, 
             {0.9985073695269602`, 0.05461714932464575`}, 
             {0.6966031018052412`, 2.0316992956026936`},   
             {0.2077512776864619`, 1.9570506765441251`}}], 

 sp@Polygon[{{0.9985073695269602`, 0.05461714932464575`}, 
             {0.6409040075686694`, 0.767621034809768`},    
             {-1.1468443539373534`, -0.12901478643123643`}, 
             {-0.7892409919790626`, -0.8420186719163586`}}]];

N[ri]

(* Polygon[{{0.40727258068338046`, 0.6504444171024929`}, 
            {0.5096555454081809`, -0.02003146973392257`}, 
            {0.9985073695269602`, 0.05461714932464575`}, 

            {0.6409040075686694`, 0.767621034809768`}}] *)

Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...
Post a Comment
Read more