Skip to main content

graphics - Find intersection of pairs of straight lines


I have a list of 24 points, in which two consecutive points (1st and 2nd, 3rd and 4th, …) are supposed to form a line:


p1={{243.8, 77.}, {467.4, 12.}, {291.8, 130.}, {476., 210.5}, {103.2, 
  327.}, {245.2, 110.5}, {47.4, 343.}, {87.4, 108.5}, {371., 
  506.5}, {384.6, 277.}, {264.6, 525.5}, {353.8, 294.5}, {113.2, 
  484.5}, {296., 304.5}, {459.6, 604.5}, {320.2, 466.5}, {288.2, 

  630.5}, {199.6, 446.5}, {138.8, 615.5}, {81.8, 410.}, {232.4, 
  795.}, {461.8, 727.}, {27.4, 671.5}, {206.8, 763.5}};

I also have another list of 24 points with the same property:


p2={{356.8, 32.}, {363.2, 120.}, {346., 245.}, {393.8, 158.}, {163.8, 
  211.5}, {230.2, 250.}, {54.6, 225.}, {139.6, 220.}, {366., 
  394.5}, {451.8, 372.}, {241., 398.}, {321., 411.5}, {163.2, 
  347.}, {213.2, 406.5}, {332.4, 596.5}, {402.4, 528.5}, {176., 
  585.5}, {256., 530.5}, {38.2, 553.}, {122.4, 507.}, {345.2, 
  774.5}, {345.2, 688.}, {104.6, 728.}, {161.8, 647.}};


My goal is to find the intersections between a line in p1 and a line in p2 as shown in the graph below. I really don't know how to start with this, and worse, a line on p1 does not match up with the intersecting line in p2 in terms of order in each list. This could be observed by different colors of 2 intersecting lines, and makes it harder for element-by-element manipulation*. How can I solve this?


Join[Partition[p1, 2], Partition[p2, 2]] // ListLinePlot

Join Partition line intersection


*I found out that this is thankfully not true, as seen below when line i in p1 and line i in p2 are plotted together, and also by Öskå in a comment to eldo's answer.


Row@Table[
  ListLinePlot[{Partition[p1, 2][[i]], Partition[p2, 2][[i]]}], {i, 1,
    Length@Partition[p1, 2]}]


line pairs


lines



Answer



p1 = Partition[{{243.8, 77.}, {467.4, 12.}, {291.8, 130.}, {476., 
    210.5}, {103.2, 327.}, {245.2, 110.5}, {47.4, 343.}, {87.4, 
    108.5}, {371., 506.5}, {384.6, 277.}, {264.6, 525.5}, {353.8, 
    294.5}, {113.2, 484.5}, {296., 304.5}, {459.6, 604.5}, {320.2, 
    466.5}, {288.2, 630.5}, {199.6, 446.5}, {138.8, 615.5}, {81.8, 
    410.}, {232.4, 795.}, {461.8, 727.}, {27.4, 671.5}, {206.8, 
    763.5}}, 2];


p2 = Partition[{{356.8, 32.}, {363.2, 120.}, {346., 245.}, {393.8, 
     158.}, {163.8, 211.5}, {230.2, 250.}, {54.6, 225.}, {139.6, 
     220.}, {366., 394.5}, {451.8, 372.}, {241., 398.}, {321., 
     411.5}, {163.2, 347.}, {213.2, 406.5}, {332.4, 596.5}, {402.4, 
     528.5}, {176., 585.5}, {256., 530.5}, {38.2, 553.}, {122.4, 
     507.}, {345.2, 774.5}, {345.2, 688.}, {104.6, 728.}, {161.8, 
     647.}}, 2];

LineIntersectionPoint[{a_, b_}, {c_, d_}] := 

  (Det[{a, b}] (c - d) - Det[{c, d}] (a - b))/Det[{a - b, c - d}]

Graphics[{Line /@ {p1, p2}, Red, PointSize@.05, 
  Point /@ MapThread[LineIntersectionPoint, {p1, p2}]}, Frame -> True]

Mathematica graphics


Ref for finding intersection of 2 lines by determinants


line graph


determinant intersection


Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
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

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