How to determine the longest edge in a graph?












4














I have a list of 2D points such as in the image. 



coord = {{0, 0}, {10, 0}, {20, 0}, {30, 0}, {25, 10}, {0, 10}, {0, 

5}};


enter image description here



I would like to determine the longest "edge" length in a way that if 2 segments are in same line, they would be considered as part of 1 edge. For example, segments 1-2, 2-3, 3-4 are continuous and in the same line, so we consider it as 1 edge connecting Vertex 1 and Vertex 4. In this example, the longest edge length would be the distance from vertex 1 to vertex 4. How can I determine the longest edge length in Mathematica?






list-manipulation graphics







share|improve this question



























    4














    I have a list of 2D points such as in the image. 



    coord = {{0, 0}, {10, 0}, {20, 0}, {30, 0}, {25, 10}, {0, 10}, {0, 
    
5}};


    enter image description here



    I would like to determine the longest "edge" length in a way that if 2 segments are in same line, they would be considered as part of 1 edge. For example, segments 1-2, 2-3, 3-4 are continuous and in the same line, so we consider it as 1 edge connecting Vertex 1 and Vertex 4. In this example, the longest edge length would be the distance from vertex 1 to vertex 4. How can I determine the longest edge length in Mathematica?






    list-manipulation graphics







    share|improve this question

























      4












      4








      4







      I have a list of 2D points such as in the image. 



      coord = {{0, 0}, {10, 0}, {20, 0}, {30, 0}, {25, 10}, {0, 10}, {0, 
      
5}};


      enter image description here



      I would like to determine the longest "edge" length in a way that if 2 segments are in same line, they would be considered as part of 1 edge. For example, segments 1-2, 2-3, 3-4 are continuous and in the same line, so we consider it as 1 edge connecting Vertex 1 and Vertex 4. In this example, the longest edge length would be the distance from vertex 1 to vertex 4. How can I determine the longest edge length in Mathematica?






      list-manipulation graphics







      share|improve this question













      I have a list of 2D points such as in the image. 



      coord = {{0, 0}, {10, 0}, {20, 0}, {30, 0}, {25, 10}, {0, 10}, {0, 
      
5}};


      enter image description here



      I would like to determine the longest "edge" length in a way that if 2 segments are in same line, they would be considered as part of 1 edge. For example, segments 1-2, 2-3, 3-4 are continuous and in the same line, so we consider it as 1 edge connecting Vertex 1 and Vertex 4. In this example, the longest edge length would be the distance from vertex 1 to vertex 4. How can I determine the longest edge length in Mathematica?






      list-manipulation graphics




      list-manipulation graphics






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 3 hours ago









      N.T.C

      36417




      36417






















          1 Answer
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          3














          Using the function noncollinearF from this answer:



          ClearAll[noncollinearF]
          
noncollinearF[verts_] := Function[{k}, Nor @@ (RegionMember[ConvexHullMesh[#], k] & /@ 
          
  Subsets[Complement[verts, {k}], {2}])]
          

          
lines =Line /@ Partition[Pick[#, noncollinearF[#] /@ #] &[#[[FindShortestTour[#][[2]]]]], 
          
   2, 1, {1, 1}] & @ coord;
          
longest = Last@SortBy[lines, N@ArcLength[#] &]; 
          
Graphics[{EdgeForm[Gray], FaceForm, Polygon@coord, 
          
  Blue, PointSize[Large], Point@coord, 
          
  Thickness[.03], CapForm["Round"], Opacity[.5], Red, longest}]


          enter image description here






          share|improve this answer























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            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            3














            Using the function noncollinearF from this answer:



            ClearAll[noncollinearF]
            
noncollinearF[verts_] := Function[{k}, Nor @@ (RegionMember[ConvexHullMesh[#], k] & /@ 
            
  Subsets[Complement[verts, {k}], {2}])]
            

            
lines =Line /@ Partition[Pick[#, noncollinearF[#] /@ #] &[#[[FindShortestTour[#][[2]]]]], 
            
   2, 1, {1, 1}] & @ coord;
            
longest = Last@SortBy[lines, N@ArcLength[#] &]; 
            
Graphics[{EdgeForm[Gray], FaceForm, Polygon@coord, 
            
  Blue, PointSize[Large], Point@coord, 
            
  Thickness[.03], CapForm["Round"], Opacity[.5], Red, longest}]


            enter image description here






            share|improve this answer




























              3














              Using the function noncollinearF from this answer:



              ClearAll[noncollinearF]
              
noncollinearF[verts_] := Function[{k}, Nor @@ (RegionMember[ConvexHullMesh[#], k] & /@ 
              
  Subsets[Complement[verts, {k}], {2}])]
              

              
lines =Line /@ Partition[Pick[#, noncollinearF[#] /@ #] &[#[[FindShortestTour[#][[2]]]]], 
              
   2, 1, {1, 1}] & @ coord;
              
longest = Last@SortBy[lines, N@ArcLength[#] &]; 
              
Graphics[{EdgeForm[Gray], FaceForm, Polygon@coord, 
              
  Blue, PointSize[Large], Point@coord, 
              
  Thickness[.03], CapForm["Round"], Opacity[.5], Red, longest}]


              enter image description here






              share|improve this answer


























                3












                3








                3






                Using the function noncollinearF from this answer:



                ClearAll[noncollinearF]
                
noncollinearF[verts_] := Function[{k}, Nor @@ (RegionMember[ConvexHullMesh[#], k] & /@ 
                
  Subsets[Complement[verts, {k}], {2}])]
                

                
lines =Line /@ Partition[Pick[#, noncollinearF[#] /@ #] &[#[[FindShortestTour[#][[2]]]]], 
                
   2, 1, {1, 1}] & @ coord;
                
longest = Last@SortBy[lines, N@ArcLength[#] &]; 
                
Graphics[{EdgeForm[Gray], FaceForm, Polygon@coord, 
                
  Blue, PointSize[Large], Point@coord, 
                
  Thickness[.03], CapForm["Round"], Opacity[.5], Red, longest}]


                enter image description here






                share|improve this answer














                Using the function noncollinearF from this answer:



                ClearAll[noncollinearF]
                
noncollinearF[verts_] := Function[{k}, Nor @@ (RegionMember[ConvexHullMesh[#], k] & /@ 
                
  Subsets[Complement[verts, {k}], {2}])]
                

                
lines =Line /@ Partition[Pick[#, noncollinearF[#] /@ #] &[#[[FindShortestTour[#][[2]]]]], 
                
   2, 1, {1, 1}] & @ coord;
                
longest = Last@SortBy[lines, N@ArcLength[#] &]; 
                
Graphics[{EdgeForm[Gray], FaceForm, Polygon@coord, 
                
  Blue, PointSize[Large], Point@coord, 
                
  Thickness[.03], CapForm["Round"], Opacity[.5], Red, longest}]


                enter image description here







                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited 2 hours ago

























                answered 2 hours ago









                kglr

                177k9198405




                177k9198405






























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