Area of a 2D convex hull












1












$begingroup$


You are given an array/list/vector of pairs of integers representing cartesian coordinates (x, y) of points on a 2D Euclidean plane; all coordinates are between −104 and 104, duplicates are allowed. Find the area of the convex hull of those points, rounded to the nearest integer; an exact midpoint should be rounded to the closest even integer. You may use floating-point numbers in intermediate computations, but only if you can guarantee that the final result will be always correct. This is a code-golf, the shortest correct program (ignoring non-significant whitespace, newlines and comments) wins.



Some test cases:



Input: [[50, -13]]

Result: 0



Input: [[-25, -26], [34, -27]]

Result: 0



Input: [[-6, -14], [-48, -45], [21, 25]]

Result: 400



Input: [[4, 30], [5, 37], [-18, 49], [-9, -2]]

Result: 562



Input: [[0, 16], [24, 18], [-43, 36], [39, -29], [3, -38]]

Result: 2978



Input: [[19, -19], [15, 5], [-16, -41], [6, -25], [-42, 1], [12, 19]]

Result: 2118



Input: [[-23, 13], [-13, 13], [-6, -7], [22, 41], [-26, 50], [12, -12], [-23, -7]]

Result: 2307



Input: [[31, -19], [-41, -41], [25, 34], [29, -1], [42, -42], [-34, 32], [19, 33], [40, 39]]

Result: 6037



Input: [[47, 1], [-22, 24], [36, 38], [-17, 4], [41, -3], [-13, 15], [-36, -40], [-13, 35], [-25, 22]]

Result: 3908



Input: [[29, -19], [18, 9], [30, -46], [15, 20], [24, -4], [5, 19], [-44, 4], [-20, -8], [-16, 34], [17, -36]]

Result: 2905





code-golf number geometry integer







share|improve this question











$endgroup$








  • 2




    $begingroup$
    Do you have any test cases?
    $endgroup$
    – Maltysen
    5 hours ago






  • 6




    $begingroup$
    Not counting whitespace in code golf is a bad idea, it leads to submissions with massive strings of whitespace plus generic code to convert the string to code and execute it.
    $endgroup$
    – xnor
    4 hours ago








  • 1




    $begingroup$
    So if someone can just make a whitespace solution...
    $endgroup$
    – attinat
    3 hours ago










  • $begingroup$
    Related
    $endgroup$
    – Giuseppe
    2 hours ago
















1












$begingroup$


You are given an array/list/vector of pairs of integers representing cartesian coordinates (x, y) of points on a 2D Euclidean plane; all coordinates are between −104 and 104, duplicates are allowed. Find the area of the convex hull of those points, rounded to the nearest integer; an exact midpoint should be rounded to the closest even integer. You may use floating-point numbers in intermediate computations, but only if you can guarantee that the final result will be always correct. This is a code-golf, the shortest correct program (ignoring non-significant whitespace, newlines and comments) wins.



Some test cases:



Input: [[50, -13]]

Result: 0



Input: [[-25, -26], [34, -27]]

Result: 0



Input: [[-6, -14], [-48, -45], [21, 25]]

Result: 400



Input: [[4, 30], [5, 37], [-18, 49], [-9, -2]]

Result: 562



Input: [[0, 16], [24, 18], [-43, 36], [39, -29], [3, -38]]

Result: 2978



Input: [[19, -19], [15, 5], [-16, -41], [6, -25], [-42, 1], [12, 19]]

Result: 2118



Input: [[-23, 13], [-13, 13], [-6, -7], [22, 41], [-26, 50], [12, -12], [-23, -7]]

Result: 2307



Input: [[31, -19], [-41, -41], [25, 34], [29, -1], [42, -42], [-34, 32], [19, 33], [40, 39]]

Result: 6037



Input: [[47, 1], [-22, 24], [36, 38], [-17, 4], [41, -3], [-13, 15], [-36, -40], [-13, 35], [-25, 22]]

Result: 3908



Input: [[29, -19], [18, 9], [30, -46], [15, 20], [24, -4], [5, 19], [-44, 4], [-20, -8], [-16, 34], [17, -36]]

Result: 2905





code-golf number geometry integer







share|improve this question











$endgroup$








  • 2




    $begingroup$
    Do you have any test cases?
    $endgroup$
    – Maltysen
    5 hours ago






  • 6




    $begingroup$
    Not counting whitespace in code golf is a bad idea, it leads to submissions with massive strings of whitespace plus generic code to convert the string to code and execute it.
    $endgroup$
    – xnor
    4 hours ago








  • 1




    $begingroup$
    So if someone can just make a whitespace solution...
    $endgroup$
    – attinat
    3 hours ago










  • $begingroup$
    Related
    $endgroup$
    – Giuseppe
    2 hours ago














1












1








1





$begingroup$


You are given an array/list/vector of pairs of integers representing cartesian coordinates (x, y) of points on a 2D Euclidean plane; all coordinates are between −104 and 104, duplicates are allowed. Find the area of the convex hull of those points, rounded to the nearest integer; an exact midpoint should be rounded to the closest even integer. You may use floating-point numbers in intermediate computations, but only if you can guarantee that the final result will be always correct. This is a code-golf, the shortest correct program (ignoring non-significant whitespace, newlines and comments) wins.



Some test cases:



Input: [[50, -13]]

Result: 0



Input: [[-25, -26], [34, -27]]

Result: 0



Input: [[-6, -14], [-48, -45], [21, 25]]

Result: 400



Input: [[4, 30], [5, 37], [-18, 49], [-9, -2]]

Result: 562



Input: [[0, 16], [24, 18], [-43, 36], [39, -29], [3, -38]]

Result: 2978



Input: [[19, -19], [15, 5], [-16, -41], [6, -25], [-42, 1], [12, 19]]

Result: 2118



Input: [[-23, 13], [-13, 13], [-6, -7], [22, 41], [-26, 50], [12, -12], [-23, -7]]

Result: 2307



Input: [[31, -19], [-41, -41], [25, 34], [29, -1], [42, -42], [-34, 32], [19, 33], [40, 39]]

Result: 6037



Input: [[47, 1], [-22, 24], [36, 38], [-17, 4], [41, -3], [-13, 15], [-36, -40], [-13, 35], [-25, 22]]

Result: 3908



Input: [[29, -19], [18, 9], [30, -46], [15, 20], [24, -4], [5, 19], [-44, 4], [-20, -8], [-16, 34], [17, -36]]

Result: 2905





code-golf number geometry integer







share|improve this question











$endgroup$




You are given an array/list/vector of pairs of integers representing cartesian coordinates (x, y) of points on a 2D Euclidean plane; all coordinates are between −104 and 104, duplicates are allowed. Find the area of the convex hull of those points, rounded to the nearest integer; an exact midpoint should be rounded to the closest even integer. You may use floating-point numbers in intermediate computations, but only if you can guarantee that the final result will be always correct. This is a code-golf, the shortest correct program (ignoring non-significant whitespace, newlines and comments) wins.



Some test cases:



Input: [[50, -13]]

Result: 0



Input: [[-25, -26], [34, -27]]

Result: 0



Input: [[-6, -14], [-48, -45], [21, 25]]

Result: 400



Input: [[4, 30], [5, 37], [-18, 49], [-9, -2]]

Result: 562



Input: [[0, 16], [24, 18], [-43, 36], [39, -29], [3, -38]]

Result: 2978



Input: [[19, -19], [15, 5], [-16, -41], [6, -25], [-42, 1], [12, 19]]

Result: 2118



Input: [[-23, 13], [-13, 13], [-6, -7], [22, 41], [-26, 50], [12, -12], [-23, -7]]

Result: 2307



Input: [[31, -19], [-41, -41], [25, 34], [29, -1], [42, -42], [-34, 32], [19, 33], [40, 39]]

Result: 6037



Input: [[47, 1], [-22, 24], [36, 38], [-17, 4], [41, -3], [-13, 15], [-36, -40], [-13, 35], [-25, 22]]

Result: 3908



Input: [[29, -19], [18, 9], [30, -46], [15, 20], [24, -4], [5, 19], [-44, 4], [-20, -8], [-16, 34], [17, -36]]

Result: 2905





code-golf number geometry integer




code-golf number geometry integer






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 4 hours ago







Vladimir Reshetnikov

















asked 5 hours ago









Vladimir ReshetnikovVladimir Reshetnikov

1,9781613




1,9781613








  • 2




    $begingroup$
    Do you have any test cases?
    $endgroup$
    – Maltysen
    5 hours ago






  • 6




    $begingroup$
    Not counting whitespace in code golf is a bad idea, it leads to submissions with massive strings of whitespace plus generic code to convert the string to code and execute it.
    $endgroup$
    – xnor
    4 hours ago








  • 1




    $begingroup$
    So if someone can just make a whitespace solution...
    $endgroup$
    – attinat
    3 hours ago










  • $begingroup$
    Related
    $endgroup$
    – Giuseppe
    2 hours ago














  • 2




    $begingroup$
    Do you have any test cases?
    $endgroup$
    – Maltysen
    5 hours ago






  • 6




    $begingroup$
    Not counting whitespace in code golf is a bad idea, it leads to submissions with massive strings of whitespace plus generic code to convert the string to code and execute it.
    $endgroup$
    – xnor
    4 hours ago








  • 1




    $begingroup$
    So if someone can just make a whitespace solution...
    $endgroup$
    – attinat
    3 hours ago










  • $begingroup$
    Related
    $endgroup$
    – Giuseppe
    2 hours ago








2




2




$begingroup$
Do you have any test cases?
$endgroup$
– Maltysen
5 hours ago




$begingroup$
Do you have any test cases?
$endgroup$
– Maltysen
5 hours ago




6




6




$begingroup$
Not counting whitespace in code golf is a bad idea, it leads to submissions with massive strings of whitespace plus generic code to convert the string to code and execute it.
$endgroup$
– xnor
4 hours ago






$begingroup$
Not counting whitespace in code golf is a bad idea, it leads to submissions with massive strings of whitespace plus generic code to convert the string to code and execute it.
$endgroup$
– xnor
4 hours ago






1




1




$begingroup$
So if someone can just make a whitespace solution...
$endgroup$
– attinat
3 hours ago




$begingroup$
So if someone can just make a whitespace solution...
$endgroup$
– attinat
3 hours ago












$begingroup$
Related
$endgroup$
– Giuseppe
2 hours ago




$begingroup$
Related
$endgroup$
– Giuseppe
2 hours ago










2 Answers
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$begingroup$

SQL Server 2012+, 84 bytes



SELECT Round(Geometry::ConvexHullAggregate(Geometry::Point(x,y,0)).STArea(),0)FROM A


Makes use of the geometry functions and aggregates in SQL Server.
Coordindates are from table A with columns x and y.






share|improve this answer









$endgroup$





















    1












    $begingroup$


    Wolfram Language (Mathematica), 27 bytes



    Round@*Area@*ConvexHullMesh


    Try it online!






    share|improve this answer









    $endgroup$














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      2 Answers
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      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      3












      $begingroup$

      SQL Server 2012+, 84 bytes



      SELECT Round(Geometry::ConvexHullAggregate(Geometry::Point(x,y,0)).STArea(),0)FROM A


      Makes use of the geometry functions and aggregates in SQL Server.
      Coordindates are from table A with columns x and y.






      share|improve this answer









      $endgroup$


















        3












        $begingroup$

        SQL Server 2012+, 84 bytes



        SELECT Round(Geometry::ConvexHullAggregate(Geometry::Point(x,y,0)).STArea(),0)FROM A


        Makes use of the geometry functions and aggregates in SQL Server.
        Coordindates are from table A with columns x and y.






        share|improve this answer









        $endgroup$
















          3












          3








          3





          $begingroup$

          SQL Server 2012+, 84 bytes



          SELECT Round(Geometry::ConvexHullAggregate(Geometry::Point(x,y,0)).STArea(),0)FROM A


          Makes use of the geometry functions and aggregates in SQL Server.
          Coordindates are from table A with columns x and y.






          share|improve this answer









          $endgroup$



          SQL Server 2012+, 84 bytes



          SELECT Round(Geometry::ConvexHullAggregate(Geometry::Point(x,y,0)).STArea(),0)FROM A


          Makes use of the geometry functions and aggregates in SQL Server.
          Coordindates are from table A with columns x and y.







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 4 hours ago









          MickyTMickyT

          10.4k21637




          10.4k21637























              1












              $begingroup$


              Wolfram Language (Mathematica), 27 bytes



              Round@*Area@*ConvexHullMesh


              Try it online!






              share|improve this answer









              $endgroup$


















                1












                $begingroup$


                Wolfram Language (Mathematica), 27 bytes



                Round@*Area@*ConvexHullMesh


                Try it online!






                share|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$


                  Wolfram Language (Mathematica), 27 bytes



                  Round@*Area@*ConvexHullMesh


                  Try it online!






                  share|improve this answer









                  $endgroup$




                  Wolfram Language (Mathematica), 27 bytes



                  Round@*Area@*ConvexHullMesh


                  Try it online!







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered 3 hours ago









                  attinatattinat

                  4997




                  4997






























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