Area of a 2D convex hull Announcing the arrival of Valued Associate #679: Cesar Manara ...

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Area of a 2D convex hull

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Area of a 2D convex hull



Announcing the arrival of Valued Associate #679: Cesar Manara
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Sandbox for Proposed ChallengesWhat is the area of this polygon?Find the Convex Hull of a set of 2D pointsFind the area of the largest convex polygonPoint in convex hull (2D)The happy Ender problemDoes the triangle contain the origin?What is the area of this polygon?Sort the points by linear distance in a 3D spaceElliptic systemMaximum Area of a Polygon with Vertices of a PolygonCircle intersection area












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
    3 hours ago






  • 5




    $begingroup$
    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
    2 hours ago








  • 1




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










  • $begingroup$
    Related
    $endgroup$
    – Giuseppe
    13 mins 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
    3 hours ago






  • 5




    $begingroup$
    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
    2 hours ago








  • 1




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










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







Vladimir Reshetnikov

















asked 3 hours ago









Vladimir ReshetnikovVladimir Reshetnikov

1,9781613




1,9781613








  • 2




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






  • 5




    $begingroup$
    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
    2 hours ago








  • 1




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










  • $begingroup$
    Related
    $endgroup$
    – Giuseppe
    13 mins ago














  • 2




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






  • 5




    $begingroup$
    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
    2 hours ago








  • 1




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










  • $begingroup$
    Related
    $endgroup$
    – Giuseppe
    13 mins ago








2




2




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




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




5




5




$begingroup$
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
2 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
2 hours ago






1




1




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




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












$begingroup$
Related
$endgroup$
– Giuseppe
13 mins ago




$begingroup$
Related
$endgroup$
– Giuseppe
13 mins ago










2 Answers
2






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









$endgroup$





















    0












    $begingroup$


    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 2 hours ago









          MickyTMickyT

          10.4k21637




          10.4k21637























              0












              $begingroup$


              Wolfram Language (Mathematica), 27 bytes



              Round@*Area@*ConvexHullMesh


              Try it online!






              share|improve this answer









              $endgroup$


















                0












                $begingroup$


                Wolfram Language (Mathematica), 27 bytes



                Round@*Area@*ConvexHullMesh


                Try it online!






                share|improve this answer









                $endgroup$
















                  0












                  0








                  0





                  $begingroup$


                  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 59 mins ago









                  attinatattinat

                  4897




                  4897






























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