How to find the closest points above and below a given point?

Question

I have a polygon defined by the following vertices, represented by their X and Y values and sorted in a counter-clockwise order:

{ 20, 10},
{110, 10},
{100, 40},
{ 80, 50},
{ 40, 50},
{ 20, 30}

I also have a List<int> containing their indices . I can zip the two lists together if I want to reorder the points while keeping track of the original order.

How should i go about getting the closest points above and below a given point, so that entering:

point = {115, 30}

Would output:

closestAbove = {100, 40}, index = 2
closestBelow = {110, 10}, index = 1

Performance isn't critical , so iterating multiple times through the list is not an issue.

Answer 1

First, let's come to terms:

  // I've put named tuples, but you can use a different type for points
  (double x, double y)[] points = new (double x, double y)[] {
    (  20, 10 ), 
    ( 110, 10 ), 
    ( 100, 40 ), 
    (  80, 50 ), 
    (  40, 50 ), 
    (  20, 30 ),
  };

  // Euclidian distance
  Func<(double x, double y), (double x, double y), double> distance = (p1, p2) =>
    Math.Sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y));

  (double x, double y) point = (115, 30);

And then query with a help of Linq ; even if ArgMin is not implemented by standard Linq, it can be easily done with a help of Aggregate :

  var above = points
    .Select((p, index) => new {
      p,
      index
    })
    .Where(item => item.p.y > point.y) // change to < for below
    .Aggregate((distance: 0.0,
                x: 0.0,
                y: 0.0,
                index: -1),
               (s, a) => s.index < 0 || s.distance > distance(point, a.p)
                  ? (distance(point, a.p), a.p.x, a.p.y, a.index)
                  : s);

Let's have a look:

  Console.Write($"Point #{above.index} ({above.x}, {above.y}) is the closest point to the ({point.x}, {point.y})");

Outcome:

Point #2 (100, 40) is the closest point to the (115, 30)