How to Determine if a Point Lies Within a Polygon in C#?

C# Point in Polygon: Determining if a Point Lies Within a Polygon

Consider the scenario where you want to determine if a point exists within the boundaries of a polygon. To accomplish this task in C# using WinForms, follow these steps:

1. Calculate Polygon Bounds: Establish the bounding box for the polygon by identifying the minimum and maximum X and Y coordinates among its vertices.
2. Determine if Point is Within Bounds: Verify if the given point lies within the polygon's bounding box. If not, the point is definitely outside the polygon.
3. Check Point Inclusion in Polygon: To determine if the point is actually within the polygon's shape, employ the Point-in-Polygon algorithm technique.

One such algorithm is the Ray Crossing method, which involves the following steps:

a. Imagine drawing horizontal rays from the given point to infinity.

b. Count the number of times the ray intersects the polygon's edges.

c. If the count is odd, the point is inside the polygon; if even, it is outside the polygon.

Here is an example implementation of the Ray Crossing algorithm in C#:

using System;
using System.Collections.Generic;
using System.Drawing;

public class Polygon
{
    List<PointF> vertices = new List<PointF>();

    public bool Contains(PointF point)
    {
        if (IsOutsideBoundingBox(point)) return false;

        int intersectionCount = 0;
        for (int i = 0; i < vertices.Count; i++)
        {
            int j = (i + 1) % vertices.Count;
            PointF a = vertices[i], b = vertices[j];
            if ((a.Y > point.Y && b.Y <= point.Y)
                || (a.Y <= point.Y && b.Y > point.Y))
            {
                double slope = (double)(b.Y - a.Y) / (b.X - a.X);
                if (point.X < a.X + (point.Y - a.Y) / slope)
                    intersectionCount++;
            }
        }

        return intersectionCount % 2 == 1;
    }

    private bool IsOutsideBoundingBox(PointF point)
    {
        return point.X < Xmin || point.X > Xmax || point.Y < Ymin || point.Y > Ymax;
    }
}

This implementation ensures accuracy and efficiency while determining if a point is within a polygon.

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