Calculating the distance between 2 points

Question

I have two points (x1,y1) and (x2,y2). I want to know whether the points are within 5 meters of one another.

Answer 1

If you are using System.Windows.Point data type to represent a point, you can use

// assuming p1 and p2 data types
Point p1, p2;
// distanc can be calculated as follows
double distance = Point.Subtract(p2, p1).Length;

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Update 2017-01-08:

• Add reference to Microsoft documentation
• Result of Point.Subtract is System.Windows.Vector and it has also property LengthSquared to save one sqrt calculation if you just need to compare distance.
• Adding reference to WindowsBase assembly may be needed in your project
• You can also use operators

Example with LengthSquared and operators

// assuming p1 and p2 data types
Point p1, p2;
// distanc can be calculated as follows
double distanceSquared = (p2 - p1).LengthSquared;

Answer 2

measure the square distance from one point to the other:

((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2)) < d*d

where d is the distance, (x1,y1) are the coordinates of the 'base point' and (x2,y2) the coordinates of the point you want to check.

or if you prefer:

(Math.Pow(x1-x2,2)+Math.Pow(y1-y2,2)) < (d*d);

Noticed that the preferred one does not call Pow at all for speed reasons, and the second one, probably slower, as well does not call Math.Sqrt , always for performance reasons. Maybe such optimization are premature in your case, but they are useful if that code has to be executed a lot of times.

Of course you are talking in meters and I supposed point coordinates are expressed in meters too.

Answer 3

Something like this in c# would probably do the job. Just make sure you are passing consistent units (If one point is in meters, make sure the second is also in meters)

private static double GetDistance(double x1, double y1, double x2, double y2)
{
   return Math.Sqrt(Math.Pow((x2 - x1), 2) + Math.Pow((y2 - y1), 2));
}

Called like so:

double distance = GetDistance(x1, y1, x2, y2)
if(distance <= 5)
{
   //Do stuff
}

Answer 4

Given points (X1,Y1) and (X2,Y2) then:

dX = X1 - X2;
dY = Y1 - Y2;

if (dX*dX + dY*dY > (5*5))
{
    //your code
}

Answer 5

Here is my 2 cents:

double dX = x1 - x2;
double dY = y1 - y2;
double multi = dX * dX + dY * dY;
double rad = Math.Round(Math.Sqrt(multi), 3);

x1, y1 is the first coordinate and x2, y2 the second. The last line is the square root with it rounded to 3 decimal places.

Answer 6

if u use System.Drawing.Point ;

Point p1 = new Point();
Point p2 = new Point();

Math.Pow(Math.Pow(p1.X - p2.X, 2) + Math.Pow(p1.Y - p2.Y, 2), 1 / 2);

if u use System.Windows.Point like wpf ;

Point.Subtract(_p1, _p2).Length;

Answer 7

Based on Jack's answer , I use the following extension method:

public static class Extensions
{
    public static double DistanceTo(this Point from, Point to)
    {
        var result = Math.Sqrt(Math.Pow((from.X - to.X), 2) + Math.Pow((from.Y - to.Y), 2));
        return result;
    }
}

Which allows for the following:

var distance = point1.DistanceTo(point2);

Answer 8

System.Numerics has this functionality for vector 3

    /// <summary>
    /// Returns the Euclidean distance between the two given points.
    /// </summary>
    /// <param name="value1">The first point.</param>
    /// <param name="value2">The second point.</param>
    /// <returns>The distance.</returns>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
public static float Distance(Vector3 value1, Vector3 value2) {
    if (Vector.IsHardwareAccelerated) {
        Vector3 difference = value1 - value2;
        float ls = Vector3.Dot(difference, difference);
        return (float) System.Math.Sqrt(ls);
    } else {
        float dx = value1.X - value2.X;
        float dy = value1.Y - value2.Y;
        float dz = value1.Z - value2.Z;

        float ls = dx * dx + dy * dy + dz * dz;

        return (float) System.Math.Sqrt((double) ls);
    }
}

/// <summary>
/// Returns the Euclidean distance squared between the two given points.
/// </summary>
/// <param name="value1">The first point.</param>
/// <param name="value2">The second point.</param>
/// <returns>The distance squared.</returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static float DistanceSquared(Vector3 value1, Vector3 value2) {
    if (Vector.IsHardwareAccelerated) {
        Vector3 difference = value1 - value2;
        return Vector3.Dot(difference, difference);
    } else {
        float dx = value1.X - value2.X;
        float dy = value1.Y - value2.Y;
        float dz = value1.Z - value2.Z;

        return dx * dx + dy * dy + dz * dz;
    }
}

Reference here https://referencesource.microsoft.com/#System.Numerics/System/Numerics/Vector3.cs

Answer 9

您可以使用以下公式来计算 2 点之间的距离：

distance*distance = ((x2 − x1)*(x2 - x1)) + ((y2 − y1)*(y2 - y1))

Answer 10

算法：（（x1-x2）^ 2 +（y1-y2）^ 2）<25