Get angle between point and origin

Question

This might have been answered before, sorry if it has. I basically need to get the angle from origin to point. So lets say Origin is (0, 0) and my target point is (3, 0).

3 O'clock = 90 degrees

6 O'clock = 180 degrees

9 O'clock = 270 degrees

12 O'clock = 0 degrees

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Somehow, I gotta do some math magic, and find out that the angle is 90 degrees (Top is 0). The origin can vary, so I need a method with two parameters, Origin, and TargetPoint, which returns double Angle in Degrees.

Yea, I realize this looks short and nonconstructive, but I made the question as simple and understandable as possible. All the other questions were closed -.-

Thanks

Answer 1

The vector between two points A and B is B-A = (B.x-A.x, B.y-A.y). The angle between two vectors can be calculated with the dot product or atan2.

var vector2 = Target - Origin;
var vector1 = new Point(0, 1) // 12 o'clock == 0°, assuming that y goes from bottom to top

double angleInRadians = Math.Atan2(vector2.Y, vector2.X) - Math.Atan2(vector1.Y, vector1.X);

See also Finding Signed Angle Between Vectors

Answer 2

Assuming x is positive, something like this:

angle = Math.Atan(y / x) * 180 / Math.PI + 90

Edited to allow for negative x values:

If it can be negative, just do it by case. Something like this:

if (x < 0) {
    angle = 270 - (Math.Atan(y / -x) * 180 / Math.PI);
} else {
    angle = 90 + (Math.Atan(y / x) * 180 / Math.PI);
}

Answer 3

public static double GetAngleDegree(Point origin, Point target) {
    var n = 270 - (Math.Atan2(origin.Y - target.Y, origin.X - target.X)) * 180 / Math.PI;
    return n % 360;
}

static void Main(string[] args)
{
    Console.WriteLine(GetAngleDegree(new Point(0, 0), new Point(0, 3)));//0
    Console.WriteLine(GetAngleDegree(new Point(0, 0), new Point(3, 0)));//90
    Console.WriteLine(GetAngleDegree(new Point(0, 0), new Point(0, -3)));//180
    Console.WriteLine(GetAngleDegree(new Point(0, 0), new Point(-3, 0)));//270 
}

Answer 4

Actually there is no way to find out the angle between point and origin due to the fact that the origin is (0,0). We can calculate the angle between 2 points beacuse they are treated like vectors and as such they have a direction, but the origin has no direction. For that reason, if you want to find the angle using the example of a clock you can calculate the angle between the point and (1,0) for example being that point at 0 degrees.

I'm sorry I'm not versed in C# but you can have a look at this java code which is similar:

double getAngle2PointsRad(double p1_x, double p1_y, double p2_x, double p2_y) {
  return Math.acos((((p1_x * p2_x) + (p1_y * p2_y)) / (Math.sqrt(Math.pow(p1_x, 2) + Math.pow(p1_y, 2)) * Math.sqrt(Math.pow(p2_x, 2) + Math.pow(p2_y, 2)))));
}

double getAngle2PointsDeg(double p1_x, double p1_y, double p2_x, double p2_y) {
  return Math.acos((((p1_x * p2_x) + (p1_y * p2_y)) / (Math.sqrt(Math.pow(p1_x, 2) + Math.pow(p1_y, 2)) * Math.sqrt(Math.pow(p2_x, 2) + Math.pow(p2_y, 2))))) * 180 / Math.PI;
}

If you try to calculate using (0,0) you will get NaN beacuse it tries to divide by zero.