How can I find the perpendicular to a 2D vector?

Question

I'm making a top down game where the player moves forwards towards the position of the mouse cursor. As part of the player's movement code, I need to determine a vector that is perpendicular to the player's current facing vector (to implement strafing behavior).

How can I compute the perpendicular vector of a given 2D vector?

Answer 1

I always forget how to do this when I need it so I wrote a couple of extension methods.

    public static Vector2 PerpendicularClockwise(this Vector2 vector2)
    {
        return new Vector2(vector2.Y, -vector2.X);
    }

    public static Vector2 PerpendicularCounterClockwise(this Vector2 vector2)
    {
        return new Vector2(-vector2.Y, vector2.X);
    }

And a unit test

    [Test]
    public void Vector2_Perpendicular_Test()
    {
        var a = new Vector2(5, -10);
        var b = a.PerpendicularClockwise();
        var c = a.PerpendicularCounterClockwise();

        Assert.AreEqual(new Vector2(-10, -5), b);
        Assert.AreEqual(new Vector2(10, 5), c);
    }

Answer 2

To get the 2D vector perpendicular to another 2D vector simply swap the X and Y components, negating the new Y component. So { x, y } becomes { y, -x }.

Answer 3

If , then a-perp obtained by a counterclockwise rotation by 90 degrees, i.e.,

See this link :)