hey everyone.

Just a quick question i hope i'm using c# with XNA and currently i have created a game which draws a spaceship on the screen and allows me to move it around using an xbox360 controller.

what i'm trying to do is make the sprite of the spaceship face the direction it is traveling.

one way i was thinking of doing this is using the vector generated by the thumbstick

for example if i'm moving full left then the vector from the joystick is x = -1 y = 0.
and if i was moving right the vector would be
x = 1 y = 0.

i was just wondering if there way to convert that to an angle in radians.

maybe i'm looking at this totally the wrong way.

thanks in advance for any advice on this


The dot product of two vectors is equal to the cosine of the angle between them divided by the vectors' magnitudes. For example:

The dot product of <1, 2> and <3, 4> is 1*3 + 2*4, i.e. 11. The magnitudes of the vectors are sqrt(1*1+2*2) and sqrt(3*3+4*4), i.e. sqrt(5) and sqrt(25).

So the cosine of the angle between the vectors is 11 / (sqrt(5)*sqrt(25)), i.e. 11 / (sqrt(5) * 5).

If we take the arccosine of that value, we get the angle:


So in general, the angle between two vectors u and v is

acos(dot(u, v) / sqrt(dot(u, u) * dot(v, v))),

where dot is the dot product function.

(It happens that the magnitude of a vector v can be written as sqrt(dot(v, v)).)

And if you haven't figured it out, the dot product of two vectors is the sum of the products of their constituent parts: <x,y,z> `dot` <x', y', z'> = x*x' + y*y' + z*z'. This works for any number of dimensions.

The Vector structure of C# also has a "dotproduct" method. (among many others)
But it may be a bit hard to find.

private Double getDotProductExample()
    Vector vector1 = new Vector(20, 30);
    Vector vector2 = new Vector(45, 70);
    Double doubleResult;

    // Return the dot product of the two specified vectors.
    // The dot product is calculated using the following 
    // formula: (vector1.X * vector2.X) + (vector1.Y * vector2.Y).
    // doubleResult is equal to 3000
    doubleResult = Vector.Multiply(vector1, vector2);

    return doubleResult;


You can also use the overloaded * operator here.

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