What's wrong with this XNA RotateVector2 function?

Question

Hi,

I know this is probably a very simple question, but I can't seem to figure it out. First of all, I want to specify that I did look over Google and SO for half an hour or so without finding the answer to my question(yes, I am serious).

Basically, I want to rotate a Vector2 around a point(which, in my case, is always the (0, 0) vector). So, I tried to make a function to do it with the parameters being the point to rotate and the angle(in degrees) to rotate by.

Here's a quick drawing showing what I'm trying to achieve:

I want to take V1(red vector), rotate it by an angle A(blue), to obtain a new vector (V2, green). In this example I used one of the simplest case: V1 on the axis, and a 90 degree angle, but I want the function to handle more "complicated" cases too.

So here's my function:

public static Vector2 RotateVector2(Vector2 point, float degrees)
{
    return Vector2.Transform(point, 
    Matrix.CreateRotationZ(MathHelper.ToRadians(degrees)));
}

So, what am I doing wrong? When I run the code and call this function with the (0, -1) vector and a 90 degrees angle, I get the vector (1, 4.371139E-08) ...

Also, what if I want to accept a point to rotate around as a parameter too? So that the rotation doesn't always happen around (0, 0)...

Answer 1

So, what am I doing wrong? When I run the code and call this function with the (0, -1) vector and a 90 degrees angle, I get the vector (1, 4.371139E-08) ...

Your code is correct, this is just a floating point representation issue. 4.371139E-08 is essentially zero (it's 0.0000000431139), but the transformation did not produce a value that was exactly zero. This is a common problem with floating point that you should be aware of. This SO answer has some additional good points about floating point.

Also, if possible, you should stick with radians instead of using degrees. This is likely introducing more error into your computations.

Answer 2

Chris Schmich's answer regarding floating point precision and using radians is correct. I suggest an alternate implementation for RotateVector2 and answer the second part of your question.

Building a 4x4 rotation matrix to rotate a vector will cause a lot of unnecessary operations. The matrix transform is actually doing the following but using a lot of redundant math:

    public static Vector2 RotateVector2(Vector2 point, float radians)
    {
        float cosRadians = (float)Math.Cos(radians);
        float sinRadians = (float)Math.Sin(radians);

        return new Vector2(
            point.X * cosRadians - point.Y * sinRadians,
            point.X * sinRadians + point.Y * cosRadians);
    }

If you want to rotate around an arbitrary point, you first need to translate your space so that the point to be rotated around is the origin, do the rotation and then reverse the translation.

    public static Vector2 RotateVector2(Vector2 point, float radians, Vector2 pivot)
    {
        float cosRadians = (float)Math.Cos(radians);
        float sinRadians = (float)Math.Sin(radians);

        Vector2 translatedPoint = new Vector2();
        translatedPoint.X = point.X - pivot.X;
        translatedPoint.Y = point.Y - pivot.Y;

        Vector2 rotatedPoint = new Vector2();
        rotatedPoint.X = translatedPoint.X * cosRadians - translatedPoint.Y * sinRadians + pivot.X;
        rotatedPoint.Y = translatedPoint.X * sinRadians + translatedPoint.Y * cosRadians + pivot.Y;

        return rotatedPoint;
    }

Note that the vector arithmetic has been inlined for maximum speed.