Currently I'm working on a vector class in C# and now I'm coming to the point, where I've to figure out, how i want to implement the functions for interpolation between two vectors. At first I came up with implementing the functions directly into the vector class...

public class Vector3D
{
    public static Vector3D LinearInterpolate(Vector3D vector1,
        Vector3D vector2, double factor) { ... }

    public Vector3D LinearInterpolate(Vector3D other, double factor { ... }
}

(I always offer both: a static method with two vectors as parameters and one non-static, with only one vector as parameter)

...but then I got the idea to use extension methods (defined in a seperate class called "Interpolation" for example), since interpolation isn't really a thing only available for vectors. So this could be another solution:

public class Vector3D { ... }

public static class Interpolation
{
    public static Vector3D LinearInterpolate(this Vector3D vector,
        Vector3D other, double factor) { ... }
}

So here an example how you'd use the different possibilities:

{
    var vec1 = new Vector3D(5, 3, 1);
    var vec2 = new Vector3D(4, 2, 0);
    Vector3D vec3;

    vec3 = vec1.LinearInterpolate(vec2, 0.5); //1
    vec3 = Vector3D.LinearInterpolate(vec1, vec2, 0.5); //2

    //or with extension-methods

    vec3 = vec1.LinearInterpolate(vec2, 0.5); //3 (same as 1)
    vec3 = Interpolation.LinearInterpolation(vec1, vec2,
    0.5); //4
}

So I really don't know which design is better. Also I don't know if there's an ultimate rule for things like this or if it's just about what someone personally prefers. But I really would like to hear your opinions, what's better (and if possible why ).