For the curve or straight line problem, I think I'd keep a list of the positions of old input. Then, I'd check the slope between every point (delta Y / delta X). If the slope does not change a lot, then it's probably a line. If it varies a lot, it's probably a curve. You could use a limit representing the slope difference that determines if the input is a line or a curve.

For the curve or straight line problem, I think I'd keep a list of the positions of old input. Then, I'd check the slope between every point (delta Y / delta X). If the slope does not change a lot, then it's probably a line. If it varies a lot, it's probably a curve. You could use a limit representing the slope difference that determines if the input is a line or a curve.

So, if I had to implement such a functionality, I think I'd go like this:

List<Vector2> inputPositions = new List<Vector2>();//the old input positions

then I'd find the slopes between every position:

float deltaY = 0f;
float deltaX = 0f;
List<float> slopes = new List<float>();
for (int i = 0; i < inputPositions.Count - 1; ++i)//check all the positions except the last one
{
    deltaY = inputPositions[i + 1].Y - inputPositions[i].Y;//next pos.Y - current.Y
    deltaX = inputPositions[i + 1].X - inputPositions[i].X;//next pos.X - current.X

    if (deltaX != 0.0f)//prevent division by 0
    {
        slopes.Add(deltaY / deltaX);
    }
    else
    {
        //I'm not really sure about using these values, but basically it
        //means that the movement was vertical
        slopes.Add(deltaY > 0.0f ? float.MaxValue : float.MinValue);
    }
}

then you can analyse the results to see if the slope difference was too huge.

bool IsLine(List<float> slopes)
{
    const float IS_NOT_LINE_SLOPE_DIFF = 0.05f;//find an appropriate constant for your program

    float slopeVariation = 0f;
    for (int i = 0; i < slopes.Count - 1; ++i)//check all but the last element
    {
        slopeVariation = slopes[i] - slopes[i + 1];
        if (Math.Abs(slopeVariation) >= IS_NOT_LINE_SLOPE_DIFF)
             return false;
    }

    return true;
}

You could even get the median of the slope variations to get a more general result.

Sure, this isn't the cleanest and certainly not the best way to solve your problem, but that's the way I would go to do it.