calculate a perpendicular offset from a diagonal line

Question

I am writing a music display program and need to draw a 'slur' between two notes. A slur is a curved line linking two notes - just to be clear.

I know the note positions and calculate where the start and end points of the curve should be - Start point A and End point B.

I now need to obtain the offset C, given the distance required, for use within a quadratic curve. This is where my, very, limited knowledge and understanding of maths formulae comes in.

I have indeed looked here in SO for my answer, but the solutions proposed either do not work or I am too limited to code them correctly.

Can someone help me with the calculation, in a NON mathematical form ?

Answer 1

I took legends2k excellent answer and converted to Java on Android. This might help someone save some time.

private PointF getPerpendicularPoint(int startX, int startY, int stopX, int stopY, float distance)
{
    PointF M = new PointF((startX + stopX) / 2, (startY + stopY) / 2);
    PointF p = new PointF(startX - stopX, startY - stopY);
    PointF n = new PointF(-p.y, p.x);
    int norm_length = (int) Math.sqrt((n.x * n.x) + (n.y * n.y));
    n.x /= norm_length;
    n.y /= norm_length;
    return new PointF(M.x + (distance * n.x), M.y + (distance * n.y));
}