Adding the 45deg angle was a small addition to Part 1.

       public void MarkLine(Point A, Point B)
        {
            if (A.X == B.X)
            {
                if (A.Y > B.Y)
                {
                    for (int i = A.Y; i >= B.Y; i--)
                    {
                        _matrix[A.X, i]++;
                        if (_matrix[A.X, i] == 2) { IntersectionCount++; }
                    }
                }
                else
                {
                    for (int i = A.Y; i <= B.Y; i++)
                    {
                        _matrix[A.X, i]++;
                        if (_matrix[A.X, i] == 2) { IntersectionCount++; }
                    }
                }
            }
            else if (A.Y == B.Y)
            {
                if (A.X > B.X)
                {
                    for (int i = A.X; i >= B.X; i--)
                    {
                        _matrix[i, A.Y]++;
                        if (_matrix[i, A.Y] == 2) { IntersectionCount++; }
                    }
                }
                else
                {
                    for (int i = A.X; i <= B.X; i++)
                    {
                        _matrix[i, A.Y]++;
                        if (_matrix[i, A.Y] == 2) { IntersectionCount++; }
                    }
                }
            }

            if (_HorizontalVerticalOnly) { return; }

            //Assume 45deg angle
            if (A.X != B.X
                && A.Y != B.Y)
            {
                int unit = Math.Abs(A.X - B.X);
                int xd = A.X;
                int yd = A.Y;

                for (int i = 0; i <= unit; i++)
                {
                    _matrix[xd, yd]++;
                    if (_matrix[xd, yd] == 2) { IntersectionCount++; }

                    xd += A.X > B.X ? -1 : 1;
                    yd += A.Y > B.Y ? -1 : 1;
                }
            }
        }