How do I fill everything over a straight line and under a curve?

I have an idea that use SeriesChartType.Range as follow.

private void UpdateChart(float straight_line, List<DataPoint> curve)
{
    float y = straight_line;    // YValue of the straight line
    var list = curve.ToList();  // Clone the curve

    int count = list.Count - 2;

    for (int i = 0; i < count; i++)  // Calculate intersection point between the straight line and a line between (x0,y0) and (x1,y1) 
    {
        double x0 = list[i + 0].XValue;
        double y0 = list[i + 0].YValues[0];
        double x1 = list[i + 1].XValue;
        double y1 = list[i + 1].YValues[0];

        if ((y0 > y && y1 < y) || (y0 < y && y1 > y))
        {
            double x = (y - y0) * (x1 - x0) / (y1 - y0) + x0;

            list.Add(new DataPoint(x, y));
        }
    }

    list.Sort((a, b) => Math.Sign(a.XValue - b.XValue));

    chart1.Series[0].Points.Clear();
    chart1.Series[0].ChartType = SeriesChartType.Range;
    chart1.Series[0].Color = Color.Red;
    chart1.Series[0].BorderColor = Color.Cyan;
    chart1.ChartAreas[0].AxisX.Minimum = 0;
    chart1.ChartAreas[0].AxisX.Interval = 1;

    for (int i = 0; i < list.Count; i++)
    {
        double xx = list[i].XValue;
        double yy = list[i].YValues[0];
        if (yy > y)
        {
            chart1.Series[0].Points.AddXY(xx, y, yy);
        }
        else
        {
            chart1.Series[0].Points.AddXY(xx, yy, yy);
        }
    }

    chart1.ChartAreas[0].AxisY.StripLines.Add(new StripLine { IntervalOffset = y, Interval = 0, BorderColor = Color.Orange, BorderWidth = 2 });

}

As in the below drawing to judge whether the straight line and a line between (x0,y0) and (x1,y1) intersect, case 1 is (y0 < y && y1 > y) and case 2 is (y0 > y && y1 < y) . In case 1 and case 2, they intersect each other. In case 3 and case 4, they don't intersect each other.