Polygon find the shortest way from start to end

I am searching the shortest way in my polygon (route). It starts on the center border on bottom left (blue) and ends on the center border on the top right (red). It is not allowed to leave the route.

Which algorithm i can use to calculate this route? I need a list of points to draw the shortest way. A example code would be great.

Example of my polygon with start and end

var points = new List<Point> { new Point(210, 540), new Point(330, 420), new Point(360, 420), new Point(420, 390), new Point(450, 330), new Point(480, 315), new Point(510, 270), new Point(570, 240), new Point(630, 240), new Point(690, 180), new Point(750, 150), new Point(810, 120), new Point(864, 120), new Point(864, 60), new Point(810, 60), new Point(750, 90), new Point(690, 120), new Point(630, 150), new Point(570, 150), new Point(510, 210), new Point(480, 255), new Point(450, 270), new Point(420, 330), new Point(360, 360), new Point(330, 360), new Point(156, 480) };

var image = new Bitmap(1000, 600);
using (var graphics = Graphics.FromImage(image))
{
    graphics.Clear(Color.White);
    graphics.FillPie(Brushes.Blue, 190, 500, 10, 10, 0, 360);
    graphics.FillPie(Brushes.Red, 840, 80, 10, 10, 0, 360);
    graphics.DrawPolygon(new Pen(Color.Black, 2), points.ToArray());
}

image.Save("example.bmp");