May as well promote my comment to an answer.
You need to add points to a
Curve2D object, then adjust the control points of the curve, and then finally draw the curve. So here's some simple, almost pseudo code:
var array_of_line_points # This already has the vectors which describe our line
for point in array_of_line_points:
# The "get_perpendicular_vector()" function returns a vector that's a copy of the point, yet has been slid along a line parallel to two neighboring points. The "distance" variable is how far the control point should be from the originating point.
var control_point1 = get_perpendicular_vector(point, distance)
var control_point2 = get_perpendicular_vector(point, -distance)
curve.add_point(point, control_point1, control_point2)
# ...In the draw function
draw_polyline(curve.get_baked_points(), red, 2.0)
I got the inspiration for this from Rob Spencer's page on Spline Interpolation. I'd like to make this more thorough (i.e. defining the
get_perpendicular_vector() function). But this is the best I can currently do.