Save line geometry as points geometry using PyQGIS

Try out with 'intersects' and 'intersection' methods. Next code produces only two points.

mapcanvas = iface.mapCanvas()

layers = mapcanvas.layers()

feats_line = [ feat for feat in layers[0].getFeatures() ]

feats_poly = [ feat for feat in layers[1].getFeatures() ]

for feat_l in feats_line:
    for feat_p in feats_poly:
        if feat_p.geometry().intersects(feat_l.geometry()):
            geom = feat_p.geometry().intersection(feat_l.geometry())
            print geom.asPolyline()[0]
            print geom.asPolyline()[1]

I tested it with next simple hypothetical situation:

and it works. Points printed at the Python Console were:

(386524,4.45324e+06)
(410342,4.44987e+06)

Editing Note:

With 4 lines:

running this code:

mapcanvas = iface.mapCanvas()

layers = mapcanvas.layers()

feats_line = [ feat for feat in layers[0].getFeatures() ]

feats_poly = [ feat for feat in layers[1].getFeatures() ]

my_list_points = []

for feat_l in feats_line:
    for feat_p in feats_poly:
        if feat_p.geometry().intersects(feat_l.geometry()):
            geom = feat_p.geometry().intersection(feat_l.geometry())
            my_list_points.append(geom.asPolyline()[0])
            my_list_points.append(geom.asPolyline()[1])

print my_list_points

produces a list with 8 points:

[(387941,4.45518e+06), (410116,4.45158e+06), (385087,4.45128e+06), (411027,4.44466e+06), (383102,4.44575e+06), (408687,4.43823e+06), (392714,4.4348e+06), (405952,4.43338e+06)]