Creating field with 1/0 values depending if point sits inside polygon in QGIS

Question

I have a layer with a single polygon and a layer with multiple points. Some of the points are inside the polygon. How can I create/update a field with a value of 1 (true) or 0 (false) depending if a point is inside the polygon.

Example from a similar question here.

I need to use this as part of a field calculator step in a graphical model. I've got scraps of code but I can't get the syntax for intersect expression right:

intersects(geometry('points'), geometry('polygon'))

I imagine using that along with some form of:

CASE
    WHEN
END

See below image for the problem:

Answer 1

Use this expression: overlay_within('polygon') (see below for alternatives):

Just for your curiosity: the syntax for the intersects function is like this (returning 0/1):

intersects(
    $geometry,
    aggregate(
        'polygon',
        'collect',
        $geometry
   )
)

or:

intersects(
    $geometry,
    geometry (
        get_feature_by_id(
        'polygon',
        1)))

Answer 2

Here is a solution that uses the CASE statement

CASE
    WHEN overlay_intersects('test2') THEN 1
    ELSE 0
END

p.s. 'test2' is the name of the polygon layer

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I think that the CASE statement is useful when there are many conditions that have to be applied, if there are just two i.e. true/false, use the if condition instead, like:

if(overlay_intersects('test2'), 1, 0)

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I will most likely use the solution provided by @Babel, however, when 1/0 is required instead of true/false, adjust the expression accordingly:

to_int(overlay_within('test2'))