Making an octagon using QGIS geometry generator

Question

I am a self-taught QGIS user and am trying my hand at the geometry generator. I have been tasked with creating a map that has gazebos as points. There are so many easier ways to get a polygon like the one I am going for (.svg marker), but I'm trying to branch out. I got to this point by following Klas Karlson awesome geometry generator video. Here is my go at making an octagon:

make_polygon(
    make_line(
        make_point($geometry, 0.414, 1.000),
        make_point($geometry, 1.000, 0.414),
        make_point($geometry,  1.000, -0.414),
        make_point($geometry,  0.414, -1.000),
        make_point($geometry,  -0.414, -1.000),
        make_point($geometry, -1.000, -0.414),
        make_point($geometry, -1.000, 0.414),
        make_point($geometry, -0.414, 1.000)
))

This is what I got so far:

10-sided "octagon"

Klas Karlson Geometry Generator Video

Answer 1

You can do this much easier with the function make_regular_polygon() like this:

make_regular_polygon(
    $geometry, 
    project($geometry,5,radians(360/16)),
    8
)

5 in line 3 is the size of the radius, radians(360/16) is the rotation for a horizontal upper line, you can change the angle inside the brackets to get other rotations - e.g. 0 for the rotation like in the screenshot:

Answer 2

A simple option:

buffer(geometry:=$geometry, distance:=100, segments:=2)

With segments:=2 each quarter circle is created using only two line segments. So 2*4=8 sides in total.

Answer 3

If you want to reproduce the solution in the video, use this expression with project() function (click the link for help to see how it works). The angle (azimuth) is expected in radians, but you can use degrees and convert it with radians()

make_polygon(
    make_line (
        project ($geometry, 1, radians (45)),
        project ($geometry, 1, radians (90)),
        project ($geometry, 1, radians (135)),
        project ($geometry, 1, radians (180)),
        project ($geometry, 1, radians (225)),
        project ($geometry, 1, radians (270)),
        project ($geometry, 1, radians (315)),
        project ($geometry, 1, radians (360))
    )
)

You can make it shorter by looping 8 times through the project() function with array_foreach():

make_polygon(
    make_line (
        array_foreach (
            generate_series(1,8),
            project($geometry, 1, radians (45*@element))
        )
    )
)

Be aware:

If you try adapting an expression, be careful to copy it correctly: The expression you provided is invalid, so you must have used another expression to create your screenshot: instead of make_point, you used project (as in the video you shared).

A second problem: the 3rd argument is an angle (azimuth in radians), whereas the second argument is a distance. You seem to mix both values, however.

Try to understand how the expression works, what each function does. See the function help in the expression string builder that describes in detail how each function works and what kind of input it requires - alternatively, see Functions List with a detailed description of each function.

Advise: Start with a simple project() function to see how changing the values influences the result. Then go on and add a make_line function with two points, then add a 3rd point etc. When done, use make_polygon.