How to correctly buffer convex polygon?

[Jihadist]

Hi, I wanna to buffer a polygon.
I have a polygon containing 12 points so I want that buffered polygon also contains 12 points. But my buffered polygon contains 33 points. Why?
Gist https://gist.github.com/Jihadist/864acc5efefd26c79fbb262ace5c5604

Image looks like ok

I tried boost::geometry::strategy::buffer::point_square and point_circle but there is no difference. What I do wrong?
Thanx in advance!

[awulkiew]

AFAIU the number of points of a buffer is not guaranteed. point_xxx strategies are used for buffer of a single point and multi-points so they won't help here. Join strategies are used at vertices so I think you need to use boost::geometry::strategy::buffer::join_miter instead of join_round. If there are still too many points in the result you could e.g. use simplify() to get rid of the points lying on straight parts.

[barendgehrels]

First of all, thank you for this lection! I use only convex polygons so it reasonable for my but now i understand that we can another polygons. Eventually, can I use this simplifing coefficient as a general coeff appropriate for smaller or bigger polygons than my?

Yes, this simplifying distance you can use in general. If it's near zero, it just removes redundant points. You can even try 0.0 too. This page describes the simplify algorithm in general https://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm (here called epsilon

[barendgehrels]

If you're only dealing with convex polygons, need only miter joins and want to preserve the number of points then maybe you could write your own algorithm?

It's possible of course - but using buffer itself should just work as desired of course. Maybe we should move this to an issue and remove the redundant points. It will not much extra code.

[vissarion]

A side note (for clarity) on the connection between simplify distance and buffer distance. To my understanding they are connected as follows: the distance of a point created by the buffer (the points on the circular arc in OGC standard buffer, miter points should be similar) to the closest segment created if we remove that point is a function of the buffer distance r and the angle $\theta$ (of the circular arc, equivalently the angle of the orthogonal normals of the polygon segments), i.e. $$\sqrt{4r^2\sin^2\frac{\theta}{4}-r^2\sin^2\frac{\theta}{2}}.$$ This is exactly the distance used by simplify algorithm to filter out points from the input. If a point is close to be "redundant" then that distance is very small (since the angle is very small) so the small numbers that @barendgehrels suggests are working. I do not know if this is needed in practice but eventually one can actually precompute those numbers before running simplify.

[barendgehrels]

Thanks @vissarion . Now I understand your reasoning a bit better.
But I don't know if I agree. It's not that we want to remove some intermediate points from the generated circle. You can specify the number of points there, so usually there is no need to remove them afterwards. We want to remove the middle point from three collinear points. That point is redundant. For that, you can always use the same simplify distance of nearly zero.

[vissarion]

Sure, I agree with you, I just wanted to argue that the is a connection
between buffer distance and simplify distance. Sorry if I made the
discussion more complicated than needed.