What exactly are cap_style and join_style in shapely buffer function?

Question

I was trying to make a function that modifies polygons removing narrow spaces inside (setting a minimum distance between a vertex and a segment that is not adjacent) and at the same time remove sharp edges (angles < 90). It is important that the resulting polygon doesn't have round edges. Something like this, the original shape is grey, while what I want is in red: The use of the function buffer seems to be the answer.

Given a polygon Shape, I need to do something like Shape.buffer(-h).buffer(h) to remove narrow spaces inside, and by using the variables cap_style, join_style and mitre_limit, it should be able to deal with the sharp edges. The problem is that I have no clue of what these variables mean, the documentation is very confusing regarding this function, the descriptions and examples are ambiguous. For instance it is not clear to me the difference between cap_style and join_style, from experience, the last seems to be overriding the former. Changing cap_style while maintaining fixed join_style doesn't change the shape at all. From experience too, mitre_ratio doesn't work while using join_style = 3. In the end, I found out that

shape2 = shape.buffer(-0.2, join_style = 2, mitre_limit=2., cap_style=2)
shape3 = shape2.buffer(0.2, join_style = 2, mitre_limit=2., cap_style=1)

Almost works, if it wasn't for a very small difference between the original polygon and the modified one. Even though the distance parameter is exactly the same, the curves deviate somehow:

What is wrong with this solution? and what exactly are those parameters, and how are explicitly defined these methods?

Answer 1

What you are doing should work, as the following minimal working example shows:

import geopandas as gpd
import shapely
shape = shapely.geometry.Polygon([(-1,0),(-1,1),(0,.05),(1,1),(1,0),(-1,0)])
cutDist = .1

cutshape = shape.buffer(-cutDist,join_style=3).buffer(cutDist,join_style=3)
print(cutshape.difference(shape).wkt) #POLYGON EMPTY

gdshape = gpd.GeoDataFrame([shape], columns=['geometry'])
gdcut = gdshape.buffer(-cutDist,join_style=3).buffer(cutDist,join_style=3)
print(gdcut.difference(gdshape)) #POLYGON  EMPTY

The buffer function of geopandas uses shapely internally. The exact inner workings of shapely can be found in the code, or GEOS documentation. It uses Geos (C++) internally for all computations. the differences between joins are best explained by this image:

and cap_style defines the behaviour around line-ends. In your case, we do not have these, because all polygons are closed. mitre_limit sets the limit for when corners should be extended. Since you use beveled joins, this parameter is not used. These small differences are caused by join_style=2(mitre). For a reference to those, read the documentation