Nick,
I assume Shapely's "centroid" function is a true, center-of-mass of centroid.
(This could be verified
If so, the ANY line though the centroid will bisect the original polygon in to
two equal portions by area.
There are two questions:
- How do you pick a "good line"?
- Once you've picked a line, how do you actually use the functions in the API
to concoct the two polygons (two halves) from the original one.
The first one is a bit subjective: "good" versus "less good" is defined by your
actual need. I could suggest some heuristics if you fill us in. (Is this
process only going to be done once? Or N times? One post mentioned the idea of
making the pieces "kinda square". Is that your need?)
For now, I'll just suggest you pick the cutline to be a simple vertical segment
from (x-centroid, y-max) to (x-centroid, y-min), where:
- x-centroid is the x-value of the centroid
- y-max is the maximum y-value of the original polygon
- y-min is the minimum y-value of the original polygon
Here's a recipe for the second part (using the API to cleave the original poly):
- "poly" is your original Polygon
- "cutline" is the LineString from the above
If the original polygon is simple (no holes or self crossing) and convex, then
I think this is the recipe:
- get the exterior LinearRing of the polygon:
exterior = poly.exterior
- use cascaded union to get the cut-up segments of where the lines "cut" each
other:
segments = cascaded_union([exterior, cutline])
- use polygonize to convert this back to polygons:
poly_parts = list(polygonize(segments))
Then these should be true:
len(poly_parts) == 2
poly_parts[0].area == poly_parts[1].area
poly_parts[0].area * 2 = poly.area
Make sense?
Now: let me know if your polygon is NOT necessarily simple and convex. (Hint:
if any of the above were NOT true, then the preconditions of simple and convex
were not met.) We'll need to add another few steps (and your result for "each
half" might be MultiPolygons). Shall I elaborate, or will that do for now?
-- Dan Harasty
The second has many steps in the general case. , but can be simplified in
certain cases
On Tue, Jul 24, 2012 at 5:18 PM, Nick Ves <[email protected]> wrote:
> Hey list,
>
> I have a question: How you can divide a polygon into two smaller
> polygons with the same area?
>
> I know this problem have infinitive answers, because there are
> infinitive lines that intersects with the a polygon, thus for a
> constrain I thought that the intersecting line should pass from the
> point which defines the the middle of the perimeter of the polyline.
>
> Did anyone came across with a solution? I've read about the problem
> here [1], but a google search didn't provide anything that can be used
> with python.
>
>
> With Regards,
>
> Nick
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