Geometry Boost List: Re: [geometry] fit an ellipse to a polygon

Subject: Re: [geometry] fit an ellipse to a polygon
From: Barend Gehrels (barend_at_[hidden])
Date: 2013-08-14 11:04:58

Hi Tanaka,

On 14-8-2013 11:55, Tanaka Simon wrote:
> Hello,
>
> I have a model::polygon, and i want to fit an ellipse to it (see link 
> below). do you have suggestions of how to use (built-in) 
> boost::geometry functionality as much as possible?
>
> do you have alternative suggestions to characterize the polygon, e.g. 
> to compute the principal axes of the inertia tensor? the solution is 
> allowed to be heuristic.

Interesting problem. You could use distance (point-linestring) to get 
the distance from each point to the ellipse-as-a-linestring. Note that 
if you model the ellipse as a polygon, the distance is zero for all 
points inside, so I would use a linestring here. This ellipse can easily 
be generated from the definition of the ellipse.

To start with you could think of calculating the convex hull of the 
points. That gives a reasonable starting-shape. Its centroid should be 
located in the neighbourhood of the center of the ellipse. And then 
indeed you would need the diameter... You could use the point at the 
furthest location from the ellipse here as a starting point (then you 
also have some idea of the direction of the axis).

Regards, Barend