Re: [Algorithms] Best fit of polygon inside another polygon

[Fabian G. <f.g...@49...>]

Ste...@gm... wrote:
> Hi,
> 
> I've been thinking about an algorithm which fits a given polygon into a 
> quad. I've stumbled upon this while trying to fit the largest possible 
> polygon out of a set of different polygons into a quadliteral. What I 
> want to find is the best-fit-polygon which can be contained completely 
> in the quadliteral. The polygon and quad can be assumed to be convex. An 
> nice feature would be to calculate the error as a function of the area 
> which doesn't fit into the quad for every polygon I throw at the quad.
> 
> I'm working in 2D right now, but might want to expand the problem for a 
> later application into a 3D case (fit a polyhedra into a hexahedron).
> 
> Any ideas how to solve this problem?
> 
> Stefan

Which transformations are allowed? "Only translations", "translations 
and rotations", "translations, rotations and uniform scaling" and 
"general affine transformation" are all sensible choices but lead to 
very different approaches.

Also, is the quad a general convex quad, or is it a rectangle or 
parallelogram?

Kind regards,
-Fabian Giesen