How to generate a voronoi? diagram for a set of non-intersecting closed 2D polygons

[tksuoran]

Hello,

I have another problem I would like to solve :)

I have a set of N non-intersecting 2D polygons / closed contours. I would like to figure out a partition of the plane into N distinct regions such that each region contains exactly one input polygon, and every point within a region is closer to its associated input polygon than to any other. The boundaries between regions should consist of line segments that are equidistant to the nearest pair of input polygons.

I think voronoi diagrams are related, and I see Geogram has some voronoi features, but sadly I not sure how to get started.

Thanks!

Edit: I've found a way around this :)

[BrunoLevy]

Voronoi diagram of polygons (or even line segments) is much more difficult to implement than Voronoi diagram of points. For instance, consider two line. The set of points equidistant to them (their bisector) is a conic curve (degree 2). Consider now two line segments, their bisector is a curve composed of up to 7 arcs, some of them are conic curves, some of them are straight lines. Managing them requires predicates that are more complicated than those involved in Voronoi diagrams. It is probably a 1y to 2y project, fulltime !
There is an implementation in CGAL in 2D.