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0 votes
1 answer
51 views

What is the most dense sample for which the Crust algorithm returns an incorrect polygonal reconstruction?

The Crust algorithm by Amenta, Bern, and Eppstein computes a polygonal reconstruction of a smooth curve $C$ without boundary from a discrete set of sample points $S$. It is known that if $S$ is an a $\...
8 votes
1 answer
231 views

Counting polygons in arrangements

For an arrangement of lines $\cal{A}$ in the plane, an inducing polygon $P$ is a simple polygon satisfying: (a) every edge $e$ of $P$ lies on some line $\ell$ of $\cal{A}$, and (b) every line $\ell \...
10 votes
1 answer
9k views

Get Largest Inscribed Rectangle of a Concave Polygon

I'm looking for an algorithm to find a set of largest inscribed rectangles of a concave polygon where each rectangle must be collinear with one of the edges of the polygon. In other words, I want to ...
6 votes
1 answer
2k views

Given a set of 2D vertices, how to create a minimum-area polygon which contains all the given vertices?

Not sure whether this question belongs here or math.stackexchange. You can assume that all the vertices are unique. The given vertices can be the vertices of the polygon, thus they do NOT have to be ...
4 votes
1 answer
2k views

Algorithms for covering a rectilinear polygon using the same multiple rectangles

Sorry for the crossing-posting: original post is here All angles of the polygon (representing a room) are right. It may be convex or concave. Use rectangles of the same size (representing a sensor ...