Orthogonal Polygonization

I am to implement an algorithm that orthogonally polygonize a set of points with the minimum number of vertices, in other words, given a set of points, the algorithm should find an orthogonal path passing through all of the points with the least number of possible vertices.

Any help here would be much appreciated!

Re: Orthogonal Polygonization

Hey aelalaily.

What exactly do you mean by an orthogonal path? Are you simply trying to fit a function to a set of points using orthogonal polynomials?

Re: Orthogonal Polygonization

I have a set of points, I want to draw a closed polygon in such a way that it passes by every point in that set, and that forms an orthogonal polygon.

So in essence a computational geometric problem where the objective is obtaining an orthogonal polygon passing by every point in a given set.

edit: I just realized it is posted in the wrong section of the forum. It should be in the Advanced Math Topics. My bad!

edit 2: http://mathhelpforum.com/advanced-ma...onization.html

Re: Orthogonal Polygonization

Does the orthogonal volume (or hyper-volume) have to pass through every single point or can it just approximate or be an approximation (like say a special kind of orthogonal convex-hull) where it doesn't go through every point but gives a good approximation?

Re: Orthogonal Polygonization

Yes, it would have to pass by every point in the set.

Re: Orthogonal Polygonization

I'm a little unsure about something: Can you have a non-convex volume or does it have to strictly convex?