I have a question

Given an irregular area which is created by combining triangles from Delaunay triangulation, and a box with fixed ratio, how to decide where to put the box so that it has maximum area (box only has fixed ratio no fixed edge length)

I can only think of something maybe just a bit better than brute force but cannot think of anything else

@Ranchonyx I’m just gonna hope the wise can crack this

This sounds fun. I'm sure I'll get it horribly wrong. At work at the moment but now I need to know more.

"for four or more points on the circle the delaunay triangulation is not unique, but has two solutions."

So the first thing I would ask is can this be related to the two zeros on a parabola and so in some fashion be related back to prime factorization?

Inquiring minds want to know!

@Wisecrack the Delaunay triangulation isn’t the important part, the assumption is that you already has a triangulation, and you combine triangles in different groups according to some property.

For example, if you have a random picture and you put points on this picture and get the triangulation, you will then try to merge triangles based on the average color of that triangles until the next triangle is too different from what has already been merged.

So a simplified version will just be, you have a irregular polygon, can be convex or concave

@K-ASS you're welcome.

@Wisecrack also no, the two solutions is not related to that, just imagine a rectangle, and there are two ways to split up since there are two diagonals

You have to rotate a line in the center off the mass inside of the irregular shape. Where the line is the longest you got the diagonal of the box.

I think there can be an optimized algorithm for convex hull polygons, but I'm afraid it won't be "easy" for any arbitrary polygon

@blindXfish it’s not that easy