There was a recent request* for coding challenges, and I stumbled over this quiz.

Given are 16 equidistant points in a 4x4 grid.

The coordinates are given with with @set = ([0,0],[0,1],...[3,3])

  y
 
  3  o  o  o  o <- [3,3]

  2  o  o  o  o

  1  o  o  o  o

  0  o  o  o  o <- [3,0]

     0  1  2  3  x
[download]

Task: Find a polygon° with 6 edges, crossing each grid-point exactly once.

@polygon = ([x0,y0],...[x6,y6])

Example: the edge ([-1,4],[3,0]) is crossing 4 points.

Hints:

• The vertices [x_i, y_i] don't need to be part of the integer grid.
• There is a solution where the polygon is closed - i.e. [x0,y0]=[x6,y6] .
• Use fractions or a scaling factor in case floating-point accuracy is posing problems.

Disclaimer: I didn't code it yet, but I saw existing solutions.

Have fun! :)

PS: Extra points for generalized solutions for bigger grids. While this can be solved with paper and pen, I'm expecting code to solve it.

update

Changed orientation of coordinate system to have 0,0 at the left lower corner like in math convention.

your questions:

• bliako: Are polygon sides allowed to intersect? -> Yes !
• bliako: Aren't all polygons closed? -> in math: yes, in computer graphics: depends ;-)
  s/Polygon/Polygonal_chain/ if you want.

I'll be off for the weekend, sorry if I can't reply earlier.

footnotes

°) or rather Polygonal_chain

*) See Coding challenges to PM

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