Polar coordinates of vertices of a hexagonal grid?

Question

Is it possible to parameterize a hexagonal grid in polar plane?

In other words, is it possible to find polar coordinates of the centers of every hexagon packed in a hexagonal grid? The central hexagon is marked by a blue circle, and its polar coordinates is (0, 0)/

Yes, it is. But you won't get integer coordinates easily. At least not with actual polar coordinates. — Nico Schertler, Sep 10 '18 at 11:29
For future reference: https://www.redblobgames.com/grids/hexagons/ — MBo, Sep 10 '18 at 13:07

score 3 · Accepted Answer · 2018-09-10T13:00:45.063

3

The centers are found every 60° and at distance twice inscribed radius. Compute the coordinates of the closest centers at 0° and 60° and every other center is obtained as a linear combination with integer coefficients.

2u + v, √3 v

Then convert to polar coordinates

r= 2√[u² + uv + v²]
tan Θ = √3 v / (2u + v)

edited Sep 10 '18 at 13:00

answered Sep 10 '18 at 11:53

Polar coordinates of vertices of a hexagonal grid?

1 Answers1