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algorithmgeometrypolar-coordinateshexagonal-tiles

Polar coordinates of vertices of a hexagonal grid?

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

enter image description here

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)/

Solution

  • 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)