Problem 1490. Shifted Hexagonal Tiling Dots in a Circle

Return how many Hexagonal Tiling grid points there are inside a circle of radius r centred at (0,0) (including points on the edge). Assume that a Hexagonal Tiling grid is a 2D Regular Hexagonal Tessellation with equal edges of size e=1.

For shifted symmetry purposes, assume that (0,0) is a grid point.

Neither string operations nor interpolations are allowed!