2D Hexagon grid - lua

Question

I recently made a simple lua class (this is using the love2D engine) that made a hexagon by plotting 6 vertices and tracing them with lines, one of the things I wanted to be able to expand to was a hexagon grid but I didn't know how
All of the websites I found didn't help and I couldn't understand why.
Here's the function where I plot the vertices based on it's radius and x and y position.
My hexagons are in a pointy-topped style.
function hexagon.new(x,y,radius)
local hexagon=setmetatable({},hexagon)
hexagon.Vertices={}
hexagon.x=x or 0
hexagon.radius = radius or 10
hexagon.y=y or 0
for i=0,6 do
local angle = 2 * math.pi / 6 * (i + .5) -- 1 is what is multipled to 90(2*math.pi) so 1*90=90(flat-topped), 0.5*90=45(pointy-topped)
local x = hexagon.x + hexagon.radius * math.cos(angle)
local y = hexagon.y + hexagon.radius * math.sin(angle)
hexagon.Vertices[i]= {x=x,y=y}
end
return hexagon
end

Answer 1

Hope i understood well.
Here is working example of how to create hex and then draw it to grid with as simplified functions as possible, using Love2d engine (v. 0.10.2).
important: made for hex which has all six points on circle, using radius.
this approach is not suitable for all hex shapes.
------------------------------
--lets create hex data with center at position 0,0
--using only simple functions
--table of 6 points
hex = {};
--radius for hex which has all 6 points lying on circle
hex.radius = 10;
--simple loop to generate hex
local i = 1
repeat
--full circle has 2 radians and hex has 6 points
--so 1/3 pi increase per point
local direction = math.pi/3 * (i+0.5)
--rotate hex by 90 degrees: direction = math.pi/3 * i
--generate empty table to insert point coordinations to
hex[i] = {};
--set x,y coordinates
hex[i].x = hex.radius*math.cos( direction )
hex[i].y = hex.radius*math.sin( direction )
i = i+1
until i > 6
------------------------------
------------------------------
function love.draw( dt )
--get distance between 2 hex tiles using trigonometry
local jxOffset = hex.radius*-math.tan( math.pi/1.5 ) --or math.sqrt(3) * hex.radius
--offset new lines by this value
local ixOffset = jxOffset/4
--use direction and distance to get "y" offset between lines
--we got distance in jxOffset, so we just apply direction
local iyOffset = jxOffset*math.sin( math.pi/3 )
--"i" = line, "j" = tile in line
local i = 1
repeat
local j = 1
repeat
love.graphics.push()
--offset drawable position (or draw hex tile at position):
love.graphics.translate( ixOffset+j*jxOffset, i*iyOffset )
--draw poly-line between all hex points - creating hex
love.graphics.line( hex[1].x,hex[1].y, hex[2].x,hex[2].y, hex[3].x,hex[3].y, hex[4].x,hex[4].y, hex[5].x,hex[5].y, hex[6].x,hex[6].y, hex[1].x,hex[1].y );
love.graphics.pop()
j = j+1
until j > 5
--invert for each new line
--keep lines from increasing x coordinates
ixOffset = -ixOffset
i = i+1
until i > 5
end
------------------------------
Excuse me if i made mistake somewhere, ran the code and worked properly on my side. If you discover anything off, comment and i will try to fix it.