How to check intersection between 2 rotated rectangles?

Question

Can someone explain how to check if one rotated rectangle intersect other rectangle?

Answer 1

Lua implementation built in love2d framework. Collision detection function works in pure lua anyway

math.inf = 1e309
function love.load()
    pol = {{0, 0}, {30, 2}, {8, 30}}
    pol2 = {{60, 60}, {90, 61}, {98, 100}, {80, 100}}
end
function love.draw()
    for k,v in ipairs(pol) do
        love.graphics.line(pol[k][1], pol[k][2], pol[k % #pol + 1][1], pol[k % #pol + 1][2])
    end
    for k,v in ipairs(pol2) do
        love.graphics.line(pol2[k][1], pol2[k][2], pol2[k % #pol2 + 1][1], pol2[k % #pol2 + 1][2])
    end
end

function love.update(dt)
    pol[1][1] = love.mouse.getX()
    pol[1][2] = love.mouse.getY()
    pol[2][1] = pol[1][1] + 30
    pol[2][2] = pol[1][2] + 2
    pol[3][1] = pol[1][1] + 8
    pol[3][2] = pol[1][2] + 30

    --lazy way to see that's function works
    print(doPolygonsIntersect(pol, pol2))
end
-------------------------------------------------------------------------
function doPolygonsIntersect(a,b)
polygons = {a,b}
for i=1, #polygons do
    polygon = polygons[i]
    for i1=1, #polygon do
        i2 = i1 % #polygon + 1
        p1 = polygon[i1]
        p2 = polygon[i2]

        nx,ny = p2[2] - p1[2], p1[1] - p2[1]

        minA = math.inf
        maxA = -math.inf
        for j=1, #a do
            projected = nx * a[j][1] + ny * a[j][2]
            if projected < minA then minA = projected end
            if projected > maxA then maxA = projected end
        end

        minB = math.inf
        maxB = -math.inf
        for j=1, #b do
            projected = nx * b[j][1] + ny * b[j][2]
            if projected < minB then minB = projected end
            if projected > maxB then maxB = projected end
        end

        if maxA < minB or maxB < minA then return false end
    end
end
return true
end