Как я вычисляю подобие косинуса двух векторов?

Такая система трилатерации уже была разработана для другого мода под названием ComputerCraft. Поскольку он, вероятно, не совместим с вашей конкретной проблемой, вам придется модифицировать и адаптировать его логику, но сам алгоритм должен работать.

Вот исходный код

CHANNEL_GPS = 65534

local function trilaterate( A, B, C )
    local a2b = B.vPosition - A.vPosition
    local a2c = C.vPosition - A.vPosition

    if math.abs( a2b:normalize():dot( a2c:normalize() ) ) > 0.999 then
        return nil
    end

    local d = a2b:length()
    local ex = a2b:normalize( )
    local i = ex:dot( a2c )
    local ey = (a2c - (ex * i)):normalize()
    local j = ey:dot( a2c )
    local ez = ex:cross( ey )

    local r1 = A.nDistance
    local r2 = B.nDistance
    local r3 = C.nDistance

    local x = (r1*r1 - r2*r2 + d*d) / (2*d)
    local y = (r1*r1 - r3*r3 - x*x + (x-i)*(x-i) + j*j) / (2*j)

    local result = A.vPosition + (ex * x) + (ey * y)

    local zSquared = r1*r1 - x*x - y*y
    if zSquared > 0 then
        local z = math.sqrt( zSquared )
        local result1 = result + (ez * z)
        local result2 = result - (ez * z)

        local rounded1, rounded2 = result1:round( 0.01 ), result2:round( 0.01 )
        if rounded1.x ~= rounded2.x or rounded1.y ~= rounded2.y or rounded1.z ~= rounded2.z then
            return rounded1, rounded2
        else
            return rounded1
        end
    end
    return result:round( 0.01 )
end

local function narrow( p1, p2, fix )
    local dist1 = math.abs( (p1 - fix.vPosition):length() - fix.nDistance )
    local dist2 = math.abs( (p2 - fix.vPosition):length() - fix.nDistance )

    if math.abs(dist1 - dist2) < 0.01 then
        return p1, p2
    elseif dist1 < dist2 then
        return p1:round( 0.01 )
    else
        return p2:round( 0.01 )
    end
end

function locate( _nTimeout, _bDebug )
    -- Let command computers use their magic fourth-wall-breaking special abilities
    if commands then
        return commands.getBlockPosition()
    end

    -- Find a modem
    local sModemSide = nil
    for n,sSide in ipairs( rs.getSides() ) do
        if peripheral.getType( sSide ) == "modem" and peripheral.call( sSide, "isWireless" ) then   
            sModemSide = sSide
            break
        end
    end

    if sModemSide == nil then
        if _bDebug then
            print( "No wireless modem attached" )
        end
        return nil
    end

    if _bDebug then
        print( "Finding position..." )
    end

    -- Open a channel
    local modem = peripheral.wrap( sModemSide )
    local bCloseChannel = false
    if not modem.isOpen( os.getComputerID() ) then
        modem.open( os.getComputerID() )
        bCloseChannel = true
    end

    -- Send a ping to listening GPS hosts
    modem.transmit( CHANNEL_GPS, os.getComputerID(), "PING" )

    -- Wait for the responses
    local tFixes = {}
    local pos1, pos2 = nil, nil
    local timeout = os.startTimer( _nTimeout or 2 )
    while true do
        local e, p1, p2, p3, p4, p5 = os.pullEvent()
        if e == "modem_message" then
            -- We received a reply from a modem
            local sSide, sChannel, sReplyChannel, tMessage, nDistance = p1, p2, p3, p4, p5
            if sSide == sModemSide and sChannel == os.getComputerID() and sReplyChannel == CHANNEL_GPS and nDistance then
                -- Received the correct message from the correct modem: use it to determine position
                if type(tMessage) == "table" and #tMessage == 3 then
                    local tFix = { vPosition = vector.new( tMessage[1], tMessage[2], tMessage[3] ), nDistance = nDistance }
                    if _bDebug then
                        print( tFix.nDistance.." metres from "..tostring( tFix.vPosition ) )
                    end
                    if tFix.nDistance == 0 then
                        pos1, pos2 = tFix.vPosition, nil
                    else
                        table.insert( tFixes, tFix )
                        if #tFixes >= 3 then
                            if not pos1 then
                                pos1, pos2 = trilaterate( tFixes[1], tFixes[2], tFixes[#tFixes] )
                            else
                                pos1, pos2 = narrow( pos1, pos2, tFixes[#tFixes] )
                            end
                        end
                    end
                    if pos1 and not pos2 then
                        break
                    end
                end
            end

        elseif e == "timer" then
            -- We received a timeout
            local timer = p1
            if timer == timeout then
                break
            end

        end 
    end

    -- Close the channel, if we opened one
    if bCloseChannel then
        modem.close( os.getComputerID() )
    end

    -- Return the response
    if pos1 and pos2 then
        if _bDebug then
            print( "Ambiguous position" )
            print( "Could be "..pos1.x..","..pos1.y..","..pos1.z.." or "..pos2.x..","..pos2.y..","..pos2.z )
        end
        return nil
    elseif pos1 then
        if _bDebug then
            print( "Position is "..pos1.x..","..pos1.y..","..pos1.z )
        end
        return pos1.x, pos1.y, pos1.z
    else
        if _bDebug then
            print( "Could not determine position" )
        end
        return nil
    end
end

Спросите, есть ли у вас какие-либо конкретные вопросы по поводу исходного кода.