Codea codify line intersection

-- line segment intersections
function setup()
    w = 0
    l1ax,l1ay,l1bx,l1by,l2ax,l2ay,l2bx,l2by = randlines()
    watch("l1ax")
    watch("l1ay")
    watch("l1bx")
    watch("l1by")
    watch("l2ax")
    watch("l2ay")
    watch("l2bx")
    watch("l2by")
end

-- This function gets called once every frame
function draw()
    background(0, 0, 0, 255)
    strokeWidth(3)
    showlines(l1ax,l1ay,l1bx,l1by,l2ax,l2ay,l2bx,l2by)
    if w % 30 == 0 then
        l1ax,l1ay,l1bx,l1by,l2ax,l2ay,l2bx,l2by = randlines()
        w = 0
    end
    w = w + 1
end

function randlines()
    l1ax = math.random()*WIDTH
    l1ay = math.random()*HEIGHT
    l1bx = math.random()*WIDTH
    l1by = math.random()*HEIGHT
    l2ax = math.random()*WIDTH
    l2ay = math.random()*HEIGHT
    l2bx = math.random()*WIDTH
    l2by = math.random()*HEIGHT
    return l1ax,l1ay,l1bx,l1by,l2ax,l2ay,l2bx,l2by
end

function showlines(l1ax,l1ay,l1bx,l1by,l2ax,l2ay,l2bx,l2by)
    stroke(255, 0, 0, 255)
    line(l1ax,l1ay,l1bx,l1by)
    stroke(0, 0, 255, 255)
    line(l2ax,l2ay,l2bx,l2by)
    stroke(0,255,0,255)
    strokeWidth(9)
    it, iax, iay, ibx, iby = getintersection(l1ax,l1ay,l1bx,l1by,l2ax,l2ay,l2bx,l2by)
    if it then
        line(iax,iay,ibx,iby)
    elseif not it then
        line(iax+10,iay+10,ibx-10,iby-10)
        line(iax-10,iay+10,ibx+10,iby-10)
    else
        line(iax,iay,ibx,iby)
    end
end

function getintersection(x1, y1, x2, y2, x3, y3, x4, y4)
    --special thanks to voiceofreason
   d = (y4-y3)*(x2-x1)-(x4-x3)*(y2-y1)
   Ua_n = ((x4-x3)*(y1-y3)-(y4-y3)*(x1-x3))
   Ub_n = ((x2-x1)*(y1-y3)-(y2-y1)*(x1-x3))
   if d == 0 then
       if Ua_n == 0 and Ua_n == Ub_n then
            --they are on the same plane
            --they are either
              --the same point
              --the same line
              --two unconnected lines
              --slightly overlapping
              --one within the other
            --find max and least x for line 1
            if x1 > x2 then
                mxl1 = x1 -- max x of line 1
                lxl1 = x2 -- least x of line 1
            elseif l1ax <= l1bx then
                mxl1 = x2 -- max x of line 1
                lxl1 = x1 -- least x of line 1
            end
            --find max and least x for line 2
            if x3 > x4 then
                mxl2 = x3 -- max x of line 2
                lxl2 = x4 -- least x of line 2
            elseif x3 <= x4 then
                mxl2 = x4 -- max x of line 2
                lxl2 = x3 -- least x of line 2
            end
            if (mxl1 < lxl2) or (lxl1 > mxl2) then
                -- no shared x
                mx = (l1ax+l1bx+l2ax+l2bx)/4 --midx
                my = (l1ay+l1by+l2ay+l2by)/4 --midy
                return false,mx,my,mx,my
            end
            --find max and least y for line 1
            if y1 > y2 then
                myl1 = y1 -- max y of line 1
                lyl1 = y2 -- least y of line 1
            elseif y1 <= y2 then
                myl1 = y2 -- max y of line 1
                lyl1 = y1 -- least y of line 1
            end
            --find max and least y for line 2
            if y3 > y4 then
                myl2 = y3 -- max y of line 2
                lyl2 = y4 -- least y of line 1
            elseif y3 <= y4 then
                myl2 = y4 -- max y of line 1
                lyl2 = y3 -- least y of line 1
            end

            if (myl1 < lyl2) or (lyl1 > myl2) then
                -- no shared y
                mx = (l1ax+l1bx+l2ax+l2bx)/4 --midx
                my = (l1ay+l1by+l2ay+l2by)/4 --midy
                return false,mx,my,mx,my
            end

            if (lxl1 == lxl2) and (mxl1 == mxl2) and (lxl1 == mxl1) then
                --x is the same for all points
                if (lyl1 == lyl2) then --the least y is common
                    if (myl1 == myl2) then -- the max y is common
                        if (lyl1 == myl2) then
                            --the lines are really just one point
                            return true, x1, y1, x1, y1
                        else --they are the same vertical line
                            return math.huge, lxl1, lyl1, mxl1, myl1
                        end
                    elseif (myl1 > myl2) then
                        --the vertical line 1 is longer
                        return math.huge, lxl1, lyl1, mxl2, myl2
                    else --the vertical line 2 is longer
                        return math.huge, lxl1, lyl1, mxl1, myl1
                    end
                elseif (myl1 == myl2) then -- the max y is common
                --point and same vertical line handled above
                    if (lyl1 > lyl2) then -- the vertcal line 2 is longer
                    --aka line 2 starts lower than line 1
                        return math.huge, lxl1, lyl1, mxl1, myl1
                    else -- the vertcal line 1 is longer
                        return math.huge, lxl1, lyl1, mxl2, myl2
                    end
                elseif (lyl1 == myl2) then
                --the vertical lines are end to end
                    --with line 1 above line 2
                    return true, lxl1, lyl1, mxl2, myl2
                elseif (lyl2 == myl1) then
                --the vertical lines are end to end
                    --with line 2 above line 1
                    return true, lxl2, lyl2, mxl1, myl1
                elseif (lyl1 < lyl2) then
                --line 1 is lowest
                    if (myl1 < myl2) then
                        --line 2 is highest
                        --overlapping lines
                        return math.huge, lxl2, lyl2, mxl1, myl1
                    else
                        --line 1 is highest
                        --line 2 lies within line 1
                        return math.huge, lxl2, lyl2, mxl2, myl2
                    end
                else --line 2 is lowest
                    if (myl1 < myl2) then
                    --line 2 is highest
                    --line 1 lies within line 2
                        return math.huge, lxl1, lyl1, mxl1, myl1
                    else
                        --line 1 is highest
                        --overlapping lines
                        return math.huge, lxl1, lyl1, mxl2, myl2
                    end
                end --all vertical line tests
            end --vertical lines

            if (lyl1 == lyl2) and (myl1 == myl2) and (lyl1 == myl1) then
                --y is the same for all points
                if (lxl1 == lxl2) then --the least x is common
                    if (mxl1 == mxl2) then -- the max x is common
                    --same point handled under vertical lines
                         --they are the same horizontal line
                        return math.huge, lxl1, lyl1, mxl1, myl1
                    elseif (mxl1 > mxl2) then
                        --the horizontal line 1 is longer
                        return math.huge, lxl1, lyl1, mxl2, myl2
                    else --the horizontal line 2 is longer
                        return math.huge, lxl1, lyl1, mxl1, myl1
                    end
                elseif (mxl1 == mxl2) then -- the max x is common
                --point and same line handled above
                    if (lxl1 > lxl2) then -- the horizontal line 2 is longer
                    --aka line 2 starts left of line 1
                        return math.huge, lxl1, lyl1, mxl1, myl1
                    else -- the horizontal line 1 is longer
                        return math.huge, lxl1, lyl1, mxl2, myl2
                    end
                elseif (lxl1 == mxl2) then
                --the horizontal lines are end to end
                    --with line 1 to the right of line 2
                    return true, lxl1, lyl1, mxl2, myl2
                elseif (lxl2 == mxl1) then
                --the horizontal lines are end to end
                    --with line 2 to the right of line 1
                    return true, lxl2, lyl2, mxl1, myl1
                elseif (lxl1 < lxl2) then
                --line 1 is left
                    if (mxl1 < mxl2) then
                        --line 2 is right
                        --overlapping lines
                        return math.huge, lxl2, lyl2, mxl1, myl1
                    else
                        --line 1 is right
                        --line 2 lies within line 1
                        return math.huge, lxl2, lyl2, mxl2, myl2
                    end
                else --line 2 is left
                    if (mxl1 < mxl2) then
                    --line 2 is right
                    --line 1 lies within line 2
                        return math.huge, lxl1, lyl1, mxl1, myl1
                    else
                        --line 1 is left
                        --overlapping lines
                        return math.huge, lxl1, lyl1, mxl2, myl2
                    end
                end --all horizontal line tests
            end --horizontal lines

            if ((lxl1 == lxl2) and (mxl1 == mxl2)) then
               --((lyl1 = lyl2) and (myl1 = myl2))
                --all remaining same lines
                return math.huge, x1, y1, x2, y2
            end

            if (lxl1 == lxl2) then --the least x is common
                if (mxl1 > mxl2) then
                --the line 1 is longer
                    return math.huge, lxl1, lyl1, mxl2, myl2
                else --the line 2 is longer
                    return math.huge, lxl1, lyl1, mxl1, myl1
                end
            elseif (mxl1 == mxl2) then --the max x is common
                if (lxl1 > lxl2) then
                --the line 1 is longer
                    return math.huge, lxl2, lyl2, mxl2, myl2
                else --the line 2 is longer
                    return math.huge, lxl1, lyl1, mxl1, myl1
                end
            elseif (lxl1 == mxl2) then
                --the horizontal lines are end to end
                    --with line 1 to the right of line 2
                return true, lxl1, lyl1, mxl2, myl2
            elseif (lxl2 == mxl1) then
                --the horizontal lines are end to end
                    --with line 2 to the right of line 1
                return true, lxl2, lyl2, mxl1, myl1
            elseif (lxl1 < lxl2) then
                --line 1 is left
                if (mxl1 < mxl2) then
                    --line 2 is right
                    --overlapping lines
                    return math.huge, lxl2, lyl2, mxl1, myl1
                else
                    --line 1 is right
                    --line 2 lies within line 1
                    return math.huge, lxl2, lyl2, mxl2, myl2
                end
           else --line 2 is left
                if (mxl1 < mxl2) then
                --line 2 is right
                --line 1 lies within line 2
                    return math.huge, lxl1, lyl1, mxl1, myl1
                else
                    --line 1 is left
                    --overlapping lines
                    return math.huge, lxl1, lyl1, mxl2, myl2
                end
            end
            --return true,x1,y1,x2,y2
        end --lines in same plane / parallel
        mx = (l1ax+l1bx+l2ax+l2bx)/4 --midx
        my = (l1ay+l1by+l2ay+l2by)/4 --midy
        return false,mx,my,mx,my
        --return false
    end
    Ua = Ua_n / d
    Ub = Ub_n / d
    ia = x1 + (Ua*(x2-x1))
    ib = y1 + (Ua*(y2-y1))
    if Ua >= 0 and Ua <= 1 and Ub >= 0 and Ub <= 1 then
        --return true
        return true,ia,ib,ia,ib
    end
    mx = (l1ax+l1bx+l2ax+l2bx)/4 --midx
    my = (l1ay+l1by+l2ay+l2by)/4 --midy
    --return false
    return false,mx,my,mx,my
end

function segmentIntersects(x1, y1, x2, y2, x3, y3, x4, y4)
    --special thanks to voiceofreason
   d = (y4-y3)*(x2-x1)-(x4-x3)*(y2-y1)
   Ua_n = ((x4-x3)*(y1-y3)-(y4-y3)*(x1-x3))
   Ub_n = ((x2-x1)*(y1-y3)-(y2-y1)*(x1-x3))
   if d == 0 then
       if Ua_n == 0 and Ua_n == Ub_n then
           return true
       end
       return false
   end
   Ua = Ua_n / d
   Ub = Ub_n / d
   if Ua >= 0 and Ua <= 1 and Ub >= 0 and Ub <= 1 then

       return true
   end

   return false
end