The　concept　of　the　Minimum　Zone　Lines　is　proposed　as　a　determinant　condition　of　the　minimum　zone　circle.　The　minimum　zone　roundness　error　from　coordinate　data　is　obtained　by　the　distance　between　the　Minimum　Zone　Lines.　The　Minimum　Zone　Lines　determined　by　four　critical　measured　points　can　be　constructed　based　on　convex　hull　and　coordinates　transmission.　The　rapid　selection　of　iteration　points　with　convex　hull　leads　to　an　efficient　way　to　solve　the　minimax　solution.　The　objective　of　this　strategy　is　to　pick　out　the　critical　data　points　as　early　as　possible　so　that　the　redundant　data　points　can　be　rejected.　The　method　developed　is　implemented　and　validated　with　the　data　available　in　the　literature.　(C)　2007　Elsevier　Ltd.　All　rights　reserved.