Curved　surface　measurement　faces　the　challenges　of　complexity　and　high　precision　now,　the　impact　of　the　surface　intrinsic　features　on　the　measurement　results　should　be　taken　into　consideration　seriously,　in　addition　to　constantly　develop　measurement　methods　and　instruments.　From　the　analysis　of　the　measured　surface　point　differential　neighborhood,　the　measurement　error　anisotropy　problem　caused　by　measured　object　itself　is　comprehensively　expounded.　The　concept　of　anisotropy　of　surface　measurement　and　the　definition　of　anisotropy　error　are　proposed,　and　its　relationship　with　the　influencing　factors　is　clarified.　The　applications　of　anisotropy　of　surface　measurement　in　four　aspects　of　curved　surface　measurement　technology　are　outlined,　and　the　maximum　allowable　positioning　error　calculation　method　of　measurement　instrument　is　proposed.　As　an　application　example,　the　anisotropy　of　involute　tooth　surface　measurement　is　analyzed,　and　the　anisotropic　measurement　error　and　maximum　allowable　positioning　error　calculation　method　are　verified.　The　research　conclusions　have　not　only　theoretical　meaning　but　also　far-reaching　practical　value　on　precision　instruments　design,　measuring　method　design,　uncertainty　analysis　of　measurement　results,　and　etc.　©　2014　Journal　of　Mechanical　Engineering