Isotropy　is　an　important　feature　of　an　area　filter　in　the　three-dimensional　surface　roughness　evaluation.　First,　the　transmission　characteristic　deviation　between　the　approximating　spline　filter　and　the　Gaussian　filter　is　reduced　by　cascading　approximating.　Second,　the　approximating　spline　filter　is　superimposed　on　the　orthogonal　direction　to　obtain　an　isotropic　areal　filter.　Then,　four　direct　methods　for　the　solving　approximating　spline　matrix　are　applied.　Based　on　the　profile　filtering　and　areal　filtering,　the　computational　efficiency　and　accuracy　are　compared.　The　experimental　results　show　that　the　improved　square　root　method　(LDLT　decomposition)　combines　both　computational　efficiency　and　filtering　precision,　and　is　a　good　choice　for　solving　the　approximating　spline　matrix.　Finally,　six　kinds　of　robust　approximating　spline　filters　are　constructed.　Taking　the　output　value　of　robust　Gaussian　regression　filter　(RGRF)　as　reference,　and　the　honing　profile　and　step　surface　with　deep　valley　characteristics　were　used　as　test　surfaces　to　compare　their　robustness　and　iteration　time.　The　experimental　results　show　that　the　approximating　spline　filter　based　on　the　ADRF　function　has　the　shortest　iteration　times,　while　its　roughness　is　close　to　the　robust　Gaussian　regression　filter.