Geometriccomputingisanimportanttoolindesignandmanufacturingandinarts.Conventionally,geometriccomputingistakenbyalgebraiccomputing.Thevividintuitionofobjectsinvisualizationislostinnumericfunctions,whichishoweververyusefultohumancognitionaswellasemotion.Inthispaper,weproposedaconceptandtheoryofgeometricbasis(GB)asthesolvingcellforgeometriccomputing.EachGBrepresentsabasicgeometricoperation.GBworksasbothexpressingandsolvingcelljustliketheconceptofbasisinlinearalgebrabywhicheveryelementofthevectorspacecanbeexpressed.For3Dproblems,withaprocedureofaprojectionsreduction,theproblemcanbereducedtoplaneandthereductionfunctioncanbedesignedasaGB.AsequenceofGBcanconstructahigherlayerGB.Then,bythetraversaloftree,asequenceofGBisgotandthissequenceisjusttheconstructionprocessandalsothesolutionofthisgeometricproblem.
