Research On Closed Surface Reconstruction Algorithm In Spline Space S₂¹(?_mn^?2?)

Multivariate splines are widely used in the fields of computational geometry,computer aided design and computer graphics,which are mainly applied to the representation,approximation and reconstruction of curves and surfaces.At present,the basic design methods of curve and surface mainly include Bezier,B spline,blossoms and NURBS method.Although the existing methods of surface reconstruction above have tended to be mature,there are still some defects and limitations which make them cannot meet the demand of manufacturing industry,natural science and other fields.According to the requirements of various application fields about the characteristics of surface reconstruction methods,the present study will construct a new kind of closed surface reconstruction method based on uniform type-2 triangulation by applying spline function with minimal local branch to complete approximation,and adopting smooth cofactor coordination theory and the characteristics of the quasi-interpolation operators.In addition,the present study presents the prerequisites when using boundary width coincidence method to treat closed surface conditions.The surface constructed by the reconstruction method has a built-in continuity,thus there is no need to take smoothing problem of splices into account in the process of blending surfaces.Reconstructed surface has relatively fewer control points,and the overall number of non-tensor product surface is comparatively lower.The constructed surface which has good geometry and approximation properties,such as variation diminishing,geometric invariance and etc.will effectively solve the deficiency of the existing surface reconstruction methods.