Curve And Surface Reconstruction From Local Fiting To Global Fitting

Curve and surface reconstruction is one of key problems in reverse engineering.It is widely applied in CAD/CAM,computer graphics,computer vision,product design, medical image processes etc.B-Spline surface is a powerful mean in reconstructing surface from the measured data.But many issues are not dealt with adequately in curve and surface reconstruction,such as parametrization,the placement of knot vectors,and the shape controlling of the surface.A survey about the study of the curve and surface construction is given in this paper firstly,a novel method for approximating data points from local fitting to global fitting is proposed.Three kinds of data are studied in this paper.(1)The ordered planar datas {Q_i}_i=1…N(2)The profile data which are organized in the form of {Q_i,j,i=1…n;j=1…m_i}.(3)The scattered space data {Q_i}_i=1…N.The curve and surface reconstuction algorithm is developed for each kind data.Firstly,a method for curve construcntion from planar ordered data is proposed.The data points are fitted by a B-spline curve with low degree,which is named controlling curve.Then,another B-spline curve is constructed to approximate the controlling curve, which is named approximating curve.The approach completely avoids the parametrization problem.Futhermore,the approximating curve has a good shape,and the knots are nearly arc-length parametrization.A new placement of knots according to the controlling curve is also proposed.Secondly,A method for fittting profile data points using B-spline surface is proposed.The profile data points are fitted by a series of contour curves using the proposed curve construction algorithm,then a B-spline surface is lofted to interpolate the contour curves,finally the lofted surface is approximated to construct the fitting surface. The approach also avoids the parametrization in surface fitting.Futhermore,the surface constructed with this method has fewer control points,and the shape of the surface is also quite fair.At the last,A multi-step B-spline surface reconstruction method for mesasured cloudy data is present.The problem of surface recontrucntion for scatered data is converted to the problem of surface reconstrution for gridded data,and the hierarchical surfaces technique is used in the surface reconstruction.With hierarchical surface technique,the refinement and increase of data process are only located in the regions where the errores between the points and the constructed surface are greater than a specified tolerance.The final surface is C² Continuous between herarchical surfaces.The fitting problem is decomposed into subproblems involving only a portion of the gidded data by the use of hierachy and griddy,which is also making the computations particularly effient and the number of control points of the surface are also very reasonable.