Research On Theory Of DP Curves And Surfaces Mathematical Modeling Based On Data Information

In the last years,searching new free curves and surfaces modeling methods is a hot research topic in Computer Aided Geometric Design(CAGD).Under this background,this masteral dissertation is devoted to some new extensions,including curves and surfaces with shape parameter,curves and surfaces in non-polynomial space and subdivision method.The main works are as follows:(1)Based on shape modification,a type of cubic DP curve with a shape parameter is constructed.Extending the definition interval of the the traditional cubic DP basis function from[0,1]to[0,?],then the properties of the new basis functions are analyzed and the cubic DP curve with a shape parameter is defined.Furthermore,we analyze the properties of the curve and its shape,the impact of the shape parameter as well as continuous conditions of adjacent curves.Using tensor product,we extend the curve to the cubic DP surface with a parameter.At last,three selection schemes of the shape parameters and several application examples are given.(2)Two kinds of shape parameters are introduced in the cubic?-DP basic function.The cubic??-?-DP curve and surface and their properties are analyzed.Then we discuss smooth continuous conditions and show several rotating surfaces.Using the singular blending technique,the singular blending cubic??-?-DP interpolation curve with shape parameters is constructed.We present its properties and the influences of multiple parameters.The approximation degree between the singular blending interpolation curve and its control polygon can be adjusted,thus enhancing the shape-control capability of the cubic??-?-DP interpolation curves.(3)The traditional cubic DP curve is extended to the trigonometric function space.A new set of triangular polynomials is obtained,which as the?1,sint,cost,cos2t?basis.Then the properties of the new basis functions are analyzed.We linearly combine the extended basis functions with the fixed control points,the cubic T-DP curve is presented.Its shape and properties are analyzed.The cubic T-DP curve can accurately represent some conic curve.Smooth continuous conditions of the cubic T-DP curve and rotating surfaces are given.Moreover,using the tensor product method,the cubic T-DP surface is deduced.(4)Two types of shape parameters are introduced in the trigonometric spline basis function.The algebraic trigonometric polynomial spline curves and surfaces with two kinds of shape parameters,called AT-?-Spline,are constructed and satisfy geometric continuity.Continuous conditions of adjacent curves and some application examples are given.By using the singular blending theory,the interpolation AT-?-Spline curve which meet the C~1?G~2continuity is constructed,the curve can solve the geometric continuity of the curve and inverse algorithm of the curve.(5)A method of discretely representing curves and surfaces,subdivision,is studied.According to the old subdivision rules,we inverse the old points and linearly combine those with new control points.A new combined approximating and interpolating five-point ternary subdivision scheme is presented.Using the Laurent polynomial method,the continuity and smoothness properties of the proposed scheme is derived.Moreover,the proposed scheme is compared with other subdivision schemes.Numerical experiments show that it generates approximate or interpolate C~1and C~2limiting curve with different parameter values.It generates limiting curve closer to the control polygon and the shape behavior of the limiting curve is guaranteed.Figures 51 Table 2 References 78...