This paper presents a method of generating a parametric G^n blending surfacebased on reparameterizing the partial surface patches in the base surfaces on the basis of ErichHartmann method. This method is expressed as ...This paper presents a method of generating a parametric G^n blending surfacebased on reparameterizing the partial surface patches in the base surfaces on the basis of ErichHartmann method. This method is expressed as follows Firstly, the partial region near contact curvesin both base surfaces is reparameterized. The contact curves are used as the boundaries of thereparameterized partial region respectively. The reparameterized partial region in two base surfacesis called the reparameterized local base surfaces. Then the parametric G^n blending surface isgenerated by a linear combination of the reparameterized local base surface patches depending on oneof the common parameters. Therefore, generating a Parametric G^n Blending Surface between two basesurfaces is translated into generating a Parametric G^n Blending Surface between the tworeparameterized local base surfaces. This paper illustrates the method to generate the G^n blendingsurface with some constraints by generating a G^2 blending surface between the aerofoil and the bodyof a missile with the constraints of the forward and rear fringe curves. When the G^n blendingsurface with some constraints is generated, the partial region near contact curves in both basesurfaces is reparameterized, and the scale factors, offset, balance factor and thumb weight aredefined by meeting the constraints through using an optimization method. Then the parametric G^nblending surface is generated by the linear combination of the reparameterized local base surfacepatches. The shape of the blending surface can be adjusted by changing the size of thereparameterized local base surface patches.展开更多
In this paper, the concepts of the ith L;-mixed affine surface area and Lp-polar curvature images are introduced, some new inequalities connecting these new notions with Lρ-centroid bodies and ρ-Blaschke bodies are ...In this paper, the concepts of the ith L;-mixed affine surface area and Lp-polar curvature images are introduced, some new inequalities connecting these new notions with Lρ-centroid bodies and ρ-Blaschke bodies are showed. Moreover, a Blaschke-Santalo type inequality for Lρ-mixed affine surface area is established. Our results also imply the similar to the inequalities for Marcus-Lopes, Bergstrom and Ky Fan.展开更多
文摘This paper presents a method of generating a parametric G^n blending surfacebased on reparameterizing the partial surface patches in the base surfaces on the basis of ErichHartmann method. This method is expressed as follows Firstly, the partial region near contact curvesin both base surfaces is reparameterized. The contact curves are used as the boundaries of thereparameterized partial region respectively. The reparameterized partial region in two base surfacesis called the reparameterized local base surfaces. Then the parametric G^n blending surface isgenerated by a linear combination of the reparameterized local base surface patches depending on oneof the common parameters. Therefore, generating a Parametric G^n Blending Surface between two basesurfaces is translated into generating a Parametric G^n Blending Surface between the tworeparameterized local base surfaces. This paper illustrates the method to generate the G^n blendingsurface with some constraints by generating a G^2 blending surface between the aerofoil and the bodyof a missile with the constraints of the forward and rear fringe curves. When the G^n blendingsurface with some constraints is generated, the partial region near contact curves in both basesurfaces is reparameterized, and the scale factors, offset, balance factor and thumb weight aredefined by meeting the constraints through using an optimization method. Then the parametric G^nblending surface is generated by the linear combination of the reparameterized local base surfacepatches. The shape of the blending surface can be adjusted by changing the size of thereparameterized local base surface patches.
基金Supported by the NNSF of China(11161024)Supported by the NSF of Jiangxi Province (2010GZC0115)
文摘In this paper, the concepts of the ith L;-mixed affine surface area and Lp-polar curvature images are introduced, some new inequalities connecting these new notions with Lρ-centroid bodies and ρ-Blaschke bodies are showed. Moreover, a Blaschke-Santalo type inequality for Lρ-mixed affine surface area is established. Our results also imply the similar to the inequalities for Marcus-Lopes, Bergstrom and Ky Fan.
