Generating Parametric Gn Blending Surface with Some Constraints

Abstract

This paper presents a method of generating a parametric Gn blending surface based on reparameterizing the partial surface patches in the base surfaces on the basis of Erich Hartmann method. This method is expressed as follows: Firstly, the partial region near contact curves in both base surfaces is reparameterized. The contact curves are used as the boundaries of the reparameterized partial region respectively. The reparameterized partial region in two base surfaces is called the reparameterized local base surfaces. Then the parametric Gn blending surface is generated by a linear combination of the reparameterized local base surface patches depending on one of the common parameters. Therefore, generating a Parametric Gn Blending Surface between two base surfaces is translated into generating a Parametric Gn Blending Surface between the two reparameterized local base surfaces. This paper illustrates the method to generate the Gn blending surface with some constraints by generating a G2 blending surface between the aerofoil and the body of a missile with the constraints of the forward and rear fringe curves. When the Gn blending surface with some constraints is generated, the partial region near contact curves in both base surfaces is reparameterized, and the scale factors, offset, balance factor and thumb weight are defined by meeting the constraints through using an optimization method. Then the parametric Gn blending surface is generated by the linear combination of the reparameterized local base surface patches. The shape of the blending surface can be adjusted by changing the size of the reparameterized local base surface patches.