Qin Xinqiang's research while affiliated with Xi'an Technological University and other places

To solve the problems in adjusting and controlling shapes of developable surfaces, a direct explicit and efficient methods of computer-aided design for developable surfaces with multiple local shape parameters are proposed. Firstly, a class of novel λμ-B-spline basis functions with two shape parameters is presented. And then, following the important idea of duality between points and planes in 3D projective space, the corresponding developable λμ-B-spline surfaces with multiple shape parameters are represented using control planes with λμ-B-spline basis functions. The developable λμ-B-spline surfaces inherit the outstanding properties of the B-spline surfaces, with a good performance on adjusting their local shapes by changing the two shape parameters. In addition, some properties of the developable λμ-B-spline surfaces and applications in developable surfaces design are discussed. The modeling examples illustrate that the developable λμ-B-spline surfaces provide a valuable ways for the design of developable surfaces.

The configuration matrix obtained through the global radial basis function collocation method is usually an asymmetry full matrix and highly ill-conditioned for parabolic equations. To overcome the deficiencies, a radial basis meshless domain decomposition algorithm is proposed. It has the advantages of both the radial basis collocation method and the domain decomposition method. The new method can transform the solution to a large-scale problem into the solutions to several small sub-area ones. It effectively reduce the condition numbers of the collocation matrix. It is shown by numerical example that this method improves the stability and accelerates convergence of the numerical solution to parabolic equations.