A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient condition...A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper.展开更多
The Darboux transformation of a 3 × 3 spectral problem which is associated with the higherorder nonlinear Schrodinger equation is given. Some solutions of the higher-order nonlinear Schrodinger equation are provi...The Darboux transformation of a 3 × 3 spectral problem which is associated with the higherorder nonlinear Schrodinger equation is given. Some solutions of the higher-order nonlinear Schrodinger equation are provided by taking different "seeds".展开更多
基金Project supported by the National Basic Research Program (973) of China (No. 2004CB719400), the National Natural Science Founda-tion of China (Nos. 60373033 and 60333010) and the National Natural Science Foundation for Innovative Research Groups (No. 60021201), China
文摘A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper.
基金Project supported by the National Basic Aesearch Project of Nonlinear Science (No.HH4712),and the Ministry of Education of Chi
文摘The Darboux transformation of a 3 × 3 spectral problem which is associated with the higherorder nonlinear Schrodinger equation is given. Some solutions of the higher-order nonlinear Schrodinger equation are provided by taking different "seeds".
