As an intrinsic measure of smoothness, geometric continuity is an important problem in the fields of computer aided geo- metric design. It can afford more degrees of freedom for manipulating the shape of curve. Howeve...As an intrinsic measure of smoothness, geometric continuity is an important problem in the fields of computer aided geo- metric design. It can afford more degrees of freedom for manipulating the shape of curve. However, piecewise polynomial functions of geometrically continuous splines are difficult to be constructed. In this paper, the conversion matrix between geometrically con- tinuous spline basis functions and Bezier representation is analyzed. Based on this, construction of arbitrary degree geometrically continuous spline basis functions can be translated into a solution of linear system of equations. The original construction of geomet- rically continuous spline is simplified.展开更多
基金Supported by NSFC (No.61100129)Long-span Building Construction Research Project (No.40006014201101)
文摘As an intrinsic measure of smoothness, geometric continuity is an important problem in the fields of computer aided geo- metric design. It can afford more degrees of freedom for manipulating the shape of curve. However, piecewise polynomial functions of geometrically continuous splines are difficult to be constructed. In this paper, the conversion matrix between geometrically con- tinuous spline basis functions and Bezier representation is analyzed. Based on this, construction of arbitrary degree geometrically continuous spline basis functions can be translated into a solution of linear system of equations. The original construction of geomet- rically continuous spline is simplified.
