In this paper we construct developable surface patches which are bounded by two rational or NURBS curves,though the resulting patch is not a rational or NURBS surface in general.This is accomplished by reparameterizin...In this paper we construct developable surface patches which are bounded by two rational or NURBS curves,though the resulting patch is not a rational or NURBS surface in general.This is accomplished by reparameterizing one of the boundary curves.The reparameterization function is the solution of an algebraic equation.For the relevant case of cubic or cubic spline curves,this equation is quartic at most,quadratic if the curves are B´ezier or splines and lie on parallel planes,and hence it may be solved either by standard analytical or numerical methods.展开更多
In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. To complete the boundary of the patch, a ...In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. To complete the boundary of the patch, a second spline curve is to be given. Up to now this interpolation problem could be solved, but without the possibility of choosing both endpoints for the rulings. We circumvent such difficulty by resorting to degree elevation of the developable surface. This is useful for solving not only this problem, but also other problems dealing with triangular developable patches.展开更多
In this paper we provide a characterisation of rational developable surfaces in terms of the blossoms of the bounding curves and three rational functions∧,M,ν.Properties of developable surfaces are revised in this f...In this paper we provide a characterisation of rational developable surfaces in terms of the blossoms of the bounding curves and three rational functions∧,M,ν.Properties of developable surfaces are revised in this framework.In particular,a closed algebraic formula for the edge of regression of the surface is obtained in terms of the functions∧,M,ν,which are closely related to the ones that appear in the standard decomposition of the derivative of the parametrisation of one of the bounding curves in terms of the director vector of the rulings and its derivative.It is also shown that all rational developable surfaces can be described as the set of developable surfaces which can be constructed with a constant∧,M,ν.The results are readily extended to rational spline developable surfaces.展开更多
基金supported by European Union (EU) (Grant No.H2020-815044)“Sloshing Wing Dynamics (SLOWD)”support from the Spanish Ministry for Science,Innovation and Universities (MCIU) (Grant No.RTI2018-096791-B-C21)“Hidrodinámica de elementos de amortiguamiento del movimiento de aerogeneradores flotantes”funding from Universidad Politécnica de Madrid under a pre-doctoral scholarship.
基金This work is partially supported by the Spanish Ministerio de Economiay Competitividad through research grant TRA2015-67788-P.
文摘In this paper we construct developable surface patches which are bounded by two rational or NURBS curves,though the resulting patch is not a rational or NURBS surface in general.This is accomplished by reparameterizing one of the boundary curves.The reparameterization function is the solution of an algebraic equation.For the relevant case of cubic or cubic spline curves,this equation is quartic at most,quadratic if the curves are B´ezier or splines and lie on parallel planes,and hence it may be solved either by standard analytical or numerical methods.
基金partially supported by the Spanish Ministerio de Economía y Competividad(No.TRA2014-56792-P)
文摘In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. To complete the boundary of the patch, a second spline curve is to be given. Up to now this interpolation problem could be solved, but without the possibility of choosing both endpoints for the rulings. We circumvent such difficulty by resorting to degree elevation of the developable surface. This is useful for solving not only this problem, but also other problems dealing with triangular developable patches.
基金This work is partially supported by the Spanish Ministerio de Economia y Competitividad through research grant TRA2015-67788-P.
文摘In this paper we provide a characterisation of rational developable surfaces in terms of the blossoms of the bounding curves and three rational functions∧,M,ν.Properties of developable surfaces are revised in this framework.In particular,a closed algebraic formula for the edge of regression of the surface is obtained in terms of the functions∧,M,ν,which are closely related to the ones that appear in the standard decomposition of the derivative of the parametrisation of one of the bounding curves in terms of the director vector of the rulings and its derivative.It is also shown that all rational developable surfaces can be described as the set of developable surfaces which can be constructed with a constant∧,M,ν.The results are readily extended to rational spline developable surfaces.
