Curvature lines are special and important curves on surfaces.It is of great significance to construct developable surface interpolated on curvature lines in engineering applications.In this paper,the shape optimizatio...Curvature lines are special and important curves on surfaces.It is of great significance to construct developable surface interpolated on curvature lines in engineering applications.In this paper,the shape optimization of generalized cubic ball developable surface interpolated on the curvature line is studied by using the improved reptile search algorithm.Firstly,based on the curvature line of generalized cubic ball curve with shape adjustable,this paper gives the construction method of SGC-Ball developable surface interpolated on the curve.Secondly,the feedback mechanism,adaptive parameters and mutation strategy are introduced into the reptile search algorithm,and the Feedback mechanism-driven improved reptile search algorithm effectively improves the solving precision.On IEEE congress on evolutionary computation 2014,2017,2019 and four engineering design problems,the feedback mechanism-driven improved reptile search algorithm is compared with other representative methods,and the result indicates that the solution performance of the feedback mechanism-driven improved reptile search algorithm is competitive.At last,taking the minimum energy as the evaluation index,the shape optimization model of SGC-Ball interpolation developable surface is established.The developable surface with the minimum energy is achieved with the help of the feedback mechanism-driven improved reptile search algorithm,and the comparison experiment verifies the superiority of the feedback mechanism-driven improved reptile search algorithm for the shape optimization problem.展开更多
The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which...The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, the authors focus on the rational developable surfaces. For a given algebraic surface, the authors first determine whether it is developable by geometric inspection, and then give a rational proper parametrization in the affrmative case. For a rational parametric surface, the authors also determine the developability and give a proper reparametrization for the developable surface.展开更多
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
Intensive land use( ILU) policies affect the demand and supply of land. These policies promote efficient land use, and demands for land must therefore be evaluated in terms of the level of land-use intensity. If the d...Intensive land use( ILU) policies affect the demand and supply of land. These policies promote efficient land use, and demands for land must therefore be evaluated in terms of the level of land-use intensity. If the demand is considered excessive, ILU policies act like a "valve"to restrict the land supply. Drawing on data from Chengdu,China,where developable land is scarce,we construct a model using system dynamics( SD) to simulate two scenarios: ILU development and non-ILU development. The results show that when ILU leads to positive land-use efficiency,land supply will exceed demand,resulting in an appropriate level of real demand for the current population level and GDP. Thus,artificial demand( inflated by investors) is reduced. By contrast,when non-ILU leads to negative land-use efficiency,land demand will exceed supply. In this scenario,artificial demand is higher than real demand.展开更多
We study the real Bonnet surfaces which accept one unique nontrivial isometry that preserves the mean curvature, in the three-dimensional Euclidean space. We give a general criterion for these surfaces and use it to d...We study the real Bonnet surfaces which accept one unique nontrivial isometry that preserves the mean curvature, in the three-dimensional Euclidean space. We give a general criterion for these surfaces and use it to determine the tangential developable surfaces of this kind. They are determined implicitly by elliptic integrals of the third kind. Only the tangential developable surfaces of circular helices are explicit examples for which we completely determine the above unique nontrivial isometry.展开更多
We propose a method for generating a ruled B-spline surface fitting to a sequence of pre-defined ruling lines and the generated surface is required to be as-developable-as-possible.Specifically,the terminal ruling lin...We propose a method for generating a ruled B-spline surface fitting to a sequence of pre-defined ruling lines and the generated surface is required to be as-developable-as-possible.Specifically,the terminal ruling lines are treated as hard constraints.Different from existing methods that compute a quasi-developable surface from two boundary curves and cannot achieve explicit ruling control,our method controls ruling lines in an intuitive way and serves as an effective tool for computing quasi-developable surfaces from freely-designed rulings.We treat this problem from the point of view of numerical optimization and solve for surfaces meeting the distance error tolerance allowed in applications.The performance and the efficacy of the proposed method are demonstrated by the experiments on a variety of models including an application of the method for path planning in 5-axis computer numerical control(CNC)flank milling.展开更多
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
While considering a mirror and light rays coming either from a point source or from infinity,the reflected light rays may have an envelope,called a caustic curve.In this paper,we study developable surfaces as mirrors....While considering a mirror and light rays coming either from a point source or from infinity,the reflected light rays may have an envelope,called a caustic curve.In this paper,we study developable surfaces as mirrors.These caustic surfaces,described in a closed form,are also developable surfaces of the same type as the original mirror surface.We provide efficient,algorithmic computation to find the caustic surface of each of the three types of developable surfaces(cone,cylinder,and tangent surface of a spatial curve).We also provide a potential application of the results in contemporary free-form architecture design.展开更多
The paper deals with the principle of envelope of a one-parameter plane family to design developable surfaces. Three methods of designing developable surfaces are presented. They are designing a developable surface ba...The paper deals with the principle of envelope of a one-parameter plane family to design developable surfaces. Three methods of designing developable surfaces are presented. They are designing a developable surface based on one curve on it and its normal line, designing a developable surface based on two curves on it and designing a developable surface based on one curve and one surface. They meet the requirements of engineering fields.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
Based on the finite-volume coastal ocean model （FVCOM）, a three-dimensional numerical model FVCOM was built to simulate the ocean dynamics in pre-dam and post-dam conditions in Bachimen （BCM）. The domain decomposi...Based on the finite-volume coastal ocean model （FVCOM）, a three-dimensional numerical model FVCOM was built to simulate the ocean dynamics in pre-dam and post-dam conditions in Bachimen （BCM）. The domain decomposition method, which is effective in describing the conservation of volume and non-conservation of mechanical energy in the utilization of tidal energy, was employed to estimate the theoretical tidal energy resources and developable energy resources, and to analyze the hydrodynamic effect of the tidal power station. This innovative approach has the advantage of linking physical oceanography with engineering problems. The results indicate that the theoretical annual tidal energy resources is about 2x 108 kwh under the influence of tidal power station; Optimized power installation is confirmed according to power generation curve from numerical analysis; the developable resources is about 38.2% of theoretical tidal energy resources with the employment of one-way electricity generation. The electricity generation time and power are 3479 hours and 2.55~104KW, respectively. The power station has no effect on the tide pattern which is semi-diumal tide in both two conditions, but the amplitudes of main constituents apparently decrease in the area near the dam, with the ME decreasing the most, about 62.92 cm. The tidal prism shrinks to 2.28×107 m3, but can still meet the flow requirement for tidal power generation. The existence of station increases the flow rate along the waterway and enhances the residual current. There are two opposite vortexes formed on the east side beside the dam of the station, which leads to pollutants gathering.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.52375264).
文摘Curvature lines are special and important curves on surfaces.It is of great significance to construct developable surface interpolated on curvature lines in engineering applications.In this paper,the shape optimization of generalized cubic ball developable surface interpolated on the curvature line is studied by using the improved reptile search algorithm.Firstly,based on the curvature line of generalized cubic ball curve with shape adjustable,this paper gives the construction method of SGC-Ball developable surface interpolated on the curve.Secondly,the feedback mechanism,adaptive parameters and mutation strategy are introduced into the reptile search algorithm,and the Feedback mechanism-driven improved reptile search algorithm effectively improves the solving precision.On IEEE congress on evolutionary computation 2014,2017,2019 and four engineering design problems,the feedback mechanism-driven improved reptile search algorithm is compared with other representative methods,and the result indicates that the solution performance of the feedback mechanism-driven improved reptile search algorithm is competitive.At last,taking the minimum energy as the evaluation index,the shape optimization model of SGC-Ball interpolation developable surface is established.The developable surface with the minimum energy is achieved with the help of the feedback mechanism-driven improved reptile search algorithm,and the comparison experiment verifies the superiority of the feedback mechanism-driven improved reptile search algorithm for the shape optimization problem.
基金supported by Beijing Nova Program under Grant No.Z121104002512065The author PerezDíaz S is a member of the Research Group ASYNACS(Ref.CCEE2011/R34)
文摘The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, the authors focus on the rational developable surfaces. For a given algebraic surface, the authors first determine whether it is developable by geometric inspection, and then give a rational proper parametrization in the affrmative case. For a rational parametric surface, the authors also determine the developability and give a proper reparametrization for the developable surface.
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Hundred-Talent Program of Ministry of Land and Resources,China
文摘Intensive land use( ILU) policies affect the demand and supply of land. These policies promote efficient land use, and demands for land must therefore be evaluated in terms of the level of land-use intensity. If the demand is considered excessive, ILU policies act like a "valve"to restrict the land supply. Drawing on data from Chengdu,China,where developable land is scarce,we construct a model using system dynamics( SD) to simulate two scenarios: ILU development and non-ILU development. The results show that when ILU leads to positive land-use efficiency,land supply will exceed demand,resulting in an appropriate level of real demand for the current population level and GDP. Thus,artificial demand( inflated by investors) is reduced. By contrast,when non-ILU leads to negative land-use efficiency,land demand will exceed supply. In this scenario,artificial demand is higher than real demand.
基金the National Natural Science Foundation of China under Grant No.60603085,60736019(国家自然科学基金)the National High- Tech Research and Development Plan of China under Grant No.2006AA01Z304,2007AA01Z336(国家高技术研究发展计划(863))the National Grand Fundamental Research 973 Program of China under Grant No.2006CB303104(国家重点基础研究发展规划(973)).
文摘We study the real Bonnet surfaces which accept one unique nontrivial isometry that preserves the mean curvature, in the three-dimensional Euclidean space. We give a general criterion for these surfaces and use it to determine the tangential developable surfaces of this kind. They are determined implicitly by elliptic integrals of the third kind. Only the tangential developable surfaces of circular helices are explicit examples for which we completely determine the above unique nontrivial isometry.
基金This work was supported by the National Key Research and Development Program of China under Grant No.2018YFB1702900the National Natural Science Foundation of China under Grant No.62072139the Joint Funds of the National Natural Science Foundation of China with Zhejiang Integration of Informatization and Industrialization Key Project under Grant No.U1609218.
文摘We propose a method for generating a ruled B-spline surface fitting to a sequence of pre-defined ruling lines and the generated surface is required to be as-developable-as-possible.Specifically,the terminal ruling lines are treated as hard constraints.Different from existing methods that compute a quasi-developable surface from two boundary curves and cannot achieve explicit ruling control,our method controls ruling lines in an intuitive way and serves as an effective tool for computing quasi-developable surfaces from freely-designed rulings.We treat this problem from the point of view of numerical optimization and solve for surfaces meeting the distance error tolerance allowed in applications.The performance and the efficacy of the proposed method are demonstrated by the experiments on a variety of models including an application of the method for path planning in 5-axis computer numerical control(CNC)flank milling.
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Project supported by the European Union and the European Social Fund(No.EFOP-3.6.3-VEKOP-16-2017-00002).Open Access funding provided by European Union and the European Social Fund。
文摘While considering a mirror and light rays coming either from a point source or from infinity,the reflected light rays may have an envelope,called a caustic curve.In this paper,we study developable surfaces as mirrors.These caustic surfaces,described in a closed form,are also developable surfaces of the same type as the original mirror surface.We provide efficient,algorithmic computation to find the caustic surface of each of the three types of developable surfaces(cone,cylinder,and tangent surface of a spatial curve).We also provide a potential application of the results in contemporary free-form architecture design.
文摘The paper deals with the principle of envelope of a one-parameter plane family to design developable surfaces. Three methods of designing developable surfaces are presented. They are designing a developable surface based on one curve on it and its normal line, designing a developable surface based on two curves on it and designing a developable surface based on one curve and one surface. They meet the requirements of engineering fields.
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.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences under contract No.XDA11010201
文摘Based on the finite-volume coastal ocean model （FVCOM）, a three-dimensional numerical model FVCOM was built to simulate the ocean dynamics in pre-dam and post-dam conditions in Bachimen （BCM）. The domain decomposition method, which is effective in describing the conservation of volume and non-conservation of mechanical energy in the utilization of tidal energy, was employed to estimate the theoretical tidal energy resources and developable energy resources, and to analyze the hydrodynamic effect of the tidal power station. This innovative approach has the advantage of linking physical oceanography with engineering problems. The results indicate that the theoretical annual tidal energy resources is about 2x 108 kwh under the influence of tidal power station; Optimized power installation is confirmed according to power generation curve from numerical analysis; the developable resources is about 38.2% of theoretical tidal energy resources with the employment of one-way electricity generation. The electricity generation time and power are 3479 hours and 2.55~104KW, respectively. The power station has no effect on the tide pattern which is semi-diumal tide in both two conditions, but the amplitudes of main constituents apparently decrease in the area near the dam, with the ME decreasing the most, about 62.92 cm. The tidal prism shrinks to 2.28×107 m3, but can still meet the flow requirement for tidal power generation. The existence of station increases the flow rate along the waterway and enhances the residual current. There are two opposite vortexes formed on the east side beside the dam of the station, which leads to pollutants gathering.
