Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right heli...Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right helicoid and catenoid as special examples. We firstly construct the Bézier-like basis called AHT Bézier basis in the space spanned by {1, t, sint, cost, sinht, cosht}, t∈[0,α], α∈[0,5π/2]. Then we propose the control mesh representation of the generalized helicoid using the AHT Bézier basis. This kind of representation enables generating the minimal surfaces using the de Casteljau-like algorithm in CAD/CAGD mod- elling systems.展开更多
An essential step for the realization of free-form surface structures is to create an efficient structural gird that satisfies not only the architectural aesthetics,but also the structural performance.Employing the ma...An essential step for the realization of free-form surface structures is to create an efficient structural gird that satisfies not only the architectural aesthetics,but also the structural performance.Employing the main stress trajectories as the representation of force flows on a free-form surface,an automatic grid generation approach is proposed for the architectural design.The algorithm automatically plots the main stress trajectories on a 3D free-form surface,and adopts a modified advancing front meshing technique to generate the structural grid.Based on the proposed algorithm,an automatic grid generator named "St-Surmesh" is developed for the practical architectural design of free-form surface structure.The surface geometry of one of the Sun Valleys in Expo Axis for the Expo Shanghai 2010 is selected as a numerical example for validating the proposed approach.Comparative studies are performed to demonstrate how different structural grids affect the design of a free-form surface structure.展开更多
For the numerical simulation of compressible flows,normally different mesh sizes are expected in different regions.For example,smaller mesh sizes are required to improve the local numerical resolution in the regions w...For the numerical simulation of compressible flows,normally different mesh sizes are expected in different regions.For example,smaller mesh sizes are required to improve the local numerical resolution in the regions where the physical variables vary violently(for example,near the shock waves or in the boundary layers)and larger elements are expected for the regions where the solution is smooth.h-adaptive mesh has been widely used for complex flows.However,there are two difficulties when employing h-adaptivity for high-order discontinuous Galerkin(DG)methods.First,locally curved elements are required to precisely match the solid boundary,which significantly increases the difficulty to conduct the"refining"and"coarsening"operations since the curved information has to be maintained.Second,h-adaptivity could break the partition balancing,which would significantly affect the efficiency of parallel computing.In this paper,a robust and automatic h-adaptive method is developed for high-order DG methods on locally curved tetrahedral mesh,for which the curved geometries are maintained during the h-adaptivity.Furthermore,the reallocating and rebalancing of the computational loads on parallel clusters are conducted to maintain the parallel efficiency.Numerical results indicate that the introduced h-adaptive method is able to generate more reasonable mesh according to the structure of flow-fields.展开更多
The construction of complex stratigraphic surfaces is widely employed in many fields, such as petroleum exploration, geological modeling, and geological structure analysis. It also serves as an important foundation fo...The construction of complex stratigraphic surfaces is widely employed in many fields, such as petroleum exploration, geological modeling, and geological structure analysis. It also serves as an important foundation for data visualization and visual analysis in these fields. The existing surface construction methods have several deficiencies and face various difficulties, such as the presence of multitype faults and roughness of resulting surfaces. In this paper, a surface modeling method that uses geometric partial differential equations （PDEs） is introduced for the construction of stratigraphic surfaces. It effectively solves the problem of surface roughness caused by the irregularity of stratigraphic data distribution. To cope with the presence of multitype complex faults, a two-way projection algorithm between three- dimensional space and a two-dimensional plane is proposed. Using this algorithm, a unified method based on geometric PDEs is developed for dealing with multitype faults. Moreover, the corresponding geometric PDE is derived, and an algorithm based on an evolutionary solution is developed. The algorithm proposed for constructing spatial surfaces with real data verifies its computational efficiency and its ability to handle irregular data distribution. In particular, it can reconstruct faulty surfaces, especially those with overthrust faults.展开更多
Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis （Adv. Comput...Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis （Adv. Comput. Math., 17 （2002）, pp. 135-152） based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Juttler＇s method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 60473130) and the National Basic Research Program (973) of China (No. 2004CB318000)
文摘Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right helicoid and catenoid as special examples. We firstly construct the Bézier-like basis called AHT Bézier basis in the space spanned by {1, t, sint, cost, sinht, cosht}, t∈[0,α], α∈[0,5π/2]. Then we propose the control mesh representation of the generalized helicoid using the AHT Bézier basis. This kind of representation enables generating the minimal surfaces using the de Casteljau-like algorithm in CAD/CAGD mod- elling systems.
基金Project(51378457)supported by the National Natural Science Foundation of China
文摘An essential step for the realization of free-form surface structures is to create an efficient structural gird that satisfies not only the architectural aesthetics,but also the structural performance.Employing the main stress trajectories as the representation of force flows on a free-form surface,an automatic grid generation approach is proposed for the architectural design.The algorithm automatically plots the main stress trajectories on a 3D free-form surface,and adopts a modified advancing front meshing technique to generate the structural grid.Based on the proposed algorithm,an automatic grid generator named "St-Surmesh" is developed for the practical architectural design of free-form surface structure.The surface geometry of one of the Sun Valleys in Expo Axis for the Expo Shanghai 2010 is selected as a numerical example for validating the proposed approach.Comparative studies are performed to demonstrate how different structural grids affect the design of a free-form surface structure.
基金supported by the funding of the Key Laboratory of Aerodynamic Noise Control(No.ANCL20190103)the State Key Laboratory of Aerodynamics(No.SKLA20180102)+1 种基金the Aeronautical Science Foundation of China(Nos.2018ZA52002,2019ZA052011)the National Natural Science Foundation of China(Nos.61672281,61732006)。
文摘For the numerical simulation of compressible flows,normally different mesh sizes are expected in different regions.For example,smaller mesh sizes are required to improve the local numerical resolution in the regions where the physical variables vary violently(for example,near the shock waves or in the boundary layers)and larger elements are expected for the regions where the solution is smooth.h-adaptive mesh has been widely used for complex flows.However,there are two difficulties when employing h-adaptivity for high-order discontinuous Galerkin(DG)methods.First,locally curved elements are required to precisely match the solid boundary,which significantly increases the difficulty to conduct the"refining"and"coarsening"operations since the curved information has to be maintained.Second,h-adaptivity could break the partition balancing,which would significantly affect the efficiency of parallel computing.In this paper,a robust and automatic h-adaptive method is developed for high-order DG methods on locally curved tetrahedral mesh,for which the curved geometries are maintained during the h-adaptivity.Furthermore,the reallocating and rebalancing of the computational loads on parallel clusters are conducted to maintain the parallel efficiency.Numerical results indicate that the introduced h-adaptive method is able to generate more reasonable mesh according to the structure of flow-fields.
基金financially supported by the National Natural Science foundation of China(No.U1562218)
文摘The construction of complex stratigraphic surfaces is widely employed in many fields, such as petroleum exploration, geological modeling, and geological structure analysis. It also serves as an important foundation for data visualization and visual analysis in these fields. The existing surface construction methods have several deficiencies and face various difficulties, such as the presence of multitype faults and roughness of resulting surfaces. In this paper, a surface modeling method that uses geometric partial differential equations （PDEs） is introduced for the construction of stratigraphic surfaces. It effectively solves the problem of surface roughness caused by the irregularity of stratigraphic data distribution. To cope with the presence of multitype complex faults, a two-way projection algorithm between three- dimensional space and a two-dimensional plane is proposed. Using this algorithm, a unified method based on geometric PDEs is developed for dealing with multitype faults. Moreover, the corresponding geometric PDE is derived, and an algorithm based on an evolutionary solution is developed. The algorithm proposed for constructing spatial surfaces with real data verifies its computational efficiency and its ability to handle irregular data distribution. In particular, it can reconstruct faulty surfaces, especially those with overthrust faults.
基金supported by the National Key Basic Research Project of China(No.2004CB318000)One Hundred Talent Project of the Chinese Academy of Sciences,the NSF of China(No.60225002,No.60533060)Doctorial Program of MOE of China and the 111 Project(No.B07033).
文摘Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis （Adv. Comput. Math., 17 （2002）, pp. 135-152） based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Juttler＇s method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.
