In isogeometric analysis,it is frequently required to handle the geometric models enclosed by four-sided or non-four-sided boundary patches,such as trimmed surfaces.In this paper,we develop a Gregory solid based metho...In isogeometric analysis,it is frequently required to handle the geometric models enclosed by four-sided or non-four-sided boundary patches,such as trimmed surfaces.In this paper,we develop a Gregory solid based method to parameterize those models.First,we extend the Gregory patch representation to the trivariate Gregory solid representation.Second,the trivariate Gregory solid representation is employed to interpolate the boundary patches of a geometric model,thus generating the polyhedral volume parametrization.To improve the regularity of the polyhedral volume parametrization,we formulate the construction of the trivariate Gregory solid as a sparse optimization problem,where the optimization objective function is a linear combination of some terms,including a sparse term aiming to reduce the negative Jacobian area of the Gregory solid.Then,the alternating direction method of multipliers(ADMM)is used to solve the sparse optimization problem.Lots of experimental examples illustrated in this paper demonstrate the effectiveness and efficiency of the developed method.展开更多
Although the isogeometric collocation(IGA-C)method has been successfully utilized in practical applications due to its simplicity and efficiency,only a little theoretical results have been established on the numerical...Although the isogeometric collocation(IGA-C)method has been successfully utilized in practical applications due to its simplicity and efficiency,only a little theoretical results have been established on the numerical analysis of the IGA-C method.In this paper,we deduce the convergence rate of the consistency of the IGA-C method.Moreover,based on the formula of the convergence rate,the necessary and sufficient condition for the consistency of the IGA-C method is developed.These results advance the numerical analysis of the IGA-C method.展开更多
We develop a data driven method(probability model) to construct a composite shape descriptor by combining a pair of scale-based shape descriptors. The selection of a pair of scale-based shape descriptors is modeled as...We develop a data driven method(probability model) to construct a composite shape descriptor by combining a pair of scale-based shape descriptors. The selection of a pair of scale-based shape descriptors is modeled as the computation of the union of two events, i.e.,retrieving similar shapes by using a single scale-based shape descriptor. The pair of scale-based shape descriptors with the highest probability forms the composite shape descriptor. Given a shape database, the composite shape descriptors for the shapes constitute a planar point set.A VoR-Tree of the planar point set is then used as an indexing structure for efficient query operation. Experiments and comparisons show the effectiveness and efficiency of the proposed composite shape descriptor.展开更多
基金supported by the National Natural Science Foundation of China(No.61872316)the National Key R&D Program of China(No.2016YFB1001501)the Fundamental Research Funds for the Central Universities(No.2017XZZX009-03)
文摘In isogeometric analysis,it is frequently required to handle the geometric models enclosed by four-sided or non-four-sided boundary patches,such as trimmed surfaces.In this paper,we develop a Gregory solid based method to parameterize those models.First,we extend the Gregory patch representation to the trivariate Gregory solid representation.Second,the trivariate Gregory solid representation is employed to interpolate the boundary patches of a geometric model,thus generating the polyhedral volume parametrization.To improve the regularity of the polyhedral volume parametrization,we formulate the construction of the trivariate Gregory solid as a sparse optimization problem,where the optimization objective function is a linear combination of some terms,including a sparse term aiming to reduce the negative Jacobian area of the Gregory solid.Then,the alternating direction method of multipliers(ADMM)is used to solve the sparse optimization problem.Lots of experimental examples illustrated in this paper demonstrate the effectiveness and efficiency of the developed method.
基金supported by the National Natural Science Foundation of China(61872316)the Natural Science Foundation of Zhejiang Province,China(LY19F020004)
文摘Although the isogeometric collocation(IGA-C)method has been successfully utilized in practical applications due to its simplicity and efficiency,only a little theoretical results have been established on the numerical analysis of the IGA-C method.In this paper,we deduce the convergence rate of the consistency of the IGA-C method.Moreover,based on the formula of the convergence rate,the necessary and sufficient condition for the consistency of the IGA-C method is developed.These results advance the numerical analysis of the IGA-C method.
基金supported by the National Key R&D Plan of China(2016YFB1001501)
文摘We develop a data driven method(probability model) to construct a composite shape descriptor by combining a pair of scale-based shape descriptors. The selection of a pair of scale-based shape descriptors is modeled as the computation of the union of two events, i.e.,retrieving similar shapes by using a single scale-based shape descriptor. The pair of scale-based shape descriptors with the highest probability forms the composite shape descriptor. Given a shape database, the composite shape descriptors for the shapes constitute a planar point set.A VoR-Tree of the planar point set is then used as an indexing structure for efficient query operation. Experiments and comparisons show the effectiveness and efficiency of the proposed composite shape descriptor.
