At present,noise reduction has become an urgent challenge across various fields.Whether in the context of household appliances in daily life or in the enhancement of stealth performance in military equipment,noise con...At present,noise reduction has become an urgent challenge across various fields.Whether in the context of household appliances in daily life or in the enhancement of stealth performance in military equipment,noise control technologies play a critical role.This study introduces a computational framework for simulating Helmholtz equationgoverned acoustic scattering using a boundary element method(BEM)integrated with Loop subdivision surfaces.By adopting the Loop subdivision scheme—a widely used computer-aided design(CAD)technique-the framework unifies geometric representation and physical field discretization,ensuring seamless compatibility with industrial CAD workflows.The core innovation lies in the novel integration of conditional generative adversarial networks(CGANs)into the subdivision surface BEM to assist and accelerate the numerical computation process.In this study,for the two cases examined,the results show that the CGAN-enhanced approach achieves substantial gains in computational efficiency without compromising accuracy.A hierarchical acceleration strategy is further proposed:the fast multipole method(FMM)first reduces baseline computational complexity,while CGAN-driven secondary acceleration and data augmentation enable real-time parameter exploration.Benchmark validations and practical engineering applications demonstrate the method’s robustness and scalability for large-scale structural-acoustic analysis.展开更多
A novel method is produced to evaluate the energy of the Catmull-Clark subdivision surface including extraordinary points in the control mesh. A closed-form analytic formula for thin plate energy of the Catmull-Clark ...A novel method is produced to evaluate the energy of the Catmull-Clark subdivision surface including extraordinary points in the control mesh. A closed-form analytic formula for thin plate energy of the Catmull-Clark subdivision surface of arbitrary topology is derived through translating the Catmull-Clark subdivision surface into bi-cubic B-spline surface pieces. Using this method, both the membrane energy and the thin plate energy can be evaluated without requiring recursive subdivision. Therefore, it is more efficient and more accurate than the existing methods for calculating the energy of the Catmull-Clark subdivision surface with arbitrary topology. The example of surface fairing demonstrates that this method is efficient and successful for evaluating the energy of subdivision surfaces.展开更多
In this paper we introduce a new reverse Loop subdivision method. In contrast to current wavelets based Loop subdivision scheme, our method applies the same rules to both regular and extraordinary vertices and reconst...In this paper we introduce a new reverse Loop subdivision method. In contrast to current wavelets based Loop subdivision scheme, our method applies the same rules to both regular and extraordinary vertices and reconstructs the sharp features easily. Furthermore, our method runs faster because it does not need analysis and synthesis procedural. Our main goal is the design of a reverse subdivision method that can reconstruct the coarser mesh from a finer subdivision surface with sharp features for multiresolution representation, The proposed method only needs a little memory storage and brings little error, and it is easy to implement.展开更多
This paper proposes a novel strategy based on fragment meshes of Shiue et al. for GPU rendering of compos- ite subdivision surfaces. Two enumeration systems are established to label the primitives of each fragment mes...This paper proposes a novel strategy based on fragment meshes of Shiue et al. for GPU rendering of compos- ite subdivision surfaces. Two enumeration systems are established to label the primitives of each fragment mesh. A sector-layer-index enumeration system is responsible for retrieving proximities for subdivision masks while a sec- tor-index enumeration system designates a 2D texture buffer in GPU. Recurring to the free conversion between them, our approach may get rid of lookup tables that are designed to record subdivision masks. In addition, relatively small composite subdivision masks make it easy to develop automatically retrieving techniques. Finally, as center vertices are often irregular, their computation is related to an average with alterable number of items. Considering that variable loop is not efficient in GPU, we evaluate the center vertex of each fragment mesh using the linear combination of its level 0, level 1 and limit positions instead of averaging schemes. Experiments demonstrate that our approach generally outper- forms that of Shiue et al. in FPS by a long way.展开更多
Based on the butterfly subdivision scheme and the modified butterfly subdivision scheme, an improved butterfly subdivision scheme is proposed. The scheme uses a small stencil of six points to calculate new inserting v...Based on the butterfly subdivision scheme and the modified butterfly subdivision scheme, an improved butterfly subdivision scheme is proposed. The scheme uses a small stencil of six points to calculate new inserting vertex, 2n new vertices are inserted in the 2n triangle faces in each recursion, and the n old vertices are kept, special treatment is given to the boundary, achieving higher smoothness while using small stencils is realized. With the proposed scheme, the number of triangle faces increases only by a factor of 3 in each refinement step. Compared with the butterfly subdivision scheme and the modified butterfly subdivision scheme, the size of triangle faces changes more gradually, which allows one to have greater control over the resolution of a refined mesh.展开更多
Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for ...Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline（NURBS） for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system（DCS） and measurement coordinate system（MCS） for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization（QPSO） is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%-22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.展开更多
On the basis of three geological models and several orebody boundaries, a method of grid subdivision and integral has been proposed to calculate and evaluate the resources of cobalt-rich crusts on the seamounts in the...On the basis of three geological models and several orebody boundaries, a method of grid subdivision and integral has been proposed to calculate and evaluate the resources of cobalt-rich crusts on the seamounts in the central Pacific Ocean. The formulas of this method are deduced and the interface of program module is designed. The method is carried out in the software ＂Auto mapping system of submarine topography and geomorphology MBChart＂. This method and program will possibly become a potential tool to calculate the resources of seamounts and determine the target diggings for China＇ s next Five-year Plan.展开更多
By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of t...By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved. The conclusion of the extreme value problem is thus further confirmed.展开更多
A subdivision vertex-edge corona G_1~S?(∪ G_3~E) is a graph that consists of S(G_1),|V(G_1)| copies of G_2 and |I(G_1)| copies of G_3 by joining the i-th vertex in V(G_1) to each vertex in the i-th copy of G_2 and i-...A subdivision vertex-edge corona G_1~S?(∪ G_3~E) is a graph that consists of S(G_1),|V(G_1)| copies of G_2 and |I(G_1)| copies of G_3 by joining the i-th vertex in V(G_1) to each vertex in the i-th copy of G_2 and i-th vertex of I(G_1) to each vertex in the i-th copy of G_3.In this paper, we determine the normalized Laplacian spectrum of G_1~S?(G_2~V∪ G_3~E) in terms of the corresponding normalized Laplacian spectra of three connected regular graphs G_1, G_2 and G_3. As applications, we construct some non-regular normalized Laplacian cospectral graphs. In addition, we also give the multiplicative degree-Kirchhoff index, the Kemeny's constant and the number of the spanning trees of G_1~S?(G_2~V∪ G_3~E) on three regular graphs.展开更多
The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable coefficients.The Computer-Aided Design(CAD)geometries are built b...The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable coefficients.The Computer-Aided Design(CAD)geometries are built by subdivision surfaces,and meantime the basis functions of subdivision surfaces are employed to discretize the boundary integral equations for heat conduction analysis.Moreover,the radial integration method is adopted to transform the additional domain integrals caused by variable coefficients to the boundary integrals.Several numerical examples are provided to demonstrate the correctness and advantages of the proposed algorithm in the integration of CAD and numerical analysis.展开更多
Arbitrary topological curve network has no restriction in topology structure,so it has more powerful representing ability in defining complex surfaces.A complex surface modeling system is presented based on arbitrary ...Arbitrary topological curve network has no restriction in topology structure,so it has more powerful representing ability in defining complex surfaces.A complex surface modeling system is presented based on arbitrary topological curve network and the improved combined subdivision method,its functions including creating and editing curve network,and generating and modifying curve network＇s interpolated surface.This modeling system can be used to the process of products＇concept design,and its applications is also significant to the development of subdivision method.展开更多
In this article, the objective is to introduce an algorithm to produce the quaternary m-point (for any integer m>1) approximating subdivision schemes, which have smaller support and higher smoothness, comparing to ...In this article, the objective is to introduce an algorithm to produce the quaternary m-point (for any integer m>1) approximating subdivision schemes, which have smaller support and higher smoothness, comparing to binary and ternary schemes. The proposed algorithm has been derived from uniform B-spline basis function using the Cox-de Boor recursion formula. In order to determine the convergence and smoothness of the proposed schemes, the Laurent polynomial method has been used.展开更多
Design of watertight subdivision inherently involves its optimization with the objective to increase the index ＂A＂ above its minimum required value. In view of a big popularity of probabilistic search methods such a...Design of watertight subdivision inherently involves its optimization with the objective to increase the index ＂A＂ above its minimum required value. In view of a big popularity of probabilistic search methods such as genetic algorithms, this task is intrinsically time consuming. Thus, even when an optimal subdivision layout （i.e. topology） is determined, it can be found that the optimal bulkhead positions can be a great challenge time-wise, often forcing designers to satisfy with suboptimal solutions. The fundamental reason why this happens is that the nature of the optimized function （e.g., index ＂A＂ as a function of bulkhead positions） is unknown and hence it has no effect upon the choice of optimization strategy, which therefore reflects subjective but not factual preferences. In this paper we study the nature of functional dependency between the subdivision index and bulkhead positions, as a simplest case, and indicate pertinent optimization strategies that consequently reduce the optimization time. In our study we use a cruise ship model to demonstrate the application results of our findings.展开更多
In this paper, we propose and analyze a subdivision scheme which unifies 3-point approximating subdivision schemes of any arity in its compact form and has less support, computational cost and error bounds.? The usefu...In this paper, we propose and analyze a subdivision scheme which unifies 3-point approximating subdivision schemes of any arity in its compact form and has less support, computational cost and error bounds.? The usefulness of the scheme is illustrated by considering different examples along with its comparison with the established subdivision schemes. Moreover, B-splines of degree 4and well known 3-point schemes [1, 2, 3, 4, 6, 11, 12, 14, 15] are special cases of our proposed scheme.展开更多
The Holocene is probably the most intensively studied series/epoch within the geological record,and embodies a wide array of geomorphological,climatic,biotic and archaeological evidence;yet little attention has hither...The Holocene is probably the most intensively studied series/epoch within the geological record,and embodies a wide array of geomorphological,climatic,biotic and archaeological evidence;yet little attention has hitherto been paid to a formal subdivision of this series/epoch.Here we report a tripartite division of the Holocene into the Greenlandian,Northgrippian and Meghalayan stages/ages and their corresponding Lower/Early,Middle,Upper/Late subseries/subepochs,each supported by a Global Boundary Stratotype Section and Point(GSSP).The GSSP for the lowermost stage,the Greenlandian,is that of the Holocene as previously defined in the NGRIP2 Greenland ice core,and dated at 11,700 yr b2k(before 2000 CE).The GSSP for the Northgrippian is in the NGRIP1 Greenland ice core,and dated at 8236 yr b2k,whereas that for the Meghalayan is located in a speleothem from Mawmluh Cave,Meghalaya,northeast India with a date of 4250 yr b2k.The proposal on which this subdivision is based was submitted by the Subcommission on Quaternary Stratigraphy,approved by the International Commission on Stratigraphy,and formally ratified by the Executive Committee of the International Union of Geological Sciences on 14th June 2018.展开更多
基金the support from the 2025 Henan Provincial Science and Technology Research Project,the Zhumadian 2023 Major Science and Technology Special Projectthe Postgraduate Education Reform and Quality Improvement Project of Henan Province.
文摘At present,noise reduction has become an urgent challenge across various fields.Whether in the context of household appliances in daily life or in the enhancement of stealth performance in military equipment,noise control technologies play a critical role.This study introduces a computational framework for simulating Helmholtz equationgoverned acoustic scattering using a boundary element method(BEM)integrated with Loop subdivision surfaces.By adopting the Loop subdivision scheme—a widely used computer-aided design(CAD)technique-the framework unifies geometric representation and physical field discretization,ensuring seamless compatibility with industrial CAD workflows.The core innovation lies in the novel integration of conditional generative adversarial networks(CGANs)into the subdivision surface BEM to assist and accelerate the numerical computation process.In this study,for the two cases examined,the results show that the CGAN-enhanced approach achieves substantial gains in computational efficiency without compromising accuracy.A hierarchical acceleration strategy is further proposed:the fast multipole method(FMM)first reduces baseline computational complexity,while CGAN-driven secondary acceleration and data augmentation enable real-time parameter exploration.Benchmark validations and practical engineering applications demonstrate the method’s robustness and scalability for large-scale structural-acoustic analysis.
文摘A novel method is produced to evaluate the energy of the Catmull-Clark subdivision surface including extraordinary points in the control mesh. A closed-form analytic formula for thin plate energy of the Catmull-Clark subdivision surface of arbitrary topology is derived through translating the Catmull-Clark subdivision surface into bi-cubic B-spline surface pieces. Using this method, both the membrane energy and the thin plate energy can be evaluated without requiring recursive subdivision. Therefore, it is more efficient and more accurate than the existing methods for calculating the energy of the Catmull-Clark subdivision surface with arbitrary topology. The example of surface fairing demonstrates that this method is efficient and successful for evaluating the energy of subdivision surfaces.
基金Supported by the High Technology Research and Development Progrmnn~ of China （No. 2003AA411310）, the National Natural Science Foundation of China （No. 60373070） and Microsoft Research Project 2005-1.
文摘In this paper we introduce a new reverse Loop subdivision method. In contrast to current wavelets based Loop subdivision scheme, our method applies the same rules to both regular and extraordinary vertices and reconstructs the sharp features easily. Furthermore, our method runs faster because it does not need analysis and synthesis procedural. Our main goal is the design of a reverse subdivision method that can reconstruct the coarser mesh from a finer subdivision surface with sharp features for multiresolution representation, The proposed method only needs a little memory storage and brings little error, and it is easy to implement.
基金supported by Natural Science Foundation of China (60973084)Fundamental Research Funds for the Central Universities (2012zz0063)
文摘This paper proposes a novel strategy based on fragment meshes of Shiue et al. for GPU rendering of compos- ite subdivision surfaces. Two enumeration systems are established to label the primitives of each fragment mesh. A sector-layer-index enumeration system is responsible for retrieving proximities for subdivision masks while a sec- tor-index enumeration system designates a 2D texture buffer in GPU. Recurring to the free conversion between them, our approach may get rid of lookup tables that are designed to record subdivision masks. In addition, relatively small composite subdivision masks make it easy to develop automatically retrieving techniques. Finally, as center vertices are often irregular, their computation is related to an average with alterable number of items. Considering that variable loop is not efficient in GPU, we evaluate the center vertex of each fragment mesh using the linear combination of its level 0, level 1 and limit positions instead of averaging schemes. Experiments demonstrate that our approach generally outper- forms that of Shiue et al. in FPS by a long way.
文摘Based on the butterfly subdivision scheme and the modified butterfly subdivision scheme, an improved butterfly subdivision scheme is proposed. The scheme uses a small stencil of six points to calculate new inserting vertex, 2n new vertices are inserted in the 2n triangle faces in each recursion, and the n old vertices are kept, special treatment is given to the boundary, achieving higher smoothness while using small stencils is realized. With the proposed scheme, the number of triangle faces increases only by a factor of 3 in each refinement step. Compared with the butterfly subdivision scheme and the modified butterfly subdivision scheme, the size of triangle faces changes more gradually, which allows one to have greater control over the resolution of a refined mesh.
基金supported by National Natural Science Foundation of China(Grant No. 51075198)Jiangsu Provincial Natural Science Foundation of China(Grant No. BK2010479)+1 种基金Jiangsu Provincial Project of 333 Talents Engineering of ChinaJiangsu Provincial Project of Six Talented Peak of China
文摘Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline（NURBS） for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system（DCS） and measurement coordinate system（MCS） for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization（QPSO） is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%-22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.
基金This study was supported by Projects under contract Nos DY105 China's 0cean-03-01-01 and DY105-03-01-07the National Natural Science Foundation of China under contract No.40506017the Youth Foundation of Marine High-tech Project of China under contract No.2002AA616010.
文摘On the basis of three geological models and several orebody boundaries, a method of grid subdivision and integral has been proposed to calculate and evaluate the resources of cobalt-rich crusts on the seamounts in the central Pacific Ocean. The formulas of this method are deduced and the interface of program module is designed. The method is carried out in the software ＂Auto mapping system of submarine topography and geomorphology MBChart＂. This method and program will possibly become a potential tool to calculate the resources of seamounts and determine the target diggings for China＇ s next Five-year Plan.
文摘By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved. The conclusion of the extreme value problem is thus further confirmed.
基金Supported by the Young Scholars Science Foundation of Lanzhou Jiaotong University(Grant Nos.20160142017004+3 种基金 2017021)the Education Foundation of Gansu Province(Grant No.2017A-021)the National Natural Science Foundation of China(Grant Nos.11461038 61163010)
文摘A subdivision vertex-edge corona G_1~S?(∪ G_3~E) is a graph that consists of S(G_1),|V(G_1)| copies of G_2 and |I(G_1)| copies of G_3 by joining the i-th vertex in V(G_1) to each vertex in the i-th copy of G_2 and i-th vertex of I(G_1) to each vertex in the i-th copy of G_3.In this paper, we determine the normalized Laplacian spectrum of G_1~S?(G_2~V∪ G_3~E) in terms of the corresponding normalized Laplacian spectra of three connected regular graphs G_1, G_2 and G_3. As applications, we construct some non-regular normalized Laplacian cospectral graphs. In addition, we also give the multiplicative degree-Kirchhoff index, the Kemeny's constant and the number of the spanning trees of G_1~S?(G_2~V∪ G_3~E) on three regular graphs.
文摘The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable coefficients.The Computer-Aided Design(CAD)geometries are built by subdivision surfaces,and meantime the basis functions of subdivision surfaces are employed to discretize the boundary integral equations for heat conduction analysis.Moreover,the radial integration method is adopted to transform the additional domain integrals caused by variable coefficients to the boundary integrals.Several numerical examples are provided to demonstrate the correctness and advantages of the proposed algorithm in the integration of CAD and numerical analysis.
基金Project supported by the Fundamental Research Foundations for the Central Universities (Grant No.2009B30514)
文摘Arbitrary topological curve network has no restriction in topology structure,so it has more powerful representing ability in defining complex surfaces.A complex surface modeling system is presented based on arbitrary topological curve network and the improved combined subdivision method,its functions including creating and editing curve network,and generating and modifying curve network＇s interpolated surface.This modeling system can be used to the process of products＇concept design,and its applications is also significant to the development of subdivision method.
文摘In this article, the objective is to introduce an algorithm to produce the quaternary m-point (for any integer m>1) approximating subdivision schemes, which have smaller support and higher smoothness, comparing to binary and ternary schemes. The proposed algorithm has been derived from uniform B-spline basis function using the Cox-de Boor recursion formula. In order to determine the convergence and smoothness of the proposed schemes, the Laurent polynomial method has been used.
文摘Design of watertight subdivision inherently involves its optimization with the objective to increase the index ＂A＂ above its minimum required value. In view of a big popularity of probabilistic search methods such as genetic algorithms, this task is intrinsically time consuming. Thus, even when an optimal subdivision layout （i.e. topology） is determined, it can be found that the optimal bulkhead positions can be a great challenge time-wise, often forcing designers to satisfy with suboptimal solutions. The fundamental reason why this happens is that the nature of the optimized function （e.g., index ＂A＂ as a function of bulkhead positions） is unknown and hence it has no effect upon the choice of optimization strategy, which therefore reflects subjective but not factual preferences. In this paper we study the nature of functional dependency between the subdivision index and bulkhead positions, as a simplest case, and indicate pertinent optimization strategies that consequently reduce the optimization time. In our study we use a cruise ship model to demonstrate the application results of our findings.
文摘In this paper, we propose and analyze a subdivision scheme which unifies 3-point approximating subdivision schemes of any arity in its compact form and has less support, computational cost and error bounds.? The usefulness of the scheme is illustrated by considering different examples along with its comparison with the established subdivision schemes. Moreover, B-splines of degree 4and well known 3-point schemes [1, 2, 3, 4, 6, 11, 12, 14, 15] are special cases of our proposed scheme.
文摘The Holocene is probably the most intensively studied series/epoch within the geological record,and embodies a wide array of geomorphological,climatic,biotic and archaeological evidence;yet little attention has hitherto been paid to a formal subdivision of this series/epoch.Here we report a tripartite division of the Holocene into the Greenlandian,Northgrippian and Meghalayan stages/ages and their corresponding Lower/Early,Middle,Upper/Late subseries/subepochs,each supported by a Global Boundary Stratotype Section and Point(GSSP).The GSSP for the lowermost stage,the Greenlandian,is that of the Holocene as previously defined in the NGRIP2 Greenland ice core,and dated at 11,700 yr b2k(before 2000 CE).The GSSP for the Northgrippian is in the NGRIP1 Greenland ice core,and dated at 8236 yr b2k,whereas that for the Meghalayan is located in a speleothem from Mawmluh Cave,Meghalaya,northeast India with a date of 4250 yr b2k.The proposal on which this subdivision is based was submitted by the Subcommission on Quaternary Stratigraphy,approved by the International Commission on Stratigraphy,and formally ratified by the Executive Committee of the International Union of Geological Sciences on 14th June 2018.
