The skewed symmetry detection plays an improtant role in three-dimensional（3-D） reconstruction. The skewed symmetry depicts a real symmetry viewed from some unknown viewing directions. And the skewed symmetry detect...The skewed symmetry detection plays an improtant role in three-dimensional（3-D） reconstruction. The skewed symmetry depicts a real symmetry viewed from some unknown viewing directions. And the skewed symmetry detection can decrease the geometric constrains and the complexity of 3-D reconstruction. The detection technique for the quadric curve ellipse proposed by Sugimoto is improved to further cover quadric curves including hyperbola and parabola. With the parametric detection, the 3-D quadric curve projection matching is automatical- ly accomplished. Finally, the skewed symmetry surface of the quadric surface solid is obtained. Several examples are used to verify the feasibility of the algorithm and satisfying results can be obtained.展开更多
This paper presents a novel algorithm for identifying quadric surfaces from scanned mechanical models. We make several important improvements over the existing variational 3D shape segmentation framework, which utiliz...This paper presents a novel algorithm for identifying quadric surfaces from scanned mechanical models. We make several important improvements over the existing variational 3D shape segmentation framework, which utilizes Lloyd＇s iteration. First, instead of using randomized initialization （which likely falls into non-optimal minimum）, the RANSAC-based initialization approach is adopted. Given a good initialization, our method converges quickly than previous approaches. Second, in order to enhance the stability and the robustness, we carefully modify the distortion-minimizing flooding algorithm by using seed regions instead of seed triangles. Third, the geometric constraints are introduced into the optimization framework. The segmentation quality is further improved. We validate the efficiency and the robustness of our proposed method on various datasets, and demonstrate that our method outperforms state-of-art approaches.展开更多
Intersecting is an important factor which influences the effociency androbustness of Boolean algorithms in solid modeling based on surved-surfaces,andintersecting algorithms are closely related to geometric representa...Intersecting is an important factor which influences the effociency androbustness of Boolean algorithms in solid modeling based on surved-surfaces,andintersecting algorithms are closely related to geometric representations of curved-surfaces.Although surfaces can be commonly represented with NURBS,unnecessary complexitiesare caused in the intersecting of quadric surfaces.Quadrics are frequently used to des-cribe geometric features of shafts,holes and grooves etc.in mechanical part designing,therefore;their intersection algorithms are required to have higher accuracy,higher efficiency and higher robustness.For this reason,a practical representation ofquadric surfaces is studied in detail,and on the basis of that,algorithms of intersectingpoints are developed between quadric suraces and their boundaies,i.e.,conics,quarticnonplanar space curves.展开更多
Quadrics are of basic importance in Computer Graphics and Computer Aided Design. In this paper,we design a subdivision scheme based on the method suggested by G. Morin and J. Warren to generate conics and quadrics con...Quadrics are of basic importance in Computer Graphics and Computer Aided Design. In this paper,we design a subdivision scheme based on the method suggested by G. Morin and J. Warren to generate conics and quadrics conveniently. Given the control polygon(poly-hedron),the corresponding ellipse (ellipsoid)can be generated. The hyperbolas and hyperboloids are generated based on the generation of ellipses and ellipsoids by a simple transformation. The method in this paper is much simpler and easier to apply than those given by Eugenia Montiel et al.展开更多
Surface/surface intersection is a fundamental problem in Compute Aided Design and Geometric Modeling since it is essential to solid modeling,numerically controlled machining,feature recognition,computer animation,etc....Surface/surface intersection is a fundamental problem in Compute Aided Design and Geometric Modeling since it is essential to solid modeling,numerically controlled machining,feature recognition,computer animation,etc.In practical applications,quadric surfaces,which are the most basic type of surfaces,are typically bounded surfaces trimmed by a sequence of planes.In this paper,a robust algorithm is proposed for computing the intersection curve segments of two trimmed quadrics based on the parametric representation of the intersection curves of two quadrics.The proposed algorithm guarantees correct topology and ensures that the approximation errors of the end points of the intersection curve segments are less than a given tolerance.The error control is based on an effective solution to a set of polynomial inequality system using the root isolation technique.Some examples are presented to validate the robustness and effectiveness of the proposed algorithm.展开更多
A method for representing quadric surfaces using NURBS is presented. By means of the necessary and sufficient conditions for NURBS cu-rves to precisely represent circular arcs and other conics, quadric surfaces can be...A method for representing quadric surfaces using NURBS is presented. By means of the necessary and sufficient conditions for NURBS cu-rves to precisely represent circular arcs and other conics, quadric surfaces can be represented by NURBS surfaces with fewer control vertices. The method can be used not only for NURBS surface representation of quadric surfaces, but also for rounding polyhedrons. Many examples are given in the paper.展开更多
We give the classification of globally generated vector bundles of rank 2 on a smooth quadric surface with c1(2,2)in terms of the indices of the bundles,and extend the result to arbitrary higher rank case.We also inve...We give the classification of globally generated vector bundles of rank 2 on a smooth quadric surface with c1(2,2)in terms of the indices of the bundles,and extend the result to arbitrary higher rank case.We also investigate their indecomposability and give the sufficient and necessary condition on numeric data of vector bundles for indecomposability.展开更多
基金Supported by the National Natural Science Foundation of China(10377007)~~
文摘The skewed symmetry detection plays an improtant role in three-dimensional（3-D） reconstruction. The skewed symmetry depicts a real symmetry viewed from some unknown viewing directions. And the skewed symmetry detection can decrease the geometric constrains and the complexity of 3-D reconstruction. The detection technique for the quadric curve ellipse proposed by Sugimoto is improved to further cover quadric curves including hyperbola and parabola. With the parametric detection, the 3-D quadric curve projection matching is automatical- ly accomplished. Finally, the skewed symmetry surface of the quadric surface solid is obtained. Several examples are used to verify the feasibility of the algorithm and satisfying results can be obtained.
基金Supported by the National Natural Science Foundation of China(61372168,61620106003 and 61331018)
文摘This paper presents a novel algorithm for identifying quadric surfaces from scanned mechanical models. We make several important improvements over the existing variational 3D shape segmentation framework, which utilizes Lloyd＇s iteration. First, instead of using randomized initialization （which likely falls into non-optimal minimum）, the RANSAC-based initialization approach is adopted. Given a good initialization, our method converges quickly than previous approaches. Second, in order to enhance the stability and the robustness, we carefully modify the distortion-minimizing flooding algorithm by using seed regions instead of seed triangles. Third, the geometric constraints are introduced into the optimization framework. The segmentation quality is further improved. We validate the efficiency and the robustness of our proposed method on various datasets, and demonstrate that our method outperforms state-of-art approaches.
文摘Intersecting is an important factor which influences the effociency androbustness of Boolean algorithms in solid modeling based on surved-surfaces,andintersecting algorithms are closely related to geometric representations of curved-surfaces.Although surfaces can be commonly represented with NURBS,unnecessary complexitiesare caused in the intersecting of quadric surfaces.Quadrics are frequently used to des-cribe geometric features of shafts,holes and grooves etc.in mechanical part designing,therefore;their intersection algorithms are required to have higher accuracy,higher efficiency and higher robustness.For this reason,a practical representation ofquadric surfaces is studied in detail,and on the basis of that,algorithms of intersectingpoints are developed between quadric suraces and their boundaies,i.e.,conics,quarticnonplanar space curves.
基金This work is supported by NKBRSF on Mathematical Mechanics(G1998030600),the National Natural Science Foundation of China(19971087,69603009)and the Doctoral Program(20010358003)and TRAPOYT of MOE,China.
文摘Quadrics are of basic importance in Computer Graphics and Computer Aided Design. In this paper,we design a subdivision scheme based on the method suggested by G. Morin and J. Warren to generate conics and quadrics conveniently. Given the control polygon(poly-hedron),the corresponding ellipse (ellipsoid)can be generated. The hyperbolas and hyperboloids are generated based on the generation of ellipses and ellipsoids by a simple transformation. The method in this paper is much simpler and easier to apply than those given by Eugenia Montiel et al.
基金supported in part by the National Natural Science Foundation of China under Grant No.61972368。
文摘Surface/surface intersection is a fundamental problem in Compute Aided Design and Geometric Modeling since it is essential to solid modeling,numerically controlled machining,feature recognition,computer animation,etc.In practical applications,quadric surfaces,which are the most basic type of surfaces,are typically bounded surfaces trimmed by a sequence of planes.In this paper,a robust algorithm is proposed for computing the intersection curve segments of two trimmed quadrics based on the parametric representation of the intersection curves of two quadrics.The proposed algorithm guarantees correct topology and ensures that the approximation errors of the end points of the intersection curve segments are less than a given tolerance.The error control is based on an effective solution to a set of polynomial inequality system using the root isolation technique.Some examples are presented to validate the robustness and effectiveness of the proposed algorithm.
文摘A method for representing quadric surfaces using NURBS is presented. By means of the necessary and sufficient conditions for NURBS cu-rves to precisely represent circular arcs and other conics, quadric surfaces can be represented by NURBS surfaces with fewer control vertices. The method can be used not only for NURBS surface representation of quadric surfaces, but also for rounding polyhedrons. Many examples are given in the paper.
基金supported by Ministero dell’Istruzione,dell’Universit`ae della Ricerca(Italy)and Gruppo Nazionale per le Strutture Algebrice,Geometriche e le loro Applicazioni of Istituto di Alta Matematica"F.Severi"(Italy),Basic Science Research Program through National Research Foundation of Korea funded by Ministry of Education and Science Technology(Grant No.2010-0009195)the framework of PRIN2010/11‘Geometria delle variet`a algebriche’,cofinanced by Ministero dell’Istruzione,dell’Universit`ae della Ricerca(Italy)
文摘We give the classification of globally generated vector bundles of rank 2 on a smooth quadric surface with c1(2,2)in terms of the indices of the bundles,and extend the result to arbitrary higher rank case.We also investigate their indecomposability and give the sufficient and necessary condition on numeric data of vector bundles for indecomposability.
