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 gets the Beltrami equations satisfied by a 1-quasiconformal mapping, which are exactly CR or anti-CR equations on （2,2）-type quadric Q0. This means a 1-quasiconformal mapping on Q0 is CR or anti-CR. This ...This paper gets the Beltrami equations satisfied by a 1-quasiconformal mapping, which are exactly CR or anti-CR equations on （2,2）-type quadric Q0. This means a 1-quasiconformal mapping on Q0 is CR or anti-CR. This reduces the determination of 1- quasiconformal mappings to a problem on the theory of several complex analysis. The result about the group of CR automorphisms is used to determine the unit component of group of 1-quasiconformal mappings.展开更多
Let Fq be a finite field with q elements, where q is a power of an odd prime,In this paperl the authors consider a projective space PG(2v + δ + l, Fq) with dimension 2v + δ + l, partitioned into an affine space AG(2...Let Fq be a finite field with q elements, where q is a power of an odd prime,In this paperl the authors consider a projective space PG(2v + δ + l, Fq) with dimension 2v + δ + l, partitioned into an affine space AG(2v + δ + l, Fq) of dimension 2v + δ + l and a hyperplane H = PG(2v + δ + l - 1, Fq) of dimension 2v + δ + l - 1 at infinity, where l ≠0.The points of the hyperplane H are next partitioned into four subsets. A pair of points a and b of the affine space is defined to belong to class i if the line ab meets the subsct i of H. Finally, a family of four-class association schemes are constructed, and parameters are also computed.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
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
By using nondegenerate and degenerate quadrics in projective space over finite fields of characteristic 2, some association schemes were constructed and their parameters were computed by the authors (see Adv. in Math....By using nondegenerate and degenerate quadrics in projective space over finite fields of characteristic 2, some association schemes were constructed and their parameters were computed by the authors (see Adv. in Math., 3(2000), 120-128 and Acta Math. Appl. Sinica, 1(1999), 96-103). In this note, their polynomial properties, eigenmatrices, imprimitivities, association subschemes and related quotient association schemes are studied.展开更多
The conventional Continuously Variable Transmission （CVT） has been classified as belt-type or toroidal CVTs. Each CVT is fundamentally composed of several components to transmit the frictional force or torque genera...The conventional Continuously Variable Transmission （CVT） has been classified as belt-type or toroidal CVTs. Each CVT is fundamentally composed of several components to transmit the frictional force or torque generated by the driving force. Since the conventional CVTs use friction force, their energy （force or torque） transfer efficiency might be inferior due to slippage and pressure between the transmission components. Consequently, we propose a new type of structural CVT. The CVT we proposed in this paper means a combined-type transmission with quadric crank chains and one-way clutches.展开更多
This paper describes the CVT （continuously variable transmission）. Generally, CVTs are classified as belt-type or toroidal CVTs, and each CVT is basically composed of two parts such as the V-belt and pulley, or fric...This paper describes the CVT （continuously variable transmission）. Generally, CVTs are classified as belt-type or toroidal CVTs, and each CVT is basically composed of two parts such as the V-belt and pulley, or friction wheels. In the belt-type CVT, the pulley is driven by a belt placed between two （left and right） circle boards, while in the toroidal CVT, two rollers rotate under the condition being pushed by strong compression power. Since these conventional CVTs use friction force, their energy transfer efficiency might be inferior. Furthermore, although these CVTs require precise structures and processing, they make noise, and are not durable. Consequently, we propose a new structural CVT in this paper.展开更多
By using the notion of Fischer–Marsden equation on real hypersurfaces in the complex hyperbolic quadric Q^(m∗)=SO^(o)_(2,m)/SO_(2)SO_(m),we can assert that there does not exist a non-trivial solution(g,ν)of Fischer...By using the notion of Fischer–Marsden equation on real hypersurfaces in the complex hyperbolic quadric Q^(m∗)=SO^(o)_(2,m)/SO_(2)SO_(m),we can assert that there does not exist a non-trivial solution(g,ν)of Fischer–Marsden equation on real hypersurfaces with isometric Reeb flow in the complex hyperbolic quadric Q^(m∗).Next,as an application we also show that there does not exist a non-trivial solution(g,ν)of the Fischer–Marsden equation on contact real hypersurfaces in the complex hyperbolic quadric Q^(m∗).Consequently,the Fischer–Marsden conjecture is true on these two kinds of real hypersurfaces in the complex hyperbolic quadric Q^(m∗).展开更多
In this letter we assume that F_q is a finite field with q elements, where q is a power of 2. Let N={x^2+x|x∈F_q} and choose a fixed element α of F_q not belonging to N. Theorem 1. Under affine transformations any q...In this letter we assume that F_q is a finite field with q elements, where q is a power of 2. Let N={x^2+x|x∈F_q} and choose a fixed element α of F_q not belonging to N. Theorem 1. Under affine transformations any quadric in AG(n, F_q), where q is even, can be carried into a quadric with one of the following quadratic equations as its equation:展开更多
The problem of a hollow thick-wall cylinder subject to quadric function pressures is solved with a new stress function, thus laying the basis for solving the spatial symmetric deformation of a hollow cylinder subject ...The problem of a hollow thick-wall cylinder subject to quadric function pressures is solved with a new stress function, thus laying the basis for solving the spatial symmetric deformation of a hollow cylinder subject to arbitrarily distributed pressures.展开更多
Modern computer graphics applications usually require high resolution object models for realistic rendering. However, it is expensive and difficult to deform such models in real time. In order to reduce the computatio...Modern computer graphics applications usually require high resolution object models for realistic rendering. However, it is expensive and difficult to deform such models in real time. In order to reduce the computational cost during deformations, a dense model is often manipulated through a simplified structure, called cage, which envelops the model. However, cages are usually built interactively by users, which is tedious and time-consuming. In this paper, we introduce a novel method that can build cages automatically for both 2D polygons and 3D triangular meshes. The method consists of two steps： 1） simplifying the input model with quadric error metrics and quadratic programming to build a coarse cage; 2） removing the self-intersections of the coarse cage with Delaunay partitions. With this new method, a user can build a cage to envelop an input model either entirely or partially with the approximate vertex number the user specifies. Experimental results show that, compared to other cage building methods with the same number of vertex, cages built by our method are more similar to the input models. Thus, the dense models can be manipulated with higher accuracy through our cages.展开更多
We introduce the notion of commuting Ricci tensor for real hypersurfaces in the complex quadric Qm = SOm＋2/SOmSO2. It is shown that the commuting Ricci tensor gives that the unit normal vector field N becomes -princ...We introduce the notion of commuting Ricci tensor for real hypersurfaces in the complex quadric Qm = SOm＋2/SOmSO2. It is shown that the commuting Ricci tensor gives that the unit normal vector field N becomes -principal or -isotropic. Then according to each case, we give a complete classification of Hopf real hypersurfaces in Qm = SOm＋2/SOmSO2 with commuting Ricci tensor.展开更多
This paper proposes an improved algorithm to construct moving quadrics from moving planes that follow a tensor product surface with no base points, assuming that there are no moving planes of low degree following the ...This paper proposes an improved algorithm to construct moving quadrics from moving planes that follow a tensor product surface with no base points, assuming that there are no moving planes of low degree following the surface. These moving quadrics provide an efficient method to implicitize the tensor product surface which outperforms a previous approach by the present authors.展开更多
Let S be a complete intersection of a smooth quadric 3-fold Q and a hypersurface of degree d in P4.We analyze GIT stability of S with respect to the natural G=SO(5,C)-action.We prove that if d 4 and S has at worst sem...Let S be a complete intersection of a smooth quadric 3-fold Q and a hypersurface of degree d in P4.We analyze GIT stability of S with respect to the natural G=SO(5,C)-action.We prove that if d 4 and S has at worst semi-log canonical singularities then S is G-stable.Also,we prove that if d 3 and S has at worst semi-log canonical singularities then S is G-semistable.展开更多
A Clifford deformation of a Koszul Frobenius algebra E is a finite dimensional Z_(2)-graded algebra E(θ),which corresponds to a noncommutative quadric hypersurface E^(!)/(z)for some central regular element z∈E_(2)^(...A Clifford deformation of a Koszul Frobenius algebra E is a finite dimensional Z_(2)-graded algebra E(θ),which corresponds to a noncommutative quadric hypersurface E^(!)/(z)for some central regular element z∈E_(2)^(!).It turns out that the bounded derived category D^(b)(gr_(Z_(2))E(θ))is equivalent to the stable category of the maximal Cohen-Macaulay modules over E^(!)/(z)provided that E!is noetherian.As a consequence,E^(!)/(z)is a noncommutative isolated singularity if and only if the corresponding Clifford deformation E(θ)is a semisimple Z_(2)-graded algebra.The preceding equivalence of triangulated categories also indicates that Clifford deformations of trivial extensions of a Koszul Frobenius algebra are related to Knörrer's periodicity theorem for quadric hypersurfaces.As an application,we recover Knörrer's periodicity theorem without using matrix factorizations.展开更多
Nested multilayer mirrors are commonly used in X ray telescope structure to increase the collecting area. To balance the difficulty and cost of producing these mirrors, Wolter-I structures are replaced with conical Wo...Nested multilayer mirrors are commonly used in X ray telescope structure to increase the collecting area. To balance the difficulty and cost of producing these mirrors, Wolter-I structures are replaced with conical Wolter-I structures, but these can lead to significantly poorer angular resolutions. In this Letter, we consider changing one of the mirror shapes（paraboloid or hyperboloid） of a Wolter-I structure to a conical mirror shape, while the other mirror shape remains a quadric surface-type structure, which can thus ensure the imaging quality. The cone-hyperboloid structure is nested to obtain on-axis angular resolution and off-axis images.展开更多
To this day for special m and small |c|, solvable, c are obtained about general equations x^2-my^2=c with positive squarefree integer m and integer c by Ankeny, Mollin et al. Afterwards, Zhang in ref. [1] greatly deve...To this day for special m and small |c|, solvable, c are obtained about general equations x^2-my^2=c with positive squarefree integer m and integer c by Ankeny, Mollin et al. Afterwards, Zhang in ref. [1] greatly developed their correspondent results and gave all proper integer solutions and solvable c about the equations for general m. Then Lu in ref. [2] gave results for small |q| about general binary quadric indefinite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 (10571155)
文摘This paper gets the Beltrami equations satisfied by a 1-quasiconformal mapping, which are exactly CR or anti-CR equations on （2,2）-type quadric Q0. This means a 1-quasiconformal mapping on Q0 is CR or anti-CR. This reduces the determination of 1- quasiconformal mappings to a problem on the theory of several complex analysis. The result about the group of CR automorphisms is used to determine the unit component of group of 1-quasiconformal mappings.
文摘Let Fq be a finite field with q elements, where q is a power of an odd prime,In this paperl the authors consider a projective space PG(2v + δ + l, Fq) with dimension 2v + δ + l, partitioned into an affine space AG(2v + δ + l, Fq) of dimension 2v + δ + l and a hyperplane H = PG(2v + δ + l - 1, Fq) of dimension 2v + δ + l - 1 at infinity, where l ≠0.The points of the hyperplane H are next partitioned into four subsets. A pair of points a and b of the affine space is defined to belong to class i if the line ab meets the subsct i of H. Finally, a family of four-class association schemes are constructed, and parameters are also computed.
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.
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The NNSF (19571024) of China Hebei Province Education Committee Fund (98103).
文摘By using nondegenerate and degenerate quadrics in projective space over finite fields of characteristic 2, some association schemes were constructed and their parameters were computed by the authors (see Adv. in Math., 3(2000), 120-128 and Acta Math. Appl. Sinica, 1(1999), 96-103). In this note, their polynomial properties, eigenmatrices, imprimitivities, association subschemes and related quotient association schemes are studied.
文摘The conventional Continuously Variable Transmission （CVT） has been classified as belt-type or toroidal CVTs. Each CVT is fundamentally composed of several components to transmit the frictional force or torque generated by the driving force. Since the conventional CVTs use friction force, their energy （force or torque） transfer efficiency might be inferior due to slippage and pressure between the transmission components. Consequently, we propose a new type of structural CVT. The CVT we proposed in this paper means a combined-type transmission with quadric crank chains and one-way clutches.
文摘This paper describes the CVT （continuously variable transmission）. Generally, CVTs are classified as belt-type or toroidal CVTs, and each CVT is basically composed of two parts such as the V-belt and pulley, or friction wheels. In the belt-type CVT, the pulley is driven by a belt placed between two （left and right） circle boards, while in the toroidal CVT, two rollers rotate under the condition being pushed by strong compression power. Since these conventional CVTs use friction force, their energy transfer efficiency might be inferior. Furthermore, although these CVTs require precise structures and processing, they make noise, and are not durable. Consequently, we propose a new structural CVT in this paper.
基金supported by Grants Proj.No.NRF-2018-R1D1A1B-05040381&NRF-2021-R1C1C-2009847 from National Research Foundation of Korea.
文摘By using the notion of Fischer–Marsden equation on real hypersurfaces in the complex hyperbolic quadric Q^(m∗)=SO^(o)_(2,m)/SO_(2)SO_(m),we can assert that there does not exist a non-trivial solution(g,ν)of Fischer–Marsden equation on real hypersurfaces with isometric Reeb flow in the complex hyperbolic quadric Q^(m∗).Next,as an application we also show that there does not exist a non-trivial solution(g,ν)of the Fischer–Marsden equation on contact real hypersurfaces in the complex hyperbolic quadric Q^(m∗).Consequently,the Fischer–Marsden conjecture is true on these two kinds of real hypersurfaces in the complex hyperbolic quadric Q^(m∗).
文摘In this letter we assume that F_q is a finite field with q elements, where q is a power of 2. Let N={x^2+x|x∈F_q} and choose a fixed element α of F_q not belonging to N. Theorem 1. Under affine transformations any quadric in AG(n, F_q), where q is even, can be carried into a quadric with one of the following quadratic equations as its equation:
文摘The problem of a hollow thick-wall cylinder subject to quadric function pressures is solved with a new stress function, thus laying the basis for solving the spatial symmetric deformation of a hollow cylinder subject to arbitrarily distributed pressures.
基金Supported by the NSFC-Guangdong Joint Fund under Grant Nos. U0735001,U0835004,U0935004the National Basic Research 973 Program of China under Grant No. 2011CB302204
文摘Modern computer graphics applications usually require high resolution object models for realistic rendering. However, it is expensive and difficult to deform such models in real time. In order to reduce the computational cost during deformations, a dense model is often manipulated through a simplified structure, called cage, which envelops the model. However, cages are usually built interactively by users, which is tedious and time-consuming. In this paper, we introduce a novel method that can build cages automatically for both 2D polygons and 3D triangular meshes. The method consists of two steps： 1） simplifying the input model with quadric error metrics and quadratic programming to build a coarse cage; 2） removing the self-intersections of the coarse cage with Delaunay partitions. With this new method, a user can build a cage to envelop an input model either entirely or partially with the approximate vertex number the user specifies. Experimental results show that, compared to other cage building methods with the same number of vertex, cages built by our method are more similar to the input models. Thus, the dense models can be manipulated with higher accuracy through our cages.
基金supported by National Research Foundation of Korea (Grant No. NRF2015-R1A2A1A-01002459)
文摘We introduce the notion of commuting Ricci tensor for real hypersurfaces in the complex quadric Qm = SOm＋2/SOmSO2. It is shown that the commuting Ricci tensor gives that the unit normal vector field N becomes -principal or -isotropic. Then according to each case, we give a complete classification of Hopf real hypersurfaces in Qm = SOm＋2/SOmSO2 with commuting Ricci tensor.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271328and 11571338the Zhejiang Provincial Natural Science Foundation under Grant No.Y7080068
文摘This paper proposes an improved algorithm to construct moving quadrics from moving planes that follow a tensor product surface with no base points, assuming that there are no moving planes of low degree following the surface. These moving quadrics provide an efficient method to implicitize the tensor product surface which outperforms a previous approach by the present authors.
基金supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Korea government(MSIP)(Grant No.2013006431)the National Research Foundation of Korea funded by the Korea government(MSIP)(Grant No.2013042157)
文摘Let S be a complete intersection of a smooth quadric 3-fold Q and a hypersurface of degree d in P4.We analyze GIT stability of S with respect to the natural G=SO(5,C)-action.We prove that if d 4 and S has at worst semi-log canonical singularities then S is G-stable.Also,we prove that if d 3 and S has at worst semi-log canonical singularities then S is G-semistable.
基金supported by ZJNSF(LY19A010011)NSFC(11971141,12371017)supported by NSFC(11971449,12131015,12371042).
文摘A Clifford deformation of a Koszul Frobenius algebra E is a finite dimensional Z_(2)-graded algebra E(θ),which corresponds to a noncommutative quadric hypersurface E^(!)/(z)for some central regular element z∈E_(2)^(!).It turns out that the bounded derived category D^(b)(gr_(Z_(2))E(θ))is equivalent to the stable category of the maximal Cohen-Macaulay modules over E^(!)/(z)provided that E!is noetherian.As a consequence,E^(!)/(z)is a noncommutative isolated singularity if and only if the corresponding Clifford deformation E(θ)is a semisimple Z_(2)-graded algebra.The preceding equivalence of triangulated categories also indicates that Clifford deformations of trivial extensions of a Koszul Frobenius algebra are related to Knörrer's periodicity theorem for quadric hypersurfaces.As an application,we recover Knörrer's periodicity theorem without using matrix factorizations.
基金supported by the National Science Instrument and Equipment Development Major Project of Ministry of Science and Technology of China(Nos.2012YQ24026402 and 2012YQ04016403)the Youth Science Fund Project of the National Natural Science Fund of China(No.11505129)
文摘Nested multilayer mirrors are commonly used in X ray telescope structure to increase the collecting area. To balance the difficulty and cost of producing these mirrors, Wolter-I structures are replaced with conical Wolter-I structures, but these can lead to significantly poorer angular resolutions. In this Letter, we consider changing one of the mirror shapes（paraboloid or hyperboloid） of a Wolter-I structure to a conical mirror shape, while the other mirror shape remains a quadric surface-type structure, which can thus ensure the imaging quality. The cone-hyperboloid structure is nested to obtain on-axis angular resolution and off-axis images.
文摘To this day for special m and small |c|, solvable, c are obtained about general equations x^2-my^2=c with positive squarefree integer m and integer c by Ankeny, Mollin et al. Afterwards, Zhang in ref. [1] greatly developed their correspondent results and gave all proper integer solutions and solvable c about the equations for general m. Then Lu in ref. [2] gave results for small |q| about general binary quadric indefinite
