为了保护易受到侵蚀与损坏的浮雕文物,运用单幅图像的三维重建技术生成三维浮雕模型,即利用SFS(Shape From Shading)方法估计浮雕模型的深度矩阵,再通过滤波变换和模型叠加对矩阵进行修复。大多数浮雕的载体表面是不规则的曲面,需要将...为了保护易受到侵蚀与损坏的浮雕文物,运用单幅图像的三维重建技术生成三维浮雕模型,即利用SFS(Shape From Shading)方法估计浮雕模型的深度矩阵,再通过滤波变换和模型叠加对矩阵进行修复。大多数浮雕的载体表面是不规则的曲面,需要将估计得到的深度矩阵映射到曲面载体模型上。将载体模型放到黎曼几何空间中,通过指数映射将指定位置、大小的局部区域参数化。进而通过纹理映射原理,改变相应顶点坐标,实现三维模型变化。设计实现了生成浮雕文物的半自动化方法,对不同模型的复原适应性良好。展开更多
Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M...Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M , a sufficient condition is given for M as a flat torus in R 4 .展开更多
Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all perio...Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all periodical maps on Σ2. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair(S3, Σg). To do this the authors first list all periodic maps on Σ2, and indeed the authors exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself should be interesting. A by-product is that for each even g,the maximum order periodic map on Σg is extendable, which contrasts sharply with the situation in the orientation preserving category.展开更多
Let S be a Riemann surface with genus p and n punctures. Assume that 3p- 3 ＋ n 〉 0 and n 〉 1. Let a be a puncture of S and let S = S∪{α}. Then all mapping classes in the mapping class group Mods that fixes the pu...Let S be a Riemann surface with genus p and n punctures. Assume that 3p- 3 ＋ n 〉 0 and n 〉 1. Let a be a puncture of S and let S = S∪{α}. Then all mapping classes in the mapping class group Mods that fixes the puncture a can be projected to mapping classes of Mod$ under the forgetful map. In this paper the author studies the mapping classes in Mods that can be projected to a given hyperbolic mapping class in Mode.展开更多
Inequalities of Korn's type on a surface with boundary have been proved in many papersusing different techniques (see e.g. [4, 5, 11]). The author proves here an inequality of Korn'stype on a compact surface w...Inequalities of Korn's type on a surface with boundary have been proved in many papersusing different techniques (see e.g. [4, 5, 11]). The author proves here an inequality of Korn'stype on a compact surface without boundary. The idea is to use a finite number of maps fordefining the surface and the inequality of Korn's type without boundary conditions for everymap and to recast these in a general functional analysis setting about quotient spaces.展开更多
A novel approach of iso-scallop trajectory generation for smooth manifold surfaces has been developed. Firstly,by defining homeomorphism mapping relations and differentiable structures,the smooth manifold surface is m...A novel approach of iso-scallop trajectory generation for smooth manifold surfaces has been developed. Firstly,by defining homeomorphism mapping relations and differentiable structures,the smooth manifold surface is mapped into several Euclidean planes,thus its trajectory generation can be decomposed into planar curve-filling tasks. Secondly,in the generation of direction-parallel trajectories,the calculation of the cutting interval and the curvature is given,depending on the generation of the first curve in the projection view. Thirdly,after automatic adherences of inverse projection curves,the filled curves are mapped into the original surface inversely to form trajectories. Although the required trajectories are iso-scallop,the trajectory intervals are variable according to the curvature changes at the projection point,which is advantageous to improving the trajectory quality. The proposed approach has appealing merits of dimensionality reduction,which decreases the algorithm complexity. Finally,numerical and machining examples are given to illustrate its feasibility and validity.展开更多
Let S be a Riemann surface that contains one puncture x. Let be the collection of simple closed geodesics on S, and let denote the set of mapping classes on S isotopic to the identity on S U {x}. Denote by tc the ...Let S be a Riemann surface that contains one puncture x. Let be the collection of simple closed geodesics on S, and let denote the set of mapping classes on S isotopic to the identity on S U {x}. Denote by tc the positive Dehn twist about a curve c ∈ . In this paper, the author studies the products of forms （tb^-m o t^na） o f^k, where a, b ∈ and f ∈ . It is easy to see that if a = b or a, b are boundary components of an x-punctured cylinder on S, then one may find an element f ∈ such that the sequence （tb^-m o t^na） ofk contains infinitely many powers of Dehn twists. The author shows that the converse statement remains true, that is, if the sequence （tb^-m o t^na） o f^k contains infinitely many powers of Dehn twists, then a, b must be the boundary components of an x-punctured cylinder on S and f is a power of the spin map tb^-1 o ta.展开更多
文摘为了保护易受到侵蚀与损坏的浮雕文物,运用单幅图像的三维重建技术生成三维浮雕模型,即利用SFS(Shape From Shading)方法估计浮雕模型的深度矩阵,再通过滤波变换和模型叠加对矩阵进行修复。大多数浮雕的载体表面是不规则的曲面,需要将估计得到的深度矩阵映射到曲面载体模型上。将载体模型放到黎曼几何空间中,通过指数映射将指定位置、大小的局部区域参数化。进而通过纹理映射原理,改变相应顶点坐标,实现三维模型变化。设计实现了生成浮雕文物的半自动化方法,对不同模型的复原适应性良好。
文摘Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M , a sufficient condition is given for M as a flat torus in R 4 .
基金supported by the National Natural Science Foundation of China(No.10631060)
文摘Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all periodical maps on Σ2. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair(S3, Σg). To do this the authors first list all periodic maps on Σ2, and indeed the authors exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself should be interesting. A by-product is that for each even g,the maximum order periodic map on Σg is extendable, which contrasts sharply with the situation in the orientation preserving category.
文摘Let S be a Riemann surface with genus p and n punctures. Assume that 3p- 3 ＋ n 〉 0 and n 〉 1. Let a be a puncture of S and let S = S∪{α}. Then all mapping classes in the mapping class group Mods that fixes the puncture a can be projected to mapping classes of Mod$ under the forgetful map. In this paper the author studies the mapping classes in Mods that can be projected to a given hyperbolic mapping class in Mode.
文摘Inequalities of Korn's type on a surface with boundary have been proved in many papersusing different techniques (see e.g. [4, 5, 11]). The author proves here an inequality of Korn'stype on a compact surface without boundary. The idea is to use a finite number of maps fordefining the surface and the inequality of Korn's type without boundary conditions for everymap and to recast these in a general functional analysis setting about quotient spaces.
基金supported by the National Natural Science Foundation of China (Grant Nos.50835004,50905131)the Natural Science Foundation of Hubei Province (Grant No.2009CDB251)
文摘A novel approach of iso-scallop trajectory generation for smooth manifold surfaces has been developed. Firstly,by defining homeomorphism mapping relations and differentiable structures,the smooth manifold surface is mapped into several Euclidean planes,thus its trajectory generation can be decomposed into planar curve-filling tasks. Secondly,in the generation of direction-parallel trajectories,the calculation of the cutting interval and the curvature is given,depending on the generation of the first curve in the projection view. Thirdly,after automatic adherences of inverse projection curves,the filled curves are mapped into the original surface inversely to form trajectories. Although the required trajectories are iso-scallop,the trajectory intervals are variable according to the curvature changes at the projection point,which is advantageous to improving the trajectory quality. The proposed approach has appealing merits of dimensionality reduction,which decreases the algorithm complexity. Finally,numerical and machining examples are given to illustrate its feasibility and validity.
文摘Let S be a Riemann surface that contains one puncture x. Let be the collection of simple closed geodesics on S, and let denote the set of mapping classes on S isotopic to the identity on S U {x}. Denote by tc the positive Dehn twist about a curve c ∈ . In this paper, the author studies the products of forms （tb^-m o t^na） o f^k, where a, b ∈ and f ∈ . It is easy to see that if a = b or a, b are boundary components of an x-punctured cylinder on S, then one may find an element f ∈ such that the sequence （tb^-m o t^na） ofk contains infinitely many powers of Dehn twists. The author shows that the converse statement remains true, that is, if the sequence （tb^-m o t^na） o f^k contains infinitely many powers of Dehn twists, then a, b must be the boundary components of an x-punctured cylinder on S and f is a power of the spin map tb^-1 o ta.
