This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum p...This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum point,the boundary gradient estimation of the solutions to the equation is obtained.展开更多
A systematic scheme is proposed to automatically extract geometric surface features from a point cloud composed of a set of unorganized three-dimensional coordinate points by data segmentation. The key technology is a...A systematic scheme is proposed to automatically extract geometric surface features from a point cloud composed of a set of unorganized three-dimensional coordinate points by data segmentation. The key technology is a algorithm that estimates the local surface curvature properties of scattered point data based on local base surface parameterization. Eight surface types from the signs of the Gaussian and mean curvatures provide an initial segmentation, which will be refined by an iterative region growing method. Experimental results show the scheme's performance on two point clouds.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
In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If the...In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If then M^n lies in a totally geodesic submanifold N^(n+1).展开更多
In this paper, we consider a class of submanifolds with parallel mean curvacture vector fields. We obitain the suffitient conditions that the above submanifolds is of tatall umbilical and that its codimension is decre...In this paper, we consider a class of submanifolds with parallel mean curvacture vector fields. We obitain the suffitient conditions that the above submanifolds is of tatall umbilical and that its codimension is decrease.展开更多
Segmenting a complex 3D surface model into some visually meaningful sub-parts is one of the fundamental problems in digital geometry processing. In this paper, a novel segmentation approach of point-sampled surfaces i...Segmenting a complex 3D surface model into some visually meaningful sub-parts is one of the fundamental problems in digital geometry processing. In this paper, a novel segmentation approach of point-sampled surfaces is proposed, which is based on the level set evolution scheme. To segment the model so as to align the patch boundaries with high curvature zones, the driven speed function for the zero level set inside narrow band is defined by the extended curvature field, which approaches zero speed as the propagating front approaches high curvature zone. The effectiveness of the proposed approach is demonstrated by our ex- perimental results. Furthermore, two applications of model segmentation are illustrated, such as piecewise parameterization and local editing for point-sampled geometry.展开更多
The pinching of n-dimensional closed hypersurface Mwith constant mean curvature H in unit sphere S^(n+1)( 1) is considered. Let A = ∑i,j,k h(ijk)~2( λi+ nH)~2,B = ∑i,j,k h(ijk)~2( λi+ nH) ·( ...The pinching of n-dimensional closed hypersurface Mwith constant mean curvature H in unit sphere S^(n+1)( 1) is considered. Let A = ∑i,j,k h(ijk)~2( λi+ nH)~2,B = ∑i,j,k h(ijk)~2( λi+ nH) ·( λj+ nH),S = ∑i( λi+ nH)~2, where h(ij)= λiδ(ij). Utilizing Lagrange's method, a sharper pointwise estimation of 3(A- 2B) in terms of S and |▽h|~2 is obtained, here |▽h|~2= ∑i,j,k h(ijk)~2. Then, with the help of this, it is proved that Mis isometric to the Clifford hypersurface if the square norm of the second fundamental form of Msatisfies certain conditions. Hence, the pinching result of the minimal hypersurface is extended to the hypersurface with constant mean curvature case.展开更多
In this paper some properties of three-dimensional spaces of quasi-constant curvature different from those of cases when dimension n≥4 are proved. In particular, two classes of non-conformally flat solutions of them ...In this paper some properties of three-dimensional spaces of quasi-constant curvature different from those of cases when dimension n≥4 are proved. In particular, two classes of non-conformally flat solutions of them are constructed. In physics,a three-dimensional space of quasi-constant curvature appears as the space-like hypersurface of the rotation-free cosmological model of type D for the fluids with heat flow in General Relativity.展开更多
Existing curve fitting algorithms of NC machining path mainly focus on the control of fitting error,but ignore the problem that the original discrete cutter position points are not enough in the high curvature area of...Existing curve fitting algorithms of NC machining path mainly focus on the control of fitting error,but ignore the problem that the original discrete cutter position points are not enough in the high curvature area of the tool path.It may cause a sudden change in the drive force of the feed axis,resulting in a large fluctuation in the feed speed.This paper proposes a new non-uniform rational B-spline(NURBS)curve fitting optimization method based on curvature smoothing preset point constraints.First,the short line segments generated by the CAM software are optimally divided into different segment regions,and then the curvature of the short line segments in each region is adjusted to make it smoother.Secondly,a set of characteristic points reflecting the change of the curvature of the fitted curve is constructed as the control apex of the fitted curve,and the curve is fitted using the NURBS curve fitting optimization method based on the curvature smoothing preset point constraint.Finally,the curve fitting error and curve volatility are analyzed with an example,which verifies that the method can significantly improve the curvature smoothness of the high-curvature tool path,reduce the fitting error,and improve the feed speed.展开更多
The difference of sintering crunodes of metal powders and fibers is discussed. The mathematical model of the surface diffusion described by the difference in mean curvature is defined as a Hamilton-Jacobi-type equatio...The difference of sintering crunodes of metal powders and fibers is discussed. The mathematical model of the surface diffusion described by the difference in mean curvature is defined as a Hamilton-Jacobi-type equation, and the model is numerically solved by the level set method. The three-dimensional numerical simulations of two metal powders and fibers(the fiber angle is 0° or 90°) are implemented by this mathematical model, respectively. The numerical simulation results accord with the experimental ones. The sintering neck growth trends of metal powders and metal fibers are similar. The sintering neck radius of metal fibers is larger than that of metal powders. The difference of the neck radius is caused by the difference of geometric structure which makes an important influence on the curvature affecting the migration rate of atoms.展开更多
In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special (α, β)-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessa...In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special (α, β)-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessary condition that F is locally projectively fiat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively fiat. Moreover, we prove that such projectively fiat Finsler metrics with constant flag curvature must be locally Minkowskian.展开更多
In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by osing the relationship between the square of the length of the second fundamental f...In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by osing the relationship between the square of the length of the second fundamental form and the mean curvature. We obtained a best pinching interval and decided the complete classification of hypersurfaces at the terminal of the interval.This improved the relative results of M. Okumura,Shen Yibihg and Sun Ziqi,etc.展开更多
基金supported by the National Natural Science Foundation of China (No.12061078)。
文摘This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum point,the boundary gradient estimation of the solutions to the equation is obtained.
文摘A systematic scheme is proposed to automatically extract geometric surface features from a point cloud composed of a set of unorganized three-dimensional coordinate points by data segmentation. The key technology is a algorithm that estimates the local surface curvature properties of scattered point data based on local base surface parameterization. Eight surface types from the signs of the Gaussian and mean curvatures provide an initial segmentation, which will be refined by an iterative region growing method. Experimental results show the scheme's performance on two point clouds.
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 .
文摘In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If then M^n lies in a totally geodesic submanifold N^(n+1).
文摘In this paper, we consider a class of submanifolds with parallel mean curvacture vector fields. We obitain the suffitient conditions that the above submanifolds is of tatall umbilical and that its codimension is decrease.
基金Project supported by the National Basic Research Program (973) of China (No. 2002CB312101)the National Natural Science Foundation of China (Nos. 60503056, 60373036, 60333010)the Education Department of Zhejiang Province, China (No. 20060797)
文摘Segmenting a complex 3D surface model into some visually meaningful sub-parts is one of the fundamental problems in digital geometry processing. In this paper, a novel segmentation approach of point-sampled surfaces is proposed, which is based on the level set evolution scheme. To segment the model so as to align the patch boundaries with high curvature zones, the driven speed function for the zero level set inside narrow band is defined by the extended curvature field, which approaches zero speed as the propagating front approaches high curvature zone. The effectiveness of the proposed approach is demonstrated by our ex- perimental results. Furthermore, two applications of model segmentation are illustrated, such as piecewise parameterization and local editing for point-sampled geometry.
文摘The pinching of n-dimensional closed hypersurface Mwith constant mean curvature H in unit sphere S^(n+1)( 1) is considered. Let A = ∑i,j,k h(ijk)~2( λi+ nH)~2,B = ∑i,j,k h(ijk)~2( λi+ nH) ·( λj+ nH),S = ∑i( λi+ nH)~2, where h(ij)= λiδ(ij). Utilizing Lagrange's method, a sharper pointwise estimation of 3(A- 2B) in terms of S and |▽h|~2 is obtained, here |▽h|~2= ∑i,j,k h(ijk)~2. Then, with the help of this, it is proved that Mis isometric to the Clifford hypersurface if the square norm of the second fundamental form of Msatisfies certain conditions. Hence, the pinching result of the minimal hypersurface is extended to the hypersurface with constant mean curvature case.
文摘In this paper some properties of three-dimensional spaces of quasi-constant curvature different from those of cases when dimension n≥4 are proved. In particular, two classes of non-conformally flat solutions of them are constructed. In physics,a three-dimensional space of quasi-constant curvature appears as the space-like hypersurface of the rotation-free cosmological model of type D for the fluids with heat flow in General Relativity.
基金the Open Foundation Project of Jiangsu Key Laboratory of Precision and Micro-manufacturing Technology Open Fund Project.
文摘Existing curve fitting algorithms of NC machining path mainly focus on the control of fitting error,but ignore the problem that the original discrete cutter position points are not enough in the high curvature area of the tool path.It may cause a sudden change in the drive force of the feed axis,resulting in a large fluctuation in the feed speed.This paper proposes a new non-uniform rational B-spline(NURBS)curve fitting optimization method based on curvature smoothing preset point constraints.First,the short line segments generated by the CAM software are optimally divided into different segment regions,and then the curvature of the short line segments in each region is adjusted to make it smoother.Secondly,a set of characteristic points reflecting the change of the curvature of the fitted curve is constructed as the control apex of the fitted curve,and the curve is fitted using the NURBS curve fitting optimization method based on the curvature smoothing preset point constraint.Finally,the curve fitting error and curve volatility are analyzed with an example,which verifies that the method can significantly improve the curvature smoothness of the high-curvature tool path,reduce the fitting error,and improve the feed speed.
基金Projects(51174236,51134003)supported by the National Natural Science Foundation of ChinaProject(2011CB606306)supported by the National Basic Research Program of ChinaProject(PMM-SKL-4-2012)supported by the Opening Project of State Key Laboratory of Porous Metal Materials(Northwest Institute for Nonferrous Metal Research),China
文摘The difference of sintering crunodes of metal powders and fibers is discussed. The mathematical model of the surface diffusion described by the difference in mean curvature is defined as a Hamilton-Jacobi-type equation, and the model is numerically solved by the level set method. The three-dimensional numerical simulations of two metal powders and fibers(the fiber angle is 0° or 90°) are implemented by this mathematical model, respectively. The numerical simulation results accord with the experimental ones. The sintering neck growth trends of metal powders and metal fibers are similar. The sintering neck radius of metal fibers is larger than that of metal powders. The difference of the neck radius is caused by the difference of geometric structure which makes an important influence on the curvature affecting the migration rate of atoms.
基金Project (No. 10571154) supported by the National Natural Science Foundation of China
文摘In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special (α, β)-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessary condition that F is locally projectively fiat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively fiat. Moreover, we prove that such projectively fiat Finsler metrics with constant flag curvature must be locally Minkowskian.
文摘In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by osing the relationship between the square of the length of the second fundamental form and the mean curvature. We obtained a best pinching interval and decided the complete classification of hypersurfaces at the terminal of the interval.This improved the relative results of M. Okumura,Shen Yibihg and Sun Ziqi,etc.