分类: 计算机科学 >> 计算机软件 提交时间: 2017-04-10
摘要: Traditional manifold learning algorithms often bear an assumption that the local neighborhood of any point on embedded manifold is roughly equal to the tangent space at that point without considering the curvature. The curvature indifferent way of manifold processing often makes traditional dimension reduction poorly neighborhood preserving. To overcome this drawback we propose a new algorithm called RF-ML to perform an operation on the manifold with help of Ricci flow before reducing the dimension of manifold.
分类: 力学 >> 应用力学 提交时间: 2020-12-18
摘要: In order to enhance the overall structural stability of 3D printed concrete wall, we propose a novel scheme to produce a wavy wall with curvature along its contour direction. To validate the idea of the scheme, a single wave wall is set as a cylindrical wall and its mechanical performances are analyzed. The mathematical 3D printing model of the wavy wall is formulated by the shell theory while taking into account of additional parameters of the printing processes, the model will be used to analyze the two failure mechanisms of the cylindrical wall: elastic buckling and plastic collapse. Compared with the results of Suiker’s straight wall, it is found that when the parameters were same, the stability of the cylindrical wall is more than twice of the rectangular wall. Our studies indicate that it’s a feasible scheme to improve the printed structural stability by increasing curvature.
分类: 数学 >> 几何与拓扑 提交时间: 2023-02-22
摘要: In this paper, we study biharmonic isometric immersions of a surface into and biharmonic Riemannian submersions from 3-dimensional Berger spheres. We obtain a classifification of proper biharmonic isometric immersions of a surface with constant mean curvature into Berger 3-spheres. We also give a complete classifification of proper biharmonic Hopf tori in Berger 3-sphere. For Riemannian submersions, we prove that a Riemannian submersion from Berger 3-spheres into a surface is biharmonic if and only if it is harmonic.
分类: 计算机科学 >> 计算机应用技术 提交时间: 2017-03-10
摘要: Principal curvatures and principal directions are exploited ubiquitously in shape analysis. On one hand, umbilical points severely hinder the analysis as the singularities in the vector field of principal directions; on the other hand, providing shape-intrinsic qualitative information about a surface, they are desirable quantities in some applications. Umbilical points are fundamental for geometric analysis, but their accurate computation on a discrete surface is still challenging. In this paper, we develop a simple and effective method to detect umbilical points on a triangle mesh, in which any parametrization works. In particular, we propose two practical processes for local parametrization by orthogonally projecting or conformally transforming the matrix onto a specified parametric plane. Furthermore, we make a systematic analysis on our method and demonstrate its convergence behavior. The algorithm of our approach is flexible and easy to implement for a triangular mesh of arbitrary topology.