ترغب بنشر مسار تعليمي؟ اضغط هنا

Embedded Delaunay triangulations for point clouds of surfaces in $mathbb{R}^3$

401   0   0.0 ( 0 )
 نشر من قبل Franco Vargas Pallete
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In the following article we discuss Delaunay triangulations for a point cloud on an embedded surface in $mathbb{R}^3$. We give sufficient conditions on the point cloud to show that the diagonal switch algorithm finds an embedded Delaunay triangulation.



قيم البحث

اقرأ أيضاً

232 - Jiuzhou Huang , Jiawei Liu 2021
In this paper, we establish the existence and uniqueness of Ricci flow that admits an embedded closed convex surface in $mathbb{R}^3$ as metric initial condition. The main point is a family of smooth Ricci flows starting from smooth convex surfaces w hose metrics converge uniformly to the metric of the initial surface in intrinsic sense.
174 - Xianfeng Gu , Ren Guo , Feng Luo 2014
A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a unique hy perbolic polyhedral metric with a given discrete curvature satisfying Gauss-Bonnet formula. Furthermore, the hyperbolic polyhedral metric with given curvature can be obtained using a discrete Yamabe flow with surgery. In particular, each hyperbolic polyhedral metric on a closed surface with negative Euler characteristic is discrete conformal to a unique hyperbolic metric.
We establish curvature estimates and a convexity result for mean convex properly embedded $[varphi,vec{e}_{3}]$-minimal surfaces in $mathbb{R}^3$, i.e., $varphi$-minimal surfaces when $varphi$ depends only on the third coordinate of $mathbb{R}^3$. Le d by the works on curvature estimates for surfaces in 3-manifolds, due to White for minimal surfaces, to Rosenberg, Souam and Toubiana, for stable CMC surfaces, and to Spruck and Xiao for stable translating solitons in $mathbb{R}^3$, we use a compactness argument to provide curvature estimates for a family of mean convex $[varphi,vec{e}_{3}]$-minimal surfaces in $mathbb{R}^{3}$. We apply this result to generalize the convexity property of Spruck and Xiao for translating solitons. More precisely, we characterize the convexity of a properly embedded $[varphi,vec{e}_{3}]$-minimal surface in $mathbb{R}^{3}$ with non positive mean curvature when the growth at infinity of $varphi$ is at most quadratic.
Delaunay has shown that the Delaunay complex of a finite set of points $P$ of Euclidean space $mathbb{R}^m$ triangulates the convex hull of $P$, provided that $P$ satisfies a mild genericity property. Voronoi diagrams and Delaunay complexes can be de fined for arbitrary Riemannian manifolds. However, Delaunays genericity assumption no longer guarantees that the Delaunay complex will yield a triangulation; stronger assumptions on $P$ are required. A natural one is to assume that $P$ is sufficiently dense. Although results in this direction have been claimed, we show that sample density alone is insufficient to ensure that the Delaunay complex triangulates a manifold of dimension greater than 2.
We present a constructive proof of Alexandrovs theorem regarding the existence of a convex polytope with a given metric on the boundary. The polytope is obtained as a result of a certain deformation in the class of generalized convex polytopes with t he given boundary. We study the space of generalized convex polytopes and discover a relation with the weighted Delaunay triangulations of polyhedral surfaces. The existence of the deformation follows from the non-degeneracy of the Hessian of the total scalar curvature of a positively curved generalized convex polytope. The latter is shown to be equal to the Hessian of the volume of the dual generalized polyhedron. We prove the non-degeneracy by generalizing the Alexandrov-Fenchel inequality. Our construction of a convex polytope from a given metric is implemented in a computer program.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا