WebTHE SPHERICAL CONVEX FLOATING BODY 3 Thenextsectiongivestheprecisestatementofourmaintheorem. InSection 3 we will briefly recall basic notions from Euclidean convex ... A convex cap, also known as a convex floating body or just floating body, is a well defined structure in mathematics commonly used in convex analysis for approximating convex shapes. In general it can be thought of as the intersection of a convex Polytope with a half-space. See more We can define the floating body of a convex shape $${\displaystyle H}$$ using the following process. Note the floating body is also convex. In the case of a 2-dimensional convex compact shape $${\displaystyle K}$$, … See more Assume $${\displaystyle K\in {\mathcal {K_{1}}}=\{K:\mathrm {vol} (K)=1\}}$$ and choose $${\displaystyle x_{1},...,x_{n}}$$ randomly, … See more
The convex floating body - ScienceDirect
WebWe show that a convex bodyK in ℝn is homothetic to an ellipsoid if there is a sequence {δk}kεℕ converging to 0 so thatK is homothetic to its floating bodiesKδk. Skip to search form Skip to main content Skip to account menu. Semantic Scholar's Logo. Search 206,949,879 papers from all fields of science ... WebCurved outwards. Example: A polygon (which has straight sides) is convex when there are NO "dents" or indentations in it (no internal angle is greater than 180°) The opposite idea … erie business association
The convex floating body and polyhedral approximation
WebSep 28, 2024 · Data depth and floating body. Little known relations of the renown concept of the halfspace depth for multivariate data with notions from convex and affine … WebAug 1, 2024 · The convex floating body Kδof Kis the intersection of all halfspaces H+whose defining hyperplanes Hcut off a set of volume δfrom K, i.e.,Kδ=⋂voln(H−∩K)=δH+,where H−denotes the complementary halfspace. Let us introduce the notion of generalized Gauß-Kronecker curvature. WebNov 27, 2014 · For a convex body on the Euclidean unit sphere the spherical convex floating body is introduced. The asymptotic behavior of the volume difference of a spherical convex body and its spherical floating body is investigated. This gives rise to a new spherical area measure, the floating area. Remarkably, this floating area turns out to be … find the invis