Related papers: Grid Peeling of Parabolas
In this paper we study an experimentally-observed connection between two seemingly unrelated processes, one from computational geometry and the other from differential geometry. The first one (which we call "grid peeling") is the…
Consider the set of points formed by the integer $n \times n$ grid, and the process that in each iteration removes from the point set the vertices of its convex-hull. Here, we prove that the number of iterations of this process is…
An edge-unfolding of a polyhedron is produced by cutting along edges and flattening the faces to a *net*, a connected planar piece with no overlaps. A *grid unfolding* allows additional cuts along grid edges induced by coordinate planes…
A grid polygon is a polygon whose vertices are points of a grid. We define an injective map between permutations of length n and a subset of grid polygons on n vertices, which we call consecutive-minima polygons. By the kernel method, we…
When we try to solve a system of linear equations, we can consider a simple iterative algorithm in which an equation including only one variable is chosen at each step, and the variable is fixed to the value satisfying the equation. The…
The peeling process is defined as follows: starting with a finite point set $X \subset \mathbb{R}^d$, we repeatedly remove the set of vertices of the convex hull of the current set of points. The number of peeling steps needed to completely…
The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k and their adjacent edges are removed until no vertices of degree less than k are left. Often…
In this paper we introduce flat grafting as a deformation of quadratic differentials on a surface of finite type that is analogous to the grafting map on hyperbolic surfaces. Flat grafting maps are generic in the strata structure and…
The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k are removed until there are no vertices of degree less than k left. The remaining hypergraph…
A procedure for interpolating between specified points of a curve or surface is described. The method guarantees slope continuity at all junctions. A surface panel divided into p x q contiguous patches is completely specified by the…
The number of steps required to exhaust a point set by iteratively removing the vertices of its convex hull is called the layer number of the point set. This article presents a short proof that the layer number of the grid…
The convex hull peeling of a point set consists in taking the convex hull, then removing the extreme points and iterating that procedure until no point remains. The boundary of each hull is called a layer. Following on from [15], we study…
A simple model for the peeling process of pressure-sensitive adhesive tape is presented. The model consists of linear springs and dashpots and can be solved analytically. Based on the modeling, the curved profile of the peeling tape is…
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods,…
Pareto hull peeling is a discrete algorithm, generalizing convex hull peeling, for sorting points in Euclidean space. We prove that Pareto peeling of a random point set in two dimensions has a scaling limit described by a first-order…
This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the signal can be modeled by generalized Gaussian random variables, we compute a critical thresholding…
This article deals with flow of plane curves driven by the curvature and external force. We make use of such a geometric flow for the purpose of image segmentation. A parametric model for evolving curves with uniform and curvature adjusted…
Grids are a general representation for capturing regularly-spaced information, but since they are uniform in space, they cannot dynamically allocate resolution to regions with varying levels of detail. There has been some exploration of…
Given a designer created free-form surface in 3d space, our method computes a grid composed of elastic elements which are completely planar and straight. Only by fixing the ends of the planar elements to appropriate locations, the 2d grid…
A pebbling step on a graph consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. A graph is said to be cover pebbled if every vertex has a pebble on it after a series of pebbling steps. The cover…