Related papers: Smoothing a Rock by Chipping
For 3D geometries, we consider stones (modeled as convex polyhedra) subject to weathering with planar slices of random orientation and depth successively removing material, ultimately yielding smooth and round (i.e. spherical) shapes. An…
We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in $\mathbb R^3$. The method is local, only modifying the original surface in a…
Not only is the geometry of rock fragments often well approximated by ideal convex polyhedra having few faces and vertices, but these numbers carry vital geophysical information on the fragmentation process. Despite their significance, the…
In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…
Compacting orthogonal drawings is a challenging task. Usually algorithms try to compute drawings with small area or edge length while preserving the underlying orthogonal shape. We present a one-dimensional compaction algorithm that alters…
We study the problem of partitioning a given simple polygon $P$ into a minimum number of connected polygonal pieces, each of bounded size. We describe a general technique for constructing such partitions that works for several notions of…
We explore an instance of the question of partitioning a polygon into pieces, each of which is as ``circular'' as possible, in the sense of having an aspect ratio close to 1. The aspect ratio of a polygon is the ratio of the diameters of…
An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron…
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
In the process of projecting the surface of a three-dimensional object onto a two-dimensional surface, due to the perspective distortion, the image on the surface of the object will have different degrees of distortion according to the…
In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…
The main issues of the original Symmetrical smoothing method consists of approximation of the extremal volume of the set by the smooth symmetric function (sum of step functions) and then solve the optimization problem. when making…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
In image processing, it can be a useful pre-processing step to smooth away small structures, such as noise or unimportant details, while retaining the overall structure of the image by keeping edges, which separate objects, sharp. Typically…
For a smoothing Y of a 2-dimensional cyclic quotient singularity X, we construct a simple handle decomposition of Y by using a particular birational map from Y to the projective plane. The manifold Y is built up from the product of an…
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…
Most technical polymers and many biopolymers contain very different molecular species (unlike chain length, molecular architecture and/or chemical composition) in contrast to pure low molecular weight compounds. This inconsistent…
We report on the erosion of flat linoleum "pebbles" under steady rotation in a slurry of abrasive grit. To quantify shape as a function of time, we develop a general method in which the pebble is photographed from multiple angles with…
We consider the problem of defining the structure of a smooth manifold on the various spaces of piecewise-smooth loops in a smooth finite dimensional manifold. We succeed for a particular type of piecewise-smooth loops. We also examine the…