Topic
Delaunay triangulation
About: Delaunay triangulation is a research topic. Over the lifetime, 5816 publications have been published within this topic receiving 126615 citations. The topic is also known as: Delone triangulation.
Papers published on a yearly basis
Papers
More filters
01 Jan 2005
TL;DR: In this article, the distinct element method was originally designed to handle spherical particles and was generalized to a wider range of particle shapes called spherosimplices, and a contact detection method was given as well which uses weighted Delaunay triangulations to detect contacts occurring in a population of particles with such shapes.
Abstract: The distinct element method was originally designed to handle spherical particles Here, this method is generalized to a wider range of particle shapes called spherosimplices A contact detection method is given as well which uses weighted Delaunay triangulations to detect contacts occurring in a population of particles with such shapes Finally, a set of numerical experiments is performed indicating that the overall contact detection complexity is linear in the number of particles
42 citations
Proceedings Article•
01 Jan 1997
TL;DR: It is found that both profile and total score based threading functions can distinguish both the native fold from incorrect folds for a sequence, and the native sequence from non-native sequences for a fold.
Abstract: We propose new algorithms for sequence-structure compatibility (fold recognition) searches in multi-dimensional sequence-structure space. Individual amino acid residues in protein structures are represented by their C alpha atoms; thus each protein is described as a collection of points in three-dimensional space. Delaunay tessellation of a protein generates an aggregate of space-filling, irregular tetrahedra, or Delaunay simplices. Statistical analysis of quadruplet residue compositions of all Delaunay simplices in a representative dataset of protein structures leads to a novel four body contact residue potential expressed as log likelihood factor q. The q factors are calculated for native 20 letter amino acid alphabet and several reduced alphabets. Two sequence-structure compatibility functions are computed as (i) the sum of q factors for all Delaunay simplices in a given protein, or (ii) 3D-1D Delaunay tessellation profiles where the individual residue profile value is calculated as the sum of q factors for all simplices that share this vertex residue. Both threading functions have been implemented in structure-recognizes-sequence and sequence-recognizes-structure protocols for protein fold recognition. We find that both profile and total score based threading functions can distinguish both the native fold from incorrect folds for a sequence, and the native sequence from non-native sequences for a fold.
42 citations
DOI•
01 Jan 2006
TL;DR: The concept of virtual particles is introduced to implement efficient refinement and coarsification operators, and to achieve a consistent coupling between particles at different resolution levels, leading to speedups of up to a factor of six as compared to single resolution simulations.
Abstract: We present a new multiresolution particle method for fluid simulation. The discretization of the fluid dynamically adapts to the characteristics of the flow to resolve fine-scale visual detail, while reducing the overall complexity ofthe computations. We introduce the concept of virtual particles to implement efficient refinement and coarsification operators, and to achieve a consistent coupling between particles at different resolution levels, leading to speedups of up to a factor of six as compared to single resolution simulations. Our system supports multiphase effects such as bubbles and foam, as well as rigid body interactions, based on a unified particle interaction metaphor. The water-air interface is tracked with a Lagrangian level set approach using a novel Delaunay-based surface contouring method that accurately resolves fine-scale surface detail while guaranteeing preservation of fluid volume.
42 citations
05 Sep 2010
TL;DR: A simple yet powerful higher-order conditional random field (CRF) is used to model optical flow which consists of a standard photoconsistency cost and a prior on affine motions both modeled in terms of higher- order potential functions.
Abstract: We use a simple yet powerful higher-order conditional random field (CRF) to model optical flow. It consists of a standard photoconsistency cost and a prior on affine motions both modeled in terms of higher-order potential functions. Reasoning jointly over a large set of unknown variables provides more reliable motion estimates and a robust matching criterion. One of the main contributions is that unlike previous region-based methods, we omit the assumption of constant flow. Instead, we consider local affine warps whose likelihood energy can be computed exactly without approximations. This results in a tractable, so-called, higher-order likelihood function. We realize this idea by employing triangulation meshes which immensely reduce the complexity of the problem. Optimization is performed by hierarchical fusion moves and an adaptive mesh refinement strategy. Experiments show that we achieve high-quality motion fields on several data sets including the Middlebury optical flow database.
42 citations
07 Sep 2009
TL;DR: It is shown that in the worst-case the algorithm needs quadratic time, but that this can only happen in degenerate cases, and that the algorithm runs in O(n logn) time under realistic assumptions.
Abstract: Incremental construction con BRIO using a space-filling curve order for insertion is a popular algorithm for constructing Delaunay triangulations So far, it has only been analyzed for the case that a worst-case optimal point location data structure is used which is often avoided in implementations In this paper, we analyze its running time for the more typical case that points are located by walking We show that in the worst-case the algorithm needs quadratic time, but that this can only happen in degenerate cases We show that the algorithm runs in O(n logn) time under realistic assumptions Furthermore, we show that it runs in expected linear time for many random point distributions
42 citations