81 research outputs found
Checking and improving the geometric accuracy of non-interpolating curved high-order meshes
Peer ReviewedPostprint (author's final draft
Fast Frechet Distance Between Curves With Long Edges
Computing the Fr\'echet distance between two polygonal curves takes roughly
quadratic time. In this paper, we show that for a special class of curves the
Fr\'echet distance computations become easier. Let and be two polygonal
curves in with and vertices, respectively. We prove four
results for the case when all edges of both curves are long compared to the
Fr\'echet distance between them: (1) a linear-time algorithm for deciding the
Fr\'echet distance between two curves, (2) an algorithm that computes the
Fr\'echet distance in time, (3) a linear-time
-approximation algorithm, and (4) a data structure that supports
-time decision queries, where is the number of vertices of
the query curve and the number of vertices of the preprocessed curve
A fast implementation of near neighbors queries for Fr\'echet distance (GIS Cup)
This paper describes an implementation of fast near-neighbours queries (also
known as range searching) with respect to the Fr\'echet distance. The algorithm
is designed to be efficient on practical data such as GPS trajectories. Our
approach is to use a quadtree data structure to enumerate all curves in the
database that have similar start and endpoints as the query curve. On these
curves we run positive and negative filters to narrow the set of potential
results. Only for those trajectories where these heuristics fail, we compute
the Fr\'echet distance exactly, by running a novel recursive variant of the
classic free-space diagram algorithm.
Our implementation won the ACM SIGSPATIAL GIS Cup 2017.Comment: ACM SIGSPATIAL'17 invited paper. 9 page
Computing the Similarity Between Moving Curves
In this paper we study similarity measures for moving curves which can, for
example, model changing coastlines or retreating glacier termini. Points on a
moving curve have two parameters, namely the position along the curve as well
as time. We therefore focus on similarity measures for surfaces, specifically
the Fr\'echet distance between surfaces. While the Fr\'echet distance between
surfaces is not even known to be computable, we show for variants arising in
the context of moving curves that they are polynomial-time solvable or
NP-complete depending on the restrictions imposed on how the moving curves are
matched. We achieve the polynomial-time solutions by a novel approach for
computing a surface in the so-called free-space diagram based on max-flow
min-cut duality
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