Related papers: Closing curves by rearranging arcs
We formulate as an inverse problem the construction of sparse parametric continuous curve models that fit a sequence of contour points. Our prior is incorporated as a regularization term that encourages rotation invariance and sparsity. We…
Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive…
This paper presents the first purely numerical (i.e., non-algebraic) subdivision algorithm for the isotopic approximation of a simple arrangement of curves. The arrangement is "simple" in the sense that any three curves have no common…
Given two simplicial complexes in R^d, and start and end vertices in each complex, we show how to compute curves (in each complex) between these vertices, such that the Fr\'echet distance between these curves is minimized. As a polygonal…
This paper describes an efficient approach to constructing a resultant polyline with a minimum number of segments and arcs. While fitting an arc can be done with complexity O(1) (see [1] and [2]), the main complexity is in checking that the…
In this paper, we give a fast algorithm for the computation of the Arf closure of an algebroid curve with more than one branch, generalizing an algorithm presented by Arslan and Sahin for the algebroid branch case.
In this paper, we develop a systematic approach to enumerate curves with a certain number of nodes and one further singularity which maybe more degenerate. As a result, we obtain an explicit formula for the number of curves in a…
In this paper we consider the following problem: is it possible to recover a smooth plane curve of degree at least three from its inflection lines? We answer positively to the posed question for a general smooth plane quartic curve, making…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…
We give necessary and sufficient topological conditions for a simple closed curve on a real rational surface to be approximable by smooth rational curves. We also study approximation by smooth rational curves with given complex…
In this article we extend the computational geometric curve reconstruction approach to curves in Riemannian manifolds. We prove that the minimal spanning tree, given a sufficiently dense sample, correctly reconstructs the smooth arcs and…
Let X be a (possibly nodal) K-trivial threefold moving in a fixed ambient space P. Suppose X contains a continuous family of curves, all of whose members satisfy certain unobstructedness conditions in P. A formula is given for computing the…
We study a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. We show that sometimes this algorithm admits a substantial reduction of complexity, and, furthermore, find…
To construct a curve with a monotonic curvature (spiral), and given tangents and curvatures at the ends, the author proposed the following method. From given boundary conditions, the values of two inverse invariants are determined. Then, on…
In this paper we introduce an algorithm of construction of cyclic space-filling curves. One particular construction provides a family of space-filling curves in all dimensions (H-curves). They are compared here with the Hilbert curve in the…
In this paper, we consider a transformation of $k$ disjoint paths in a graph. For a graph and a pair of $k$ disjoint paths $\mathcal{P}$ and $\mathcal{Q}$ connecting the same set of terminal pairs, we aim to determine whether $\mathcal{P}$…
Given an ordered sequence of $N$-choose-2 integers, we give necessary and sufficient conditions to have an ordered collection of $N$ simple closed curves on a torus such that the algebraic pairwise intersections of those curves are the…
We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a curve with no inflection points. We also…
The order in which plane-filling curves visit points in the plane can be exploited to design efficient algorithms. Typically, the curves are useful because they preserve locality: points that are close to each other along the curve tend to…
Shape recognition and classification is a problem with a wide variety of applications. Several recent works have demonstrated that topological descriptors can be used as summaries of shapes and utilized to compute distances. In this…