Related papers: Uncertain Curve Simplification
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 propose sublinear algorithms for probabilistic testing of the discrete and continuous Fr\'echet distance - a standard similarity measure for curves. We assume the algorithm is given access to the input curves via a query oracle: a query…
A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…
Budgeted uncertainty sets have been established as a major influence on uncertainty modeling for robust optimization problems. A drawback of such sets is that the budget constraint only restricts the global amount of cost increase that can…
We propose a new approach for solving a class of discrete decision making problems under uncertainty with positive cost. This issue concerns multiple and diverse fields such as engineering, economics, artificial intelligence, cognitive…
Invariant manifolds of unstable periodic orbits organize the dynamics of chaotic orbits in phase space. They provide insight into the mechanisms of transport and chaotic advection and have important applications in physical situations…
A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…
The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a…
In this paper, the recoverable robust shortest path problem under interval uncertainty representations is discussed. This problem is known to be strongly NP-hard and also hard to approximate in general digraphs. In this paper, the class of…
The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both…
We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This…
For many fundamental problems in computational topology, such as unknot recognition and $3$-sphere recognition, the existence of a polynomial-time solution remains unknown. A major algorithmic tool behind some of the best known algorithms…
Any two equivalent discrete curves must have the same invariants at the corresponding points under an affine transformation. In this paper, we construct the moving frame and invariants for the discrete centroaffine curves, which could be…
It is a major unsolved problem as to whether unknot recognition - that is, testing whether a given closed loop in R^3 can be untangled to form a plain circle - has a polynomial time algorithm. In practice, trivial knots (which can be…
Of concern is the study of the space of curves in homogeneous spaces. Motivated by applications in shape analysis we identify two curves if they only differ by their parametrization and/or a rigid motion. For curves in Euclidean space the…
We propose a method for tracing implicit real algebraic curves defined by polynomials with rank-deficient Jacobians. For a given curve $f^{-1}(0)$, it first utilizes a regularization technique to compute at least one witness point per…
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…
We prove that circle graphs (intersection graphs of circle chords) can be embedded as intersection graphs of rays in the plane with polynomial-size bit complexity. We use this embedding to show that the global curve simplification problem…
In this paper we compute the Hausdorff distance between sets of continuous curves and sets of piecewise constant or linear discretizations. These sets are Sobolev balls given by the continuous or discrete $L^p$-norm of the derivatives. We…
We study a map matching problem, the task of finding in an embedded graph a path that has low distance to a given curve in R^2. The Fr\'echet distance is a common measure for this problem. Efficient methods exist to compute the best path…