Related papers: Compass Constructions
Let $B$ be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most one, and let $P$ be a convex polygon with $n$ vertices. Given a starting configuration (a location and a direction of travel)…
The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of…
Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, different algorithms for the same clustering task may return…
As an important practice of map generalization, the aim of line simplification is to reduce the number of points without destroying the essential shape or the salient character of a cartographic curve. This subject has been well-studied in…
A (multi)set of segments in the plane may form a TSP tour, a matching, a tree, or any multigraph. If two segments cross, then we can reduce the total length with the following flip operation. We remove a pair of crossing segments, and…
With this work we aim to show how Mathematica can be a useful tool to investigate properties of combinatorial structures. Specifically, we will face enumeration problems on independent subsets of powers of paths and cycles, trying to…
In this paper we present algorithms for collective construction systems in which a large number of autonomous mobile robots trans- port modular building elements to construct a desired structure. We focus on building block structures…
TO APPEAR IN AEQUATIONES MATHEMATICAE - WITHOUT THEOREM 2. THEOREM 2 IS CORRECTLY PROVED IN PREVIOUS VERSIONS 1 AND 2. AUTHOR'S VERSION 3 (WITH A NEW FIGURE 6A) IS UNNECESSARY. Let F \subseteq R denote the field of numbers which are…
Euclidean geometry consists of straightedge-and-compass constructions and reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. We consider three versions of…
We propose a novel method that renders point clouds as if they are surfaces. The proposed method is differentiable and requires no scene-specific optimization. This unique capability enables, out-of-the-box, surface normal estimation,…
Discovering a solution in a combinatorial space is prevalent in many real-world problems but it is also challenging due to diverse complex constraints and the vast number of possible combinations. To address such a problem, we introduce a…
We present a framework for deformable object manipulation that interleaves planning and control, enabling complex manipulation tasks without relying on high-fidelity modeling or simulation. The key question we address is when should we use…
The projection onto the intersection of sets generally does not allow for a closed form even when the individual projection operators have explicit descriptions. In this work, we systematically analyze the projection onto the intersection…
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 study the computational complexity of routing multiple objects through a network in such a way that only few collisions occur: Given a graph $G$ with two distinct terminal vertices and two positive integers $p$ and $k$, the question is…
We construct curves with many points over finite fields using the class group
The Carpenter's Rule Theorem states that any chain linkage in the plane can be folded continuously between any two configurations while preserving the bar lengths and without the bars crossing. However, this theorem applies only to strictly…
In this work, we introduce the problem of scenic routes among points in Rd. The key development is the nature of the problem in terms of both defining the concept of scenic points and scenic routes and then coming up with algorithms that…
Reconstructing 3D point clouds into triangle meshes is a key problem in computational geometry and surface reconstruction. Point cloud triangulation solves this problem by providing edge information to the input points. Since no vertex…
A quadruple crossing is a crossing in a projection of a knot or link that has four strands of the knot passing straight through it. A quadruple crossing projection is a projection such that all of the crossings are quadruple crossings. In a…