Related papers: Carving Polytopes with Saws in 3D

[libralesso_anytime_2020] proposed an anytime tree search algorithm for the 2018 ROADEF/EURO challenge glass cutting problem (https://www.roadef.org/challenge/2018/en/index.php). The resulting program was ranked first among 64 participants.…

We present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing…

Given a convex region in the plane, and a sweep-line as a tool, what is best way to reduce the region to a single point by a sequence of sweeps? The problem of sweeping points by orthogonal sweeps was first studied in [2]. Here we consider…

A dissection of a convex d-polytope is a partition of the polytope into d-simplices whose vertices are among the vertices of the polytope. Triangulations are dissections that have the additional property that the set of all its simplices…

Various applications of graphs, in particular applications related to finding shortest paths, naturally get inputs with real weights on the edges. However, for algorithmic or visualization reasons, inputs with integer weights would often be…

We consider the problem of triangulating a polygon with $n$ vertices and $h$ holes, or relatedly the problem of computing the trapezoidal decomposition of a collection of $h$ disjoint simple polygonal chains with $n$ vertices total.…

We present a practical algorithm to test whether a 3-manifold given by a triangulation or an ideal triangulation contains a closed essential surface. This property has important theoretical and algorithmic consequences. As a testament to…

Thin leaves, fine stems, self-occlusion, non-rigid and slowly changing structures make plants difficult for three-dimensional (3D) scanning and reconstruction -- two critical steps in automated visual phenotyping. Many current solutions…

In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…

There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…

In this paper we analyze O'Hara's partition bijection. We present three type of results. First, we show that O'Hara's bijection can be viewed geometrically as a certain scissor congruence type result. Second, we obtain a number of new…

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…

3D shape editing is widely used in a range of applications such as movie production, computer games and computer aided design. It is also a popular research topic in computer graphics and computer vision. In past decades, researchers have…

Solving optimal control problems (OCPs) of autonomous agents operating under spatial and temporal constraints fast and accurately is essential in applications ranging from eco-driving of autonomous vehicles to quadrotor navigation. However,…

This paper presents a learning based planner for computing optimized 3D printing toolpaths on prescribed graphs, the challenges of which include the varying graph structures on different models and the large scale of nodes & edges on a…

The paper is an introduction to the use of the classical Newton-Puiseux procedure, oriented to an algorithmic description of it. This procedure enables to get polynomial approximations for parameterizations of branches of an algebraic plane…

We give an algorithm that constructs the Hasse diagram of the face lattice of a convex polytope P from its vertex-facet incidences in time O(min{n,m}*a*f), where n is the number of vertices, m is the number of facets, a is the number of…

We study the complexity of computing the projection of an arbitrary $d$-polytope along $k$ orthogonal vectors for various input and output forms. We show that if $d$ and $k$ are part of the input (i.e. not a constant) and we are interested…

This paper begins with a class of convex quadratic programs (QPs) with bounded variables solvable by the parametric principal pivoting algorithm with $\mathcal{O}(n^3)$ strongly polynomial complexity, where $n$ is the number of variables of…

The motion of a mechanical system can be defined as a path through its configuration space. Computing such a path has a computational complexity scaling exponentially with the dimensionality of the configuration space. We propose to reduce…