Related papers: Combinatorics and the Rigidity of CAD Systems
In this paper, we compute a conservative approximation of the path-connected components of the free space of a rigid object in a 2D workspace in order to solve two closely related problems: to determine whether there exists a collision-free…
Identifying the parameters of robotic systems, such as motor inertia or joint friction, is critical to satisfactory controller synthesis, model analysis, and observer design. Conventional identification techniques are designed primarily for…
We propose a simple and efficient scheme based on adaptive finite elements over conforming quadtree meshes for collapse plastic analysis of structures. Our main interest in kinematic limit analysis is concerned with both purely…
Parametric computer-aided design (CAD) is the dominant paradigm in mechanical engineering for physical design. Distinguished by relational geometry, parametric CAD models begin as two-dimensional sketches consisting of geometric primitives…
Combinatorial mechanical metamaterials are made of anisotropic, flexible blocks, such that multiple metamaterials may be constructed using a single block type, and the system's response depends on the frustration (or its absence) due to the…
Rod-based structures are commonly used in practical applications in science and engineering. However, in many design, analysis, and manufacturing tasks, handling the rod-based structures in three dimensions directly is generally…
This work proposes a fully decentralized strategy for maintaining the formation rigidity of a multi-robot system using only range measurements, while still allowing the graph topology to change freely over time. In this direction, a first…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
Compacting orthogonal drawings is a challenging task. Usually algorithms try to compute drawings with small area or edge length while preserving the underlying orthogonal shape. We present a one-dimensional compaction algorithm that alters…
Combinatorial characterisations are obtained of symmetric and anti-symmetric infinitesimal rigidity for two-dimensional frameworks with reflectional symmetry in the case of norms where the unit ball is a quadrilateral and where the…
Tightness is a generalisation of the notion of convexity: a space is tight if and only if it is "as convex as possible", given its topological constraints. For a simplicial complex, deciding tightness has a straightforward exponential time…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A special case of this correspondence identifies the problem of…
Following a review of related results in rigidity theory, we provide a construction to obtain generically universally rigid frameworks with the minimum number of edges, for any given set of n nodes in two or three dimensions. When a set of…
Cylindrical algebraic decomposition (CAD) is a key tool for problems in real algebraic geometry and beyond. When using CAD there is often a choice over the variable ordering to use, with some problems infeasible in one ordering but simple…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
This paper defines the basis of a new hierarchical framework for segmentation algorithms based on energy minimization schemes. This new framework is based on two formal tools. First, a combinatorial pyramid encode efficiently a hierarchy of…
We consider the problem of finding a continuous and non-rigid matching between a 2D contour and a 3D mesh. While such problems can be solved to global optimality by finding a shortest path in the product graph between both shapes, existing…
Abstractions of crystalline materials known as periodic body-and-bar frameworks are made of rigid bodies connected by fixed-length bars and subject to the action of a group of translations. In this paper, we give a Maxwell-Laman…
The number of embeddings of minimally rigid graphs in $\mathbb{R}^D$ is (by definition) finite, modulo rigid transformations, for every generic choice of edge lengths. Even though various approaches have been proposed to compute it, the gap…