Related papers: Reconstructing a convex polygon from its $\omega$-…
Minimizing the number of probes is one of the main challenges in reconstructing geometric objects with probing devices. In this paper, we investigate the problem of using an $\omega$-wedge probing tool to determine the exact shape and…
Reconstructing a composition (union) of convex polytopes that perfectly fits the corresponding input point-cloud is a hard optimization problem with interesting applications in reverse engineering and rigid body dynamics simulations. We…
Let $P$ be a set of $n$ points in general position on the plane. A set of closed convex polygons with vertices in $P$, and with pairwise disjoint interiors is called a convex decomposition of $P$ if their union is the convex hull of $P$,…
We show that a polygon can be uniquely determined by the lengths of non-central sections supporting a piecewise-analytic hedgehog in the interior of the polygon. We also prove the analogous result for slab areas - centrally-symmetric…
In this work we deal with the problem of support estimation under shape restrictions. The shape restriction we deal with is an extension of the notion of convexity named alpha-convexity. Instead of assuming, as in the convex case, the…
In this paper, we study the following problem of reconstructing a simple polygon: Given a cyclically ordered vertex sequence of an unknown simple polygon P of n vertices and, for each vertex v of P, the sequence of angles defined by all the…
We conjecture that a convex polytope is uniquely determined up to isometry by its edge-graph, edge lengths and the collection of distances of its vertices to some arbitrary interior point, across all dimensions and all combinatorial types.…
Let $S$ be a set of $n$ points in the plane, $\wp(S)$ be the set of all simple polygons crossing $S$, $\gamma_P$ be the maximum angle of polygon $P \in \wp(S)$ and $\theta =min_{P\in\wp(S)} \gamma_P$. In this paper, we prove that…
Let $P$ be a polygon with $r>0$ reflex vertices and possibly with holes and islands. A subsuming polygon of $P$ is a polygon $P'$ such that $P \subseteq P'$, each connected component $R$ of $P$ is a subset of a distinct connected component…
Tomography is the area of reconstructing objects from projections. Here we wish to reconstruct a set of cells in a two dimensional grid, given the number of cells in every row and column. The set is required to be an hv-convex polyomino,…
Imprecise measurements of a point set P = (p1, ..., pn) can be modelled by a family of regions F = (R1, ..., Rn), where each imprecise region Ri contains a unique point pi. A retrieval models an accurate measurement by replacing an…
We propose a variational functional and fast algorithms to reconstruct implicit surface from point cloud data with a curvature constraint. The minimizing functional balances the distance function from the point cloud and the mean curvature…
Let $P$ be a set of $n$ labeled points in the plane. The radial system of $P$ describes, for each $p\in P$, the order in which a ray that rotates around $p$ encounters the points in $P \setminus \{p\}$. This notion is related to the order…
We consider the planar two-center problem for a convex polygon: given a convex polygon in the plane, find two congruent disks of minimum radius whose union contains the polygon. We present an $O(n\log n)$-time algorithm for the two-center…
A closed convex conic subset $\mathcal{S}$ of the positive semidefinite (PSD) cone is rank-one generated (ROG) if all of its extreme rays are generated by rank-one matrices. The ROG property of $\mathcal{S}$ is closely related to the…
A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and…
A polycube is an orthogonal polyhedron composed of unit cubes glued together along entire faces, and homeomorphic to a sphere. A layer of a polycube refers to the portion lying between two horizontal cross-sections spaced one unit apart. We…
Suppose a graph $G$ is stochastically created by uniformly sampling vertices along a line segment and connecting each pair of vertices with a probability that is a known decreasing function of their distance. We ask if it is possible to…
Given a convex polyhedral surface P, we define a tailoring as excising from P a simple polygonal domain that contains one vertex v, and whose boundary can be sutured closed to a new convex polyhedron via Alexandrov's Gluing Theorem. In…
Let $\mathcal{O}$ be a set of $k$ orientations in the plane, and let $P$ be a simple polygon in the plane. Given two points $p,q$ inside $P$, we say that $p$ $\mathcal{O}$-\emph{sees} $q$ if there is an $\mathcal{O}$-\emph{staircase}…