A tetrahedralization of a point set in 3-dimensional space is Hamiltonian if its dual graph has a Hamiltonian cycle. Let S be a set of n points in general position in 3-dimensional space. We prove that by adding to S at most ⌊ 2 ⌋ Steiner points in the interior of the convex hull of S, we obtain a point set that admits a Hamiltonian tetrahedralization. We also obtain an O(m 3 2 ) + O(n log n) a...

The parallel complexity of the problem of constructing the convex hull of a sorted planar point set is studied. For any point p in the plane, let x(p) and y(p) denote the xand y-coordinate of p. A planar point set S = {p1, p2, . . . , pN} is said to be x-sorted if the points of S are given by increasing x-coordinate, i.e., x(pi) ≤ x(pi+1) for all i ∈ {1, 2, . . . , N − 1}. The following two res...

Proton computed tomography (pCT) is a novel imaging modality developed for patients receiving proton radiation therapy. The purpose of this work was to investigate hull-detection algorithms used for preconditioning of the large and sparse linear system of equations that needs to be solved for pCT image reconstruction. The hull-detection algorithms investigated here included silhouette/space car...

We consider the planar convex hull range query problem. Let P be a set of points in the plane. We preprocess these points into a data structure such that given an orthogonal range query, we can report the convex hull of the points in the range in O(log n + h) time, where h is the size of the output. The data structure uses O(n log n) space. This improves the previous bound of O(log n+h) time an...

We prove that every topological space (T0-space, T1-space) can be embedded in a pseudoradial space (in a pseudoradial T0-space, T1-space). This answers the Problem 3 in [2]. We describe the smallest coreflective subcategory A of Top such that the hereditary coreflective hull of A is the whole category Top.

The asymptotic properties of Rapidly exploring Random Tree (RRT) growth in large spaces is studied both in simulation and analysis. The main phenomenon is that the convex hull of the RRT reliably evolves into an equilateral triangle when grown in a symmetric planar region (a disk). To characterize this and related phenomena from flocking and swarming, a family of dynamical systems based on incr...

The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log log n) time, point deletions in amortized O(log n · log log n) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure req...

In this paper, we arithmetically describe the convex hull of a digital straight segment by three recurrence relations. This characterization gives new insights into the combinatorial structure of digital straight segments of arbitrary length and intercept. It also leads to two on-line algorithms that computes a part of the convex hull of a given digital straight segment. They both run in consta...

The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log logn) time, point deletions in amortized O(log n · log logn) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requi...

Many categories of semantic domains can be considered from an order-theoretic point of view and from a topological point of view via the Scott topology. The topological point of view is particularly fruitful for considerations of computability in classical spaces such as the Euclidean real line. When one embeds topological spaces into domains, one requires that the Scott continuous maps between...