We present output sensitive techniques for the generalized reporting versions of the planar range maxima problem and the planar range convex hull problem. Our solutions are in the pointer machine model, for orthogonal range queries on a static point set. We solve the planar range maxima problem for two-sided, three-sided and four-sided queries. We achieve a query time of O(log n+c) using O(n) s...

We propose data structures for answering a geodesic-distance query between two query points in a two-dimensional or three-dimensional dynamic environment, in which obstacles are deforming continuously. Each obstacle in the environment is modeled as the convex hull of a continuously deforming point cloud. The key to our approach is to avoid maintaining the convex hull of each point cloud explici...

In this paper we introduce an algorithm for the creation of polyhedral approximations for certain kinds of digital objects in a three-dimensional space. The objects are sets of voxels represented as strongly connected subsets of an abstract cell complex. The proposed algorithm generates the convex hull of a given object and modifies the hull afterwards by recursive repetitions of generating con...

An element of an effectively given domain is computable iff its basic Scott open neighbourhoods are recursively enumerable. We thus refer to computable elements as Scott computable and define an element to be Lawson computable if its basic Lawson open neighbourhoods are recursively enumerable. Since the Lawson topology is finer than the Scott topology, a stronger notion of computability is obta...

In this paper we consider the problem of representing the shape of a region, qualitatively, within a logical theory of space. Using just two primitive notions, that of two regions connecting, and the convex hull of a region, a wide variety of concave shapes can be distinguished. Moreover, by applying the technique recursively to the inside of a region (i.e. that part of the convex hull not occu...

Color Halftoning, Dithering. This report introduces the problem of dithering in a simplex, and suggests a few possible solutions. In general, dithering can be viewed as a method for describing color images using a combination of allowed output colors. Usually the convex hull of the set of allowed output colors is a cube in the color space. However, there are cases when the convex hull is a simp...

Place types taxonomies tend to have a shallow structure, which limits their predictive value. Although existing place type taxonomies could in principle be refined, the result would inevitably be highly subjective and application-specific. Instead, in this paper, we propose a methodology to enrich place types taxonomies with a ternary betweenness relation derived from Flickr. In particular, we ...

This paper presents a new active convex hull model to be used for search space partitioning to decrease the time needed for image retrieval from large image database. The model is based on the geometric heat differential equation and has the following advantages: capable of automatic image segmentation to shells; large capture range; invariant with respect to scaling, rotations and translations...

In this paper, we aim to use a continuous formulation efficiently calculate the well-known wrench-based grasp metric proposed by Ferrari and Canny which is minimum distance from wrench space origin boundary of space. Considering L∞ nonlinear friction cone model, challenge calculating determine Instead relying on convex hull construction, propose formulate as functions. By doing so, problem qual...