Computational geometry

By M. D. Berg, Bettina Speckmann. 1994

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Citations in the corpus

A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles (2016, background): “A feedback control adjusts actuation variables to correct errors in executing the reference path.”
FarmBeats: An IoT Platform for Data-Driven Agriculture (2017, background): “For each edge and its antipodal (diametrically opposite) vertex [50], draw two parallel lines and measures the distance between them.”
Visual Exploration of Big Spatio-Temporal Urban Data: A Study of New York City Taxi Trips (2013, methodology): “Our implementation is based on a spacepartitioning data structure, k-d tree [11], that treats each taxi trip as a point in a k-dimensional space.”
Texture Analysis (1993, unknown): “An optimal algorithm to compute the Voronoi tessellation for a point pattern is described by Preparata and Shamos [53].”
Comparing Images Using the Hausdorff Distance (1993, unknown): “Thus note that the local maxima are equidistant from two or more local minima (hence the name Voronoi surface, by analogy to Voronoi diagrams that specify the locations equidistant from two or more points of a given set [16]).”
3D mesoscale finite element modelling of concrete (2017, unknown): “The convex hull for a set of points is the minimum convex polyhedron containing all the predefined points [27].”
Autozoner: an algorithm for automatic thermal zoning of buildings with unknown interior space definitions (2016, methodology): “As underlying data structure, we use a doubly connected edge list (DCEL), a planar graph that allows efficient topological manipulation of our core and perimeter cells (De Berg et al. 2008).”
An Improved Dimension-Sweep Algorithm for the Hypervolume Indicator (2006, unknown): “More recently, While et al. [9] have proposed the socalled HSO (Hypervolume by Slicing Objectives) algorithm, which is, in fact, a dimension-sweep [10] approach.”
Query Indexing and Velocity Constrained Indexing: Scalable Techniques for Continuous Queries on Moving Objects (2002, unknown): “The related problem of finding a largest empty rectangle has been studied extensively and solutions vary from O(n) to O(nlog3n) time, (wheren is the number of query rectangles) depending on restrictions on the regions [4, 5, 6, 22].”
A comparison of computational color constancy algorithms. I: Methodology and experiments with synthesized data (2002, methodology): “D entity, we can often simply use it implicitly by observing that an is inside the cone, if the corresponding is in the convex hull of the projected points used to define the cone.”
Optimization Approaches for the Traveling Salesman Problem with Drone (2016, methodology): “It can be used to obtain a minimum spanning tree for a Euclidean graph in expected time using a Delaunay Triangulation [Shamos, 1978], circumventing the need to consider all entries in the distance matrix.”
From Isovists to Visibility Graphs: A Methodology for the Analysis of Architectural Space (2001, unknown): “…representations capable of being automated, such as ‘all-line’ axial maps, in which all the lines that (1) rate not calculable in polynomial time (see deBerg et al, 1997, pages 45^ 61), but Hillier and Hanson show that, in practice, it is simple to decide on a sensible spatial breakup for a given…”