Improved Implementation of Point Location in General Two-Dimensional Subdivisions

We present a major revamp of the point-location data structure for general two-dimensional subdivisions via randomized incremental construction, implemented in CGAL, the Computational Geometry Algorithms Library. We can now guarantee that the constructed directed acyclic graph G is of linear size and provides logarithmic query time. Via the construction of the Voronoi diagram for a given point set S of size n, this also enables nearest-neighbor queries in guaranteed O(log n) time. Another major innovation is the support of general unbounded subdivisions as well as subdivisions of two-dimensional parametric surfaces such as spheres, tori, cylinders. The implementation is exact, complete, and general, i.e., it can also handle non-linear subdivisions. Like the previous version, the data structure supports modifications of the subdivision, such as insertions and deletions of edges, after the initial preprocessing. A major challenge is to retain the expected O(n log n) preprocessing time while providing the above (deterministic) space and query-time guarantees. We describe an efficient preprocessing algorithm, which explicitly verifies the length L of the longest query path in O(n log n) time. However, instead of using L, our implementation is based on the depth D of G. Although we prove that the worst case ratio of D and L is Theta(n/log n), we conjecture, based on our experimental results, that this solution achieves expected O(n log n) preprocessing time.Comment: 21 page

Exclusive Strategy for Generalization Algorithms in Micro-data Disclosure

Abstract. When generalization algorithms are known to the public, an adver-sary can obtain a more precise estimation of the secret table than what can be deduced from the disclosed generalization result. Therefore, whether a general-ization algorithm can satisfy a privacy property should be judged based on such an estimation. In this paper, we show that the computation of the estimation is inherently a recursive process that exhibits a high complexity when generaliza-tion algorithms take a straightforward inclusive strategy. To facilitate the design of more efficient generalization algorithms, we suggest an alternative exclusive strategy, which adopts a seemingly drastic approach to eliminate the need for recursion. Surprisingly, the data utility of the two strategies are actually not com-parable and the exclusive strategy can provide better data utility in certain cases.

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem: for every integer $\ell \geq 2$, every sufficiently large set of points in the plane contains $\ell$ collinear points or an empty pentagon. As an application, we settle the next open case of the "big line or big clique" conjecture of K\'ara, P\'or, and Wood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005]

Six Degrees of Freedom Implicit Haptic Rendering

Part 13: AI Applications - Mobile ApplicationsInternational audienceThis paper introduces a six degrees of freedom haptic rendering scheme based on an implicit support plane mapping representation of the object geometries. The proposed scheme enables, under specific assumptions, the analytical reconstruction of the rigid 3D object’s surface, using the equations of the support planes and their respective distance map. As a direct consequence, the problem of calculating the force feedback can be analytically solved using only information about the 3D object’s spatial transformation and position of the haptic probe. Several haptic effects are derived by the proposed mesh-free haptic rendering formulation. Experimental evaluation and computational complexity analysis demonstrates that the proposed approach can reduce significantly the computational cost when compared to existing methods

A computational basis for conic arcs and boolean operations on conic polygons

Abstract. We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately leads to a realization of regularized boolean operations on conic polygons. A conic polygon, or polygon for short, is anything that can be obtained from linear or conic halfspaces ( = the set of points where a linear or quadratic function is non-negative) by regularized boolean operations. The algorithm and its implementation are complete (they can handle all cases), exact (they give the mathematically correct result), and efficient (they can handle inputs with several hundred primitives).

Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries

SCOPUS: ar.kinfo:eu-repo/semantics/publishe

Partitioning space for range queries

SIGLEAvailable from British Library Document Supply Centre- DSC:7769.09285(WU-DCS-RR--118) / BLDSC - British Library Document Supply CentreGBUnited Kingdo