Results 1  10
of
15
Dynamic Trees and Dynamic Point Location
 In Proc. 23rd Annu. ACM Sympos. Theory Comput
, 1991
"... This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using ..."
Abstract

Cited by 46 (11 self)
 Add to MetaCart
This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using a centroid decomposition of the dual tree to drive searches in the primal tree. These trees are maintained via the linkcut trees structure of Sleator and Tarjan, leading to a scheme that achieves vertex insertion/deletion in O(log n) time, insertion/deletion of kedge monotone chains in O(log n + k) time, and answers queries in O(log 2 n) time, with O(n) space, where n is the current size of subdivision S. The techniques described also allow for the dual operations expand and contract to be implemented in O(log n) time, leading to an improved method for spatial pointlocation in a 3dimensional convex subdivision. In addition, the interlacedtree approach is applied to online pointlo...
Shapes And Implementations In ThreeDimensional Geometry
, 1993
"... Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is often useful or required to compute what one might call the "shape" of the set. For that purpose, this thesis deals with the formal notion of the family of alpha shapes of a finite point set in th ..."
Abstract

Cited by 37 (5 self)
 Add to MetaCart
Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is often useful or required to compute what one might call the "shape" of the set. For that purpose, this thesis deals with the formal notion of the family of alpha shapes of a finite point set in three dimensional space. Each shape is a welldefined polytope, derived from the Delaunay triangulation of the point set, with a real parameter controlling the desired level of detail. Algorithms and data structures are presented that construct and store the entire family of shapes, with a quadratic time and space complexity, in the worst case.
Experiments in Competence Acquisition for Autonomous Mobile Robots
, 1992
"... This thesis addresses the problem of intelligent control of autonomous mobile robots, particularly under circumstances unforeseen by the designer. As the range of applications for autonomous robots widens and increasingly includes operation in unknown environments (exploration) and tasks which are n ..."
Abstract

Cited by 27 (16 self)
 Add to MetaCart
This thesis addresses the problem of intelligent control of autonomous mobile robots, particularly under circumstances unforeseen by the designer. As the range of applications for autonomous robots widens and increasingly includes operation in unknown environments (exploration) and tasks which are not clearly specifiable a priori (maintenance work), this question is becoming more and more important. It is argued that in order to achieve such flexibility in unforeseen situations it is necessary to equip a mobile robot with the ability to autonomously acquire the necessary task achieving competences, through interaction with the world. Using mobile robots equipped with selforganising, behaviourbased controllers, experiments in the autonomous acquisition of motor competences and navigational skills were conducted to investigate the viability of this approach. A controller architecture is presented that allows extremely fast acquisition of motor competences such as obstacle avoidance, wa...
Query processing for distance metrics
 Proc. of 16th VLDB Conf
, 1990
"... In applications such as vision and molecular biology, a common problem is to find the similar objects to a given target (according to some distance measure) in a large database. This paper presents a scheme for query processing in such situations. The basic strategy is to (partially) precompute in ..."
Abstract

Cited by 21 (2 self)
 Add to MetaCart
In applications such as vision and molecular biology, a common problem is to find the similar objects to a given target (according to some distance measure) in a large database. This paper presents a scheme for query processing in such situations. The basic strategy is to (partially) precompute interobject distances, and by using the distance information and the triangle inequality, we eliminate the need to calculate certain object distances while evaluating queries. We propose several heuristics that may speed up query evaluation. A series of experiments are then performed to evaluate the effectiveness of our scheme and the relative performance of the heuristics for different queries. Finally we investigate the possibility of parallelizing our scheme through simulation. Our results show that parallelism is best applied in the later stages in evaluating a query. 1
Lineartime reconstruction of Delaunay triangulations with applications
 In Proc. Annu. European Sympos. Algorithms, number 1284 in Lecture Notes Comput. Sci
, 1997
"... Many of the computational geometers' favorite data structures are planar graphs, canonically determined by a set of geometric data, that take \Theta(n log n) time to compute. Examples include 2d Delaunay triangulation, trapezoidations of segments, and constrained Voronoi diagrams, and 3d convex hu ..."
Abstract

Cited by 20 (3 self)
 Add to MetaCart
Many of the computational geometers' favorite data structures are planar graphs, canonically determined by a set of geometric data, that take \Theta(n log n) time to compute. Examples include 2d Delaunay triangulation, trapezoidations of segments, and constrained Voronoi diagrams, and 3d convex hulls. Given such a structure, one can determine a permutation of the data in O(n) time such that the data structure can be reconstructed from the permuted data in O(n) time by a simple incremental algorithm. As a consequence, one can permute a data file to "hide" a geometric structure, such as a terrian model based on the Delaunay triangulation of a set of sampled points, without disrupting other applications. One can even include "importance" in the ordering so the incremental reconstruction produces approximate terrain models as the data is read or received. For the Delaunay triangulation, we can also handle input in degenerate position, even though the data structures may no longer be cano...
Efficient Algorithms for Line and Curve Segment Intersection Using Restricted Predicates
, 1999
"... We consider whether restricted sets of geometric predicates support efficient algorithms to solve line and curve segment intersection problems in the plane. Our restrictions are based on the notion of algebraic degree, proposed by Preparata and others as a way to guide the search for efficient al ..."
Abstract

Cited by 16 (3 self)
 Add to MetaCart
We consider whether restricted sets of geometric predicates support efficient algorithms to solve line and curve segment intersection problems in the plane. Our restrictions are based on the notion of algebraic degree, proposed by Preparata and others as a way to guide the search for efficient algorithms that can be implemented in more realistic computational models than the Real RAM.
Computational Geometry
 in optimization 2.5D and 3D NC surface machining. Computers in Industry
, 1996
"... Introduction Computational geometry evolves from the classical discipline of design and analysis of algorithms, and has received a great deal of attention in the last two decades since its inception in 1975 by M. Shamos[108]. It is concerned with the computational complexity of geometric problems t ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
Introduction Computational geometry evolves from the classical discipline of design and analysis of algorithms, and has received a great deal of attention in the last two decades since its inception in 1975 by M. Shamos[108]. It is concerned with the computational complexity of geometric problems that arise in various disciplines such as pattern recognition, computer graphics, computer vision, robotics, VLSI layout, operations research, statistics, etc. In contrast with the classical approach to proving mathematical theorems about geometryrelated problems, this discipline emphasizes the computational aspect of these problems and attempts to exploit the underlying geometric properties possible, e.g., the metric space, to derive efficient algorithmic solutions. The classical theorem, for instance, that a set S is convex if and only if for any 0 ff 1 the convex combination ffp + (1 \Gamma<F
Computer Graphics
, 1996
"... INTRODUCTION Computer graphics is often given as a prime application area for the techniques of computational geometry. The histories of the two fields have a great deal of overlap, with similar methods (e.g. sweepline and area subdivision algorithms) arising independently in each. Both fields hav ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
INTRODUCTION Computer graphics is often given as a prime application area for the techniques of computational geometry. The histories of the two fields have a great deal of overlap, with similar methods (e.g. sweepline and area subdivision algorithms) arising independently in each. Both fields have often focused on similar problems, although with different computational models. For example, hidden surface removal (visible surface identification) is a fundamental problem of computer graphics. This problem has also motivated many researchers in computational geometry. At the same time, as the fields have matured, they have brought different requirements to similar problems. Here, we aim to highlight both similarities and differences between the fields. Computational geometry is fundamentally concerned with the efficient quantitative representation and manipulation of ideal geometric entities to produce exact results. Computer graphics shares these goals, in part. However, graphi
Local tests for consistency of support hyperplane data
 J. Math. Imaging and Vision
, 1995
"... Abstract. Support functions and samples of convex bodies in R ~ are studied with regard to conditions for their validity or consistency. Necessary and sufficient conditions for a function to be a support function are reviewed in a general setting. An apparently little known classical such result for ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
Abstract. Support functions and samples of convex bodies in R ~ are studied with regard to conditions for their validity or consistency. Necessary and sufficient conditions for a function to be a support function are reviewed in a general setting. An apparently little known classical such result for the planar case due to Rademacher and based on a determinantal inequality is presented and a generalization to, arbitrary dimensions is developed. These conditions are global in the sense that they involve values of the support function at widely separated points. The corresponding discrete problem of determining the validity of a set of samples of a support function is treated. Conditions similar to the continuous inequality results are given for the consistency of a set of discrete support observations. These conditions are in terms of a series of local inequality tests involving only neighboring support samples. Our results serve to generalize existing planar conditions to arbitrary dimensions by providing a generalization of the notion of nearest neighbor for plane vectors which utilizes a simple positive cone condition on the respective support sample normals.