On the identification of the convex hull of a finite set of points in the plane

Jarvis, Ray

doi:10.1016/0020-0190(73)90020-3

Cited by 555 publications

(259 citation statements)

References 1 publication

Supporting

Mentioning

255

Contrasting

Unclassified

Order By: Relevance

“…We use a technique similar to Jarvis' march [38]. Given a current maximal point q, we can find the next maximal point q using O n r log r comparisons.…”

Section: Our New Bottom-up Algorithmmentioning

confidence: 99%

On Constant Factors in Comparison-Based Geometric Algorithms and Data Structures

Chan

Lee

2015

Discrete Comput Geom

View full text Add to dashboard Cite

Many standard problems in computational geometry have been solved asymptotically optimally as far as comparison-based algorithms are concerned, but there has been little work focusing on improving the constant factors hidden in big-Oh bounds on the number of comparisons needed. In this thesis, we consider orthogonal-type problems and present a number of results that achieve optimality in the constant factors of the leading terms, including:

show abstract

“…We use a technique similar to Jarvis' march [38]. Given a current maximal point q, we can find the next maximal point q using O n r log r comparisons.…”

Section: Our New Bottom-up Algorithmmentioning

confidence: 99%

On Constant Factors in Comparison-Based Geometric Algorithms and Data Structures

Chan

Lee

2015

Discrete Comput Geom

View full text Add to dashboard Cite

show abstract

“…Therefore, one can only reason about voxels that are not occluded by any other "on" voxels in each view. To remedy this, we project the eight corners of each voxel into each view, and compute the convex hull of these eight points via the gift wrapping algorithm (Jarvis 1973). We then at each pixel p i keep track the closest voxel from T for which p i was in the projection of its convex hull (i.e., v j is the voxel closest to p i which is along p i 's line of sight).…”

Section: Updating the Occlusion Modelmentioning

confidence: 99%

Recovery and Reasoning About Occlusions in 3D Using Few Cameras with Applications to 3D Tracking

Keck

Davis

2011

Int J Comput Vis

View full text Add to dashboard Cite

In this work we propose algorithms to learn the locations of static occlusions and reason about both static and dynamic occlusion scenarios in multi-camera scenes for 3D surveillance (e.g., reconstruction, tracking). We will show that this leads to a computer system which is able to more effectively track (follow) objects in video when they are obstructed from some of the views. Because of the nature of the application area, our algorithm will be under the constraints of using few cameras (no more than 3) that are configured wide-baseline. Our algorithm consists of a learning phase, where a 3D probabilistic model of occlusions is estimated per-voxel, per-view over time via an iterative framework. In this framework, at each frame the visual hull of each foreground object (person) is computed via a Markov Random Field that integrates the occlusion model. The model is then updated at each frame using this solution, providing an iterative process that can accurately estimate the occlusion model over time and overcome the few-camera constraint. We demonstrate the application of such a model to a number of areas, including visual hull reconstruction, the reconstruction of the occluding structures themselves, and 3D tracking.

show abstract

“…Then, we can deduce that the edges of a zonogon are segments of the form [P ; P + 2g] where P is a vertex of the zonogon and g a generator. Therefore, it is sufficient to scan the generators in trigonometric (or anti-trigonometric) order to scan the vertices of the zonogon in a way that is similar to the gift wrapping algorithm [17]. This idea is implemented in Algorithm 3.…”

Section: Intersection Of a Zonogon And A Linementioning

confidence: 99%

Zonotope/Hyperplane Intersection for Hybrid Systems Reachability Analysis

Girard

Guernic

2008

Hybrid Systems: Computation and Control

View full text Add to dashboard Cite

Abstract. In this paper, we are concerned with the problem of computing the reachable sets of hybrid systems with (possibly high dimensional) linear continuous dynamics and guards defined by switching hyperplanes. For the reachability analysis of the continuous dynamics, we use an efficient approximation algorithm based on zonotopes. In order to use this technique for the analysis of hybrid systems, we must also deal with the discrete transitions in a satisfactory (i.e. scalable and accurate) way. For that purpose, we need to approximate the intersection of the continuous reachable sets with the guards enabling the discrete transitions. The main contribution of this paper is a novel algorithm for computing efficiently a tight over-approximation of the intersection of (possibly high-order) zonotopes with a hyperplane. We show the accuracy and the scalability of our approach by considering two examples of reachability analysis of hybrid systems.

show abstract

On the identification of the convex hull of a finite set of points in the plane

Cited by 555 publications

References 1 publication

On Constant Factors in Comparison-Based Geometric Algorithms and Data Structures

On Constant Factors in Comparison-Based Geometric Algorithms and Data Structures

Recovery and Reasoning About Occlusions in 3D Using Few Cameras with Applications to 3D Tracking

Zonotope/Hyperplane Intersection for Hybrid Systems Reachability Analysis

Contact Info

Product

Resources

About