Related papers: Convex Hulls: Surface Mapping onto a Sphere

Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…

Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set representation for 2-dimensional data. The first one is an exact…

We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…

Convex hulls are fundamental geometric tools used in a number of algorithms. This paper presents a fast, simple to implement and robust Smart Convex Hull (S-CH) algorithm for computing the convex hull of a set of points in E3. This…

This paper presents an alternate choice of computing the convex hulls (CHs) for planar point sets. We firstly discard the interior points and then sort the remaining vertices by x- / y- coordinates separately, and later create a group…

The Convex Hull algorithm is one of the most important algorithms in computational geometry, with many applications such as in computer graphics, robotics, and data mining. Despite the advances in the new algorithms in this area, it is…

In this article, a new solution for the convex hull problem has been presented. The convex hull is a widely known problem in computational geometry. As nature is a rich source of ideas in the field of algorithms, the solution has been…

A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and…

In recent years, applications such as real-time simulations, autonomous systems, and video games increasingly demand the processing of complex geometric models under stringent time constraints. Traditional geometric algorithms, including…

We present a convex hull algorithm that is accelerated on commodity graphics hardware. We analyze and identify the hurdles of writing a recursive divide and conquer algorithm on the GPU and divise a framework for representing this class of…

This paper presents a new O(nlog(n)) algorithm for computing the convex hull of a set of 3 dimensional points. The algorithm first sorts the point in (x,y,z) then incrementally adds sorted points to the convex hull using the constraint that…

We describe a pure divide-and-conquer parallel algorithm for computing 3D convex hulls. We implement that algorithm on GPU hardware, and find a significant speedup over comparable CPU implementations.

The convex hull of a set of points, $C$, serves to expose extremal properties of $C$ and can help identify elements in $C$ of high interest. For many problems, particularly in the presence of noise, the true vertex set (and facets) may be…

This paper evaluates several improvements to the memory layout of convex hulls to improve computation times for support point queries. The support point query is a fundamental part of common collision algorithms, and the work presented…

The convex hull is a fundamental geometrical structure for many applications where groups of points must be enclosed or represented by a convex polygon. Although efficient sequential convex hull algorithms exist, and are constantly being…

Convex hulls are useful as tight bounding proxies for a variety of tasks including collision detection, ray intersection, and distance computation. Unfortunately, the complexity of polyhedral convex hulls grows linearly with their input. We…

We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…

Region extraction is necessary in a wide range of applications, from object detection in autonomous driving to analysis of subcellular morphology in cell biology. There exist two main approaches: convex hull extraction, for which exact and…

In this paper, an effective method with time complexity of $\mathcal{O}(K^{3/2}N^2\log \frac{K}{\epsilon_0})$ is introduced to find an approximation of the convex hull for $N$ points in dimension $n$, where $K$ is close to the number of…

This paper investigates the transformation of a convex hull, derived from a d-dimensional point cloud, into a concave surface. Our primary focus is on the development of a methodology that ensures all points in the point cloud are…