Related papers: On Deletion in Delaunay Triangulation

Images are an important source of information for spacecraft navigation and for three-dimensional reconstruction of observed space objects. Both of these applications take the form of a triangulation problem when the camera has a known…

We provide a new algorithm for the treatment of the deconvolution problem on the sphere which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. We establish upper bounds for the…

Learning well-separated features in high-dimensional spaces, such as text or image embeddings, is crucial for many machine learning applications. Achieving such separation can be effectively accomplished through the dispersion of…

According to the Hughes phenomenon, the major challenges encountered in computations with learning models comes from the scale of complexity, e.g. the so-called curse of dimensionality. There are various approaches for accelerate learning…

For a given point set $S$ in a plane, we develop a distributed algorithm to compute the $\alpha-$shape of $S$. $\alpha-$shapes are well known geometric objects which generalize the idea of a convex hull, and provide a good definition for…

A blurring algorithm with linear time complexity can reduce the small-scale content of data observed at scattered locations in a spatially extended domain of arbitrary dimension. The method works by forming a Gaussian interpolant of the…

The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k are removed until there are no vertices of degree less than k left. The remaining hypergraph…

Macaulay dual spaces provide a local description of an affine scheme and give rise to computational machinery that is compatible with the methods of numerical algebraic geometry. We introduce eliminating dual spaces, use them for computing…

A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian…

We first prove a new separating hyperplane theorem characterizing when a pair of compact convex subsets $K, K'$ of the Euclidean space intersect, and when they are disjoint. The theorem is distinct from classical separation theorems. It…

Given a convex region in the plane, and a sweep-line as a tool, what is best way to reduce the region to a single point by a sequence of sweeps? The problem of sweeping points by orthogonal sweeps was first studied in [2]. Here we consider…

We give a new algorithm to simplify a given triangulation with respect to a given curve. The simplification uses flips together with powers of Dehn twists in order to complete in polynomial time in the bit-size of the curve.

Intrinsic Delaunay triangulation (IDT) is a fundamental data structure in computational geometry and computer graphics. However, except for some theoretical results, such as existence and uniqueness, little progress has been made towards…

In the Split Vertex Deletion problem, given a graph G and an integer k, we ask whether one can delete k vertices from the graph G to obtain a split graph (i.e., a graph, whose vertex set can be partitioned into two sets: one inducing a…

We present a method for reconstructing triangle meshes from point clouds. Existing learning-based methods for mesh reconstruction mostly generate triangles individually, making it hard to create manifold meshes. We leverage the properties…

Triangulation of a three-dimensional point from at least two noisy 2-D images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite…

A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with different absolute order, writes the conversion as…

An efficient algorithm is required to extract moving objects (asteroids, satellites, and space debris) from enormous data with advances in observational instruments. We have developed an algorithm, tracee, to swiftly detect points aligned…

In this article, recent works on 2D Constrained Delaunay triangulation(CDT) algorithms have been reported. Since the review of CDT algorithms presented by de Floriani(Issues on Machine Vision, Springer Vienna, pg. 95--104, 1989), different…

This paper considers the problem of nonlinear dimensionality reduction. Unlike existing methods, such as LLE, ISOMAP, which attempt to unfold the true manifold in the low dimensional space, our algorithm tries to preserve the nonlinear…