Related papers: Computing Overlaps of Two Quadrilateral Mesh Of th…
We present a general algorithm for finding the overlap area between two ellipses. The algorithm is based on finding a segment area (the area between an ellipse and a secant line) given two points on the ellipse. The Gauss-Green formula is…
Mesh simplification is the process of reducing the number of vertices, edges and triangles in a three-dimensional (3D) mesh while preserving the overall shape and salient features of the mesh. A popular strategy for this is edge collapse,…
This paper presents a novel intersection-based remapping method for isoparametric curvilinear meshes within the indirect arbitrary Lagrangian-Eulerian (ALE) framework, addressing the challenges of transferring physical quantities between…
Given two convex polygons $P$ and $Q$ with $n$ and $m$ edges, the maximum overlap problem is to find a translation of $P$ that maximizes the area of its intersection with $Q$. We give the first randomized algorithm for this problem with…
High-order quadrilateral meshes offer superior accuracy and computational efficiency in numerical simulations. However, existing methods struggle to simultaneously preserve boundary/interface features, ensure high quality, and achieve…
In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…
We present an overlapping Schwarz decomposition algorithm for constrained quadratic programs (QPs). Schwarz algorithms have been traditionally used to solve linear algebra systems arising from partial differential equations, but we have…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
We present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…
This paper presents a complete Pascal interpolation scheme for use in the plane geometry mapping applied in association with numerical methods. The geometry of a domain element is approximated by a complete Pascal polynomial. The…
Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…
In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection…
An overlap representation is an assignment of sets to the vertices of a graph in such a way that two vertices are adjacent if and only if the sets assigned to them overlap. The overlap number of a graph is the minimum number of elements…
The problem of mesh matching is addressed in this work. For a given n-sided planar region bounded by one loop of n polylines we are selecting optimal quadrilateral mesh from existing catalogue of meshes. The formulation of matching between…
We present a simple mathematical framework and API for parallel mesh and data distribution, load balancing, and overlap generation. It relies on viewing the mesh as a Hasse diagram, abstracting away information such as cell shape,…
High-quality quadrilateral mesh generation is a fundamental challenge in computer graphics. Traditional optimization-based methods are often constrained by the topological quality of input meshes and suffer from severe efficiency…
We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two properly embedded 1-manifolds $C_1$ and $C_2$ in a compact…
A fundamental problem in shape matching and geometric similarity is computing the maximum area overlap between two polygons under translation. For general simple polygons, the best-known algorithm runs in $O((nm)^2 \log(nm))$ time [Mount,…
Manual preparation of tissue slices for microscopy imaging can introduce tissue tears and overlaps. Typically, further digital processing algorithms such as registration and 3D reconstruction from tissue image stacks cannot handle images…