Related papers: Calculating ellipse overlap areas
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…
The problem deals with an exact calculation of the intersection area of a circle arbitrary placed on a grid of square shaped elements with gaps between them (finite fill factor). Usually an approximation is used for the calculation of the…
An exact conservative remapping scheme requires overlaps between two meshes and a reconstruction scheme on the old cells (Lagrangian mesh). While the are intensive discussion on reconstruction schemes, there are relative sparse discussion…
Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…
A complete treatment of the intersections of two geodesics on the surface of an ellipsoid of revolution is given. With a suitable metric for the distances between intersections, bounds are placed on their spacing. This leads to fast and…
We describe a method by which the number of intersections one ellipse makes inside the plane of another can be determined. The method is based on applying a transformation that reverts one ellipse to the unit circle, and examining the…
We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and…
This paper attacks the following problem. We are given a large number $N$ of rectangles in the plane, each with horizontal and vertical sides, and also a number $r<N$. The given list of $N$ rectangles may contain duplicates. The problem is…
This paper describes a 2-D graphics algorithm that uses shifts and adds to precisely plot a series of points on an ellipse of any shape and orientation. The algorithm can also plot an elliptic arc that starts and ends at arbitrary angles.…
The formula for the area of a rhumb polygon, a polygon whose edges are rhumb lines on an ellipsoid of revolution, is derived and a method is given for computing the area accurately. This paper also points out that standard methods for…
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.…
Given a rational elliptic surface X over an algebraically closed field, we investigate whether a given natural number k can be the intersection number of two sections of X. If not, we say that k a gap number. We try to answer when gap…
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…
For two independent Erd\H{o}s-R\'enyi graphs $\mathbf G(n,p)$, we study the maximal overlap (i.e., the number of common edges) of these two graphs over all possible vertex correspondence. We present a polynomial-time algorithm which finds a…
We show how the Eulcidean algorithm for polynomials can be used to find the intersection points, with multiplicities, of two plane algebraic curves.
We propose a simple derivation of an upper bound for the perimeter of an ellipse. The procedure, which relies on the use of elliptic integrals, consists in introducing, via inequalities and convexity properties, specific integrals which can…
The article proposes a new method for finding the triangle-triangle intersection in 3D space, based on the use of computer graphics algorithms -- cutting off segments on the plane when moving and rotating the beginning of the coordinate…
The Douglas-Rachford splitting algorithm is a classical optimization method that has found many applications. When specialized to two normal cone operators, it yields an algorithm for finding a point in the intersection of two convex sets.…
Generalized Pythagoras trees were developed for visualizing hierarchical data, producing organic, fractal-like representations. However, the drawback of the original layout algorithm is visual overlap of tree branches. To avoid such…
We study the surface area of an ellipsoid in n-dimensional Euclidean space as the function of the lengths of their major semi-axes. We write down an explicit formula as an integral over the unit sphere, use the formula to derive convexity…