Related papers: Efficiently constructing tangent circles
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
Difference triangle sets are useful in many practical problems of information transmission. This correspondence studies combinatorial and computational constructions for difference triangle sets having small scopes. Our algorithms have been…
We construct explicit maximal symplectic packings of minimal rational and ruled symplectic 4-manifolds by few balls in a very simple way.
We define a new measurement of entanglement, the entanglement of projection, and find that it is natural to write the entanglements of formation and assistance in terms of it. Our measure allows us to describe a new class of quantum erasers…
The goal of the paper is an exposition of the simplest $(2+1)$-TQFTs in a sense following a pictorial approach. In the end, we fell short on details in the later sections where new results are stated and proofs are outlined. Comments are…
We use twisted stable maps to compute the number of rational degree d plane curves having prescribed contacts to a smooth plane cubic.
Discrete geometric estimators aim at estimating geometric characteristics of a shape with only its digitization as input data. Such an estimator is multigrid convergent when its estimates tend toward the geometric characteristics of the…
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…
We investigate a version of Waring's Problem over quaternion rings, focusing on cubes in quaternion rings with integer coefficients. We determine the global upper and lower bounds for the number of cubes necessary to represent all such…
To construct a curve with a monotonic curvature (spiral), and given tangents and curvatures at the ends, the author proposed the following method. From given boundary conditions, the values of two inverse invariants are determined. Then, on…
Consider two circles, externally tangential,and with integer radii R1, R2; and with R1>R2.The two circles have three tangent lines in common, one of them being T1T2. If M is the midpoint of T1T2, and K the point of intersection of the lines…
We present explicit algorithms for computing structured matrix-vector products that are optimal in the sense of Strassen, i.e., using a provably minimum number of multiplications. These structures include Toeplitz/Hankel/circulant,…
In this paper, we prove that if a finite number of rectangles, every of which has at least one integer side, perfectly tile a big rectangle then there exists a strategy which reduces the number of these tiles (rectangles) without violating…
We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in algebraic geometry. For example, we show that every such curve admits either…
In this paper we present two new ideas for generating star patterns and filling the gaps during the tile operation. Firstly, we introduce a novel parametric method based on concentric circles for generating stars and rosettes. Using…
Tackling the many open questions in particle physics will require the construction of new colliders. This short note includes a few considerations that seem to be brought up rarely.
The development of methods to guide the design of neural networks is an important open challenge for deep learning theory. As a paradigm for principled neural architecture design, we propose the translation of high-performing kernels, which…
Because the problem of Apollonius is generally considered over the reals, it suffers from variance of number: there are at most eight circles simultaneously tangent to a given trio of circles, but some configurations have fewer than eight…
This paper considers the shape formation problem within the 3D hybrid model, where a single agent with a strictly limited viewing range and the computational capacity of a deterministic finite automaton manipulates passive tiles through…
We use circle-packing methods to generate quadrilateral meshes for polygonal domains, with guaranteed bounds both on the quality and the number of elements. We show that these methods can generate meshes of several types: (1) the elements…