Related papers: B\"urgi's "Kunstweg" - geometric approach
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
Let $S_g$ denote a closed, orientable surface of genus $g \geq 2$ and $\mathcal{C}(S_g)$ be the associated curve complex. The mapping class group of $S_g$, $Mod(S_g)$ acts on $\mathcal{C}(S_g)$ by isometries. Since Dehn twists about certain…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
The intersection of two orthogonal cylinders represents a classical problem in computational geometry with direct applications to engineering design, manufacturing, and numerical simulation. While analytical solutions exist for the fully…
Algorithms for the fast and exact computation of Wigner matrices are described and their application to a fast and massively parallel 4pi convolution code between a beam and a sky is also presented.
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
Comparison to traditionally accurate computing, approximate computing focuses on the rapidity of the satisfactory solution, but not the unnecessary accuracy of the solution. Approximate bisimularity is the approximate one corresponding to…
We give new positive and negative results (some conditional) on speeding up computational algebraic geometry over the reals: (1) A new and sharper upper bound on the number of connected components of a semialgebraic set. Our bound is novel…
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…
We study collections of curves in generic position on a closed surface whose complement consists of one disk only, up to orientation-preserving homeomorphism of the surface. We define a surgery operation on the set of such collections and…
We generalize Artin's three main algebraicity theorems to the setting of supergeometry: Artin approximation, algebraization of formal moduli, and algebraization of stacks.
Line intersection with convex and un-convex polygons or polyhedron algorithms are well known as line clipping algorithms and very often used in computer graphics. Rendering of geometrical problems often leads to ray tracing techniques, when…
Minimal surfaces and Einstein manifolds are among the most natural structures in differential geometry. Whilst minimal surfaces are well understood, Einstein manifolds remain far less so. This exposition synthesises together a set of…
We consider the problem of finding an optimal piecewise linear path (polygonal line) connecting two given points with the possibility of making n turns at some points (the absolute value of each turn angle does not exceed a prescribed…
B\'ezier curves provide the basic building blocks of graphic design in 2D. In this paper, we port B\'ezier curves to manifolds. We support the interactive drawing and editing of B\'ezier splines on manifold meshes with millions of…
When the sequence of regular polygons with consecutively increasing numbers of sides is joined edge-to-edge in a single direction while minimizing bending, the resulting structure assumes the shape of a logarithmic spiral. This paper proves…
This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polyloga- rithms. By using the approach, we establish some relations between…
The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer.…
We give a survey of geometric approaches to the topological 4-dimensional surgery and 5-dimensional s-cobordism conjectures, with a focus on the study of surfaces in 4-manifolds. The geometric lemma underlying these conjectures is a…