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Cauchy problems for discrete affine minimal surfaces

Marcos Craizer, Thomas Lewiner, Ralph Teixeira (2012)

Archivum Mathematicum

In this paper we discuss planar quadrilateral (PQ) nets as discrete models for convex affine surfaces. As a main result, we prove a necessary and sufficient condition for a PQ net to admit a Lelieuvre co-normal vector field. Particular attention is given to the class of surfaces with discrete harmonic co-normals, which we call discrete affine minimal surfaces, and the subclass of surfaces with co-planar discrete harmonic co-normals, which we call discrete improper affine spheres. Within this classes,...

Closed-form expressions for the approximation of arclength parameterization for Bézier curves

Mohsen Madi (2004)

International Journal of Applied Mathematics and Computer Science

In applications such as CNC machining, highway and railway design, manufacturing industry and animation, there is a need to systematically generate sets of reference points with prescribed arclengths along parametric curves, with sufficient accuracy and real-time performance. Thus, mechanisms to produce a parameter set that yields the coordinates of the reference points along the curve Q(t) = {x(t), y(t)} are sought. Arclength parameterizable expressions usually yield a parameter set that is necessary...

Close-to-optimal algorithm for rectangular decomposition of 3D shapes

Cyril Höschl IV, Jan Flusser (2019)

Kybernetika

In this paper, we propose a novel algorithm for a decomposition of 3D binary shapes to rectangular blocks. The aim is to minimize the number of blocks. Theoretically optimal brute-force algorithm is known to be NP-hard and practically infeasible. We introduce its sub-optimal polynomial heuristic approximation, which transforms the decomposition problem onto a graph-theoretical problem. We compare its performance with the state of the art Octree and Delta methods. We show by extensive experiments...

Comparison of explicit and implicit difference schemes for parabolic functional differential equations

Zdzisław Kamont, Karolina Kropielnicka (2012)

Annales Polonici Mathematici

Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that the assumptions on the regularity of the given functions are the same for both methods. It...

Complexity of the method of averaging

Dalík, Josef (2010)

Programs and Algorithms of Numerical Mathematics

The general method of averaging for the superapproximation of an arbitrary partial derivative of a smooth function in a vertex a of a simplicial triangulation 𝒯 of a bounded polytopic domain in ℜ d for any d ≥ 2 is described and its complexity is analysed.

Computing homology.

Kaczynski, Tomasz, Mischaikow, Konstantin, Mrozek, Marian (2003)

Homology, Homotopy and Applications

Computing the distribution of a linear combination of inverted gamma variables

Viktor Witkovský (2001)

Kybernetika

A formula for evaluation of the distribution of a linear combination of independent inverted gamma random variables by one-dimensional numerical integration is presented. The formula is direct application of the inversion formula given by Gil–Pelaez [gil-pelaez]. This method is applied to computation of the generalized p -values used for exact significance testing and interval estimation of the parameter of interest in the Behrens–Fisher problem and for variance components in balanced mixed linear...

Currently displaying 241 – 260 of 1088