Minimal enclosing parallelepiped in 3D

Minimal enclosing parallelepiped in 3D

An Interval Method for Initial Value Problems in Linear Ordinary Differential Equations

Interval numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs) compute bounds that contain the solution of an IVP for an ODE. This paper develops and studies an interval method for computing bounds on the solution of a linear ODE. Our method is based on enclosing the terms in the formula for the closed form solution using Taylor series and various interv...

A Line Generation Algorithm over 3D Body-centered Cubic Lattice

New line generation algorithm is proposed for generating lines over 3D body-centered cubic lattice, a kind of optimal lattice in 3D space. The main contribution in this paper is employing the 3D Bresenham algorithm, a popular algorithm for generating 3D lines on a cubic lattice, to produce the BCC lattice occupied by 3D lines, with the help of the adjunct parallelepiped space, having the same c...

Uniqueness results for minimal enclosing ellipsoids

We prove uniqueness of the minimal enclosing ellipsoid with respect to strictly eigenvalue convex size functions. Special examples include the classic case of minimal volume ellipsoids (Löwner ellipsoids), minimal surface area ellipsoids or, more generally, ellipsoids that are minimal with respect to quermass integrals.

Enclosing Surfaces for Point Clusters Using 3D Discrete Voronoi Diagrams

Point clusters occur in both spatial and non-spatial data. In the former context they may represent segmented particle data, in the latter context they may represent clusters in scatterplots. In order to visualize such point clusters, enclosing surfaces lead to much better comprehension than pure point renderings. We propose a flexible system for the generation of enclosing surfaces for 3D poin...