К планированию маршрутов в 3D-среде с многовариантной моделью

We present the results of the research on the planning of routes of unmanned vehicles (autonomous moving objects). The routing is based on the multivariant route model (MRM) formed a priori as a set of alternative paths from an initial point to the target one.. The MRM construction is done using the computer method of functional voxel modeling, combining the analytical form of describing a 3D-environment with the voxel representation of its local geometrical characteristics. Synthesis of the motion control and stabilization of the path trajectory are done by representing the control object as a multimode model and applying the reduction method to it.В данной статье излагаются результаты исследований по планированию маршрутов автономных подвижных объектов на априорно сформированной многовариантной модели маршрута (МММ) как множестве альтернативных путей из начальной точки в целевую. Построение МММ основывается на компьютерном методе функционально-воксельного моделирования, сочетающем аналитическую форму описания 3D-сцены с воксельным представлением ее локальных геометрических характеристик. Синтез управления движением и стабилизация траектории движения обеспечиваются представлением объекта управления в форме многорежимной модели и применением к ней метода редукции

Using natural shape statistics of urban form to model social capital

The social aspect is an important but often overlooked part of sustainable development philosophy. In hoping to popularise and show the importance of social sustainable development, this study tries to find a relation between the social environment and urban form. Research in the social capital field provided the methodology to acquire social computational data. The relation between human actions and the environment is noted in many theories, and used in some practices. Human cognition is computationally predictable with natural shape analysis and machine learning methods. In the analysis of shape, a topological skeleton is a proven method to acquire statistical data that correlates with data collected from human experiments. In this study, the analysis of urban form with respect to human cognition was used to acquire computational data for a machine learning model of social capital in counties in the USA Article in English. Socialinio kapitalo modeliavimas taikant pastatų formos statistinę analizę Santrauka Tvarios plėtros teorijoje socialinė aplinka yra pripažinta kaip svarbus veiksnys, tačiau trūksta praktinės metodikos. Ryšio tarp urbanistinės formos ir socialinės aplinkos radimas aktualizuotų ir padėtų populiarinti socialinę tvarią plėtrą. Aplinkos įtaka žmonių tarpusavio elgesiui yra ne kartą aptartas reiškinys, tačiau praktikoje retai taikomas. Ankstesniuose socialinio kapitalo tyrimuose pateikiamos metodologijos ir statistiniai duomenys esamos situacijos analizei atlikti. Kaip žmonės suvokia formas, yra nuspėjama taikant statistinę formos analizę ir dirbtinio intelekto metodologiją – sistemos mokymąsi. Klasifikuojant formas topologinio skeleto metodologija gaunami rezultatai koreliuoja su duomenimis, surinktais per eksperimentą, kuriame žmonės klasifikuoja formas. Taikant žinomas formos analizės metodologijas, atspindinčias suvokimą, buvo surinkti duomenys modeliuoti socialinį kapitalą su sisteminio mokymosi modeliu. Sisteminis mokymasis yra dirbtinio intelekto sritis, kurioje remiantis pateiktais duomenimis automatiškai sukalibruojama kompleksinė matematinė formulė. Modeliuojant socialinį kapitalą su formos skeleto statistiniais duomenimis, geriausi rezultatai pasiekti taikant neuroniniais tinklais pagristą sisteminį mokymąsi. Reikšminiai žodžiai: urbanistinė forma,  formos analizė statis­tiniais metodais, socialinis kapitalas, sisteminis mokymasis, daugiasluoksnis perceptronas

Generalized offsetting of planar structures using skeletons

We study different means to extend offsetting based on skeletal structures beyond the well-known constant-radius and mitered offsets supported by Voronoi diagrams and straight skeletons, for which the orthogonal distance of offset elements to their respective input elements is constant and uniform over all input elements. Our main contribution is a new geometric structure, called variable-radius Voronoi diagram, which supports the computation of variable-radius offsets, i.e., offsets whose distance to the input is allowed to vary along the input. We discuss properties of this structure and sketch a prototype implementation that supports the computation of variable-radius offsets based on this new variant of Voronoi diagrams

Continuously Flattening Polyhedra Using Straight Skeletons

We prove that a surprisingly simple algorithm folds the surface of every convex polyhedron, in any dimension, into a flat folding by a continuous motion, while preserving intrinsic distances and avoiding crossings. The flattening respects the straight-skeleton gluing, meaning that points of the polyhedron touched by a common ball inside the polyhedron come into contact in the flat folding, which answers an open question in the book Geometric Folding Algorithms. The primary creases in our folding process can be found in quadratic time, though necessarily, creases must roll continuously, and we show that the full crease pattern can be exponential in size. We show that our method solves the fold-and-cut problem for convex polyhedra in any dimension. As an additional application, we show how a limiting form of our algorithm gives a general design technique for flat origami tessellations, for any spiderweb (planar graph with all-positive equilibrium stress)

Geometric Multicut

We study the following separation problem: Given a collection of colored objects in the plane, compute a shortest "fence" $F$, i.e., a union of curves of minimum total length, that separates every two objects of different colors. Two objects are separated if $F$ contains a simple closed curve that has one object in the interior and the other in the exterior. We refer to the problem as GEOMETRIC $k$-CUT, where $k$ is the number of different colors, as it can be seen as a geometric analogue to the well-studied multicut problem on graphs. We first give an $O(n^4\log^3 n)$-time algorithm that computes an optimal fence for the case where the input consists of polygons of two colors and $n$ corners in total. We then show that the problem is NP-hard for the case of three colors. Finally, we give a $(2-4/3k)$-approximation algorithm.Comment: 24 pages, 15 figure