Scientific Visualization, 2019, volume 11, number 1, pages 1 - 10, DOI: 10.26583/sv.11.1.01
Construction of linear structure of a skeleton for the closed path of complex geometry on the basis of the method of functional voxel modeling
Authors: A.B. Tolok1,A, M.A. Loktev2,A, N.B. Tolok3,B, N.D. Zhilina4,C, M.B. Lagunova5,C
A ÌSÒU «STANKIN», Moscow, Russia
B ICS of RAS, Moscow, Russia
C NNGASU, Nizhny Novgorod, Russia
1 ORCID: 0000-0002-7257-9029, a.tolok@stankin.ru
2 ORCID: 0000-0002-0465-1201, m.loktev@stankin.ru
3 ORCID: 0000-0002-5511-4852, nat_tolok@mail.ru
4 ORCID: 0000-0002-4814-2716, zhilina@nngasu.ru
5 ORCID: 0000-0002-0671-8609, logunova@nngasu.ru
Abstract
In this paper the way of construction of straight skeleton for complex closed contours described by means of a mathematical apparatus of R-functions is proposed. Applied a-system for the R-functional of description of the circuit and shown the results of the function at various values of the ratio a. Shows the transition from the organization of separate extreme points of R-functional surfaces to the organization of the linear structure of the skeleton of the zero contour. Here we describe the principle of M-images constructing on the basis of the method of functional voxel modeling (FVM). FVM-method, is the organizing principle of symbolic-graphic information, combining the analytic form of the description of a multidimensional model with a voxel representation of its local geometric characteristics. Selected class of M-images allows to automate the definition of the points and lines making a skeleton structure on the basis of delimitation of color transition. Such approach is based on preliminary representation of graphic information as a functional voxel model and allows to considerably simplify the computational process of search for solutions. Also we make the comparative analysis of a classical way of construction of straight skeleton with the offered computer graphic approach.
Keywords: functional Voxel Modeling, M-image, R-functions, straight skeleton.
