Journal ArticleDOI
Approximation of Physical Spline with Large Deflections
Viktor Korotkiy,Igor' Vitovtov +1 more
Reads0
Chats0
TLDR
In this paper polynomial and parametric methods for approximation of experimentally produced physical spline with large deflections are considered and it has been shown that standard cubic Bézier curves have a significant computational advantage over Ferguson ones.Abstract:
Physical spline is a resilient element whose cross-sectional dimensions are very small compared to its axis’s length and radius of curvature. Such a resilient element, passing through given points, acquires a "nature-like" form, having a minimum energy of internal stresses, and, as a consequence, a minimum of average curvature. For example, a flexible metal ruler, previously used to construct smooth curves passing through given coplanar points, can be considered as a physical spline. The theoretical search for the equation of physical spline’s axis is a complex mathematical problem with no elementary solution. However, the form of a physical spline passing through given points can be obtained experimentally without much difficulty. In this paper polynomial and parametric methods for approximation of experimentally produced physical spline with large deflections are considered. As known, in the case of small deflections it is possible to obtain a good approximation to a real elastic line by a set of cubic polynomials ("cubic spline"). But as deflections increase, the polynomial model begins to differ markedly from the experimental physical spline, that limits the application of polynomial approximation. High precision approximation of an elastic line with large deflections is achieved by using a parameterized description based on Ferguson or Bezier curves. At the same time, not only the basic points, but also the tangents to the elastic line of the real physical spline should be given as boundary conditions. In such a case it has been shown that standard cubic Bezier curves have a significant computational advantage over Ferguson ones. Examples for modelling of physical splines with free and clamped ends have been considered. For a free spline an error of parametric approximation is equal to 0.4 %. For a spline with clamped ends an error of less than 1.5 % has been obtained. The calculations have been performed with SMath Studio computer graphics system.read more
Citations
More filters
Journal ArticleDOI
Functional-Voxel Modelling of Bezie Curves
TL;DR: Two approaches to construction a functional-voxel model of the Bezier curve based on the application of a two-dimensional function for local zeroing (FLOZ) and a nil segment on the positive area of function values are proposed.
Journal ArticleDOI
Content of the “Geometric Modeling” Course for the “Mathematics and Computer Science” Training Program
A. V. Zaharov,Yulia Zakharova +1 more
TL;DR: The paper may be interesting for teachers of “Geometric Modeling” and “Computer Graphics” courses aimed to students with a specialization in mathematics and information, as well as to those who independently develop software interfaces for algorithms of geometric modeling.
Journal ArticleDOI
All-Russian Scientific and Methodological Conference «Problems of Engineering Geometry» and the Seminar «Geometry and Graphics» 2021
TL;DR: In 2021, in terms of the success of the seminar "Geometry and Graphics" and the conference "Problems of Engineering Geometry", the success rate increased and judging by the number of reports, scientific work on the profile of the department is carried out in a small number of departments.
Journal ArticleDOI
Geometric modeling of the contour arcs passing through the predefined points
TL;DR: In this paper , the authors proposed a method based on modification of Bezier's curve with preservation of tangents in its initial and/or final points, which helps to reduce the piecewise character of composite curves when building curves.
References
More filters
BookDOI
Geometrie und ihre Anwendungen in Kunst, Natur und Technik
TL;DR: Allgemeine anwendungen mathematik de de kunstobjekten verschlungene, de kundenrezensionen geometrie und ihre, überall geometries wissenschaft, €n sachunterricht 3 4 klasse natur und leben.
Journal ArticleDOI
The Geometric Component Of Technical Innovations
Николай Сальков,Nikolay Sal'kov +1 more
TL;DR: In technical inventions related to innovative developments, the role of one of the main components belongs to geometry, and in technical inventions the geometrical component is the determining one, this statement is proved by examples developed based on geometry of following inventions.
Journal ArticleDOI
Modern Approaches to Products Design in the Process of Students Teaching in Computer Graphics
Татьяна Усатая,Tat'yana Usataya,Любовь Дерябина,Lyubov' Deryabina,Елена Решетникова,Elena Reshetnikova +5 more
TL;DR: The problem related to improvement of quality in engineering training for students of technical high educational institutions, that today is considered as one of the main tasks for the system of higher professional education, is solved by proposed method.
Journal ArticleDOI
Constructive geometric modeling as graphic disciplines’ teaching prospect
Journal ArticleDOI
Cubic Curves in Engineering Geometry
TL;DR: It has been shown that the cubic curve vector equation (for example, the standard equation of a Bezier curve) can be represented in a point form and examples for constructing segments of cubic curves meeting the given boundary conditions are considered.