Universal software platform for visualizing class F curves, log-aesthetic curves and development of applied CAD systems

Ziatdinov, Rushan; Muftejev, Valerijan G.; Akhmetshin, Rustam I.; Zelev, Alexander P.; Nabiyev, Rifkat I.; Mardanov, Albert R.

doi:10.26583/sv.10.3.06

Cited by 3 publications

(3 citation statements)

References 5 publications

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“…Thus, building a very smooth trajectory of the motion requires a minimum number of reference points of the generated spline motion trajectory and a high level of smoothness of at least the 4th order, smooth torsion of the spatial curve, restriction of the maximum value of curvature and the variation rate of curvature, and minimization of the potential energy function. Functional curves satisfying these requirements are called class F curves 4,5 [29], [36]. The authors do not set themselves the task of giving a simple and precise mathematical definition of such curves.…”

Section: Modelling Methodsmentioning

confidence: 99%

Multi-Criteria Assessment of Shape Quality in CAD Systems of the Future

Muftejev

Ziatdinov

Nabiyev

2020

Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2

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Unlike many other works, where authors are usually focused on one or two quality criteria, the current manuscript, which is a generalization of the article [35] published in Russian, offers a multi-criteria approach to the assessment of the shape quality of curves that constitute component parts of the surfaces used for the computer modelling of object shapes in various types of design. Based on the analysis of point particle motion along a curved path, requirements for the quality of functional curves are proposed: a high order of smoothness, a minimum number of curvature extrema, minimization of the maximum value of curvature and its variation rate, minimization of the potential energy of the curve, and aesthetic analysis from the standpoint of the laws of technical aesthetics. The authors do not set themselves the task of giving a simple and precise mathematical definition of such curves. On the contrary, this category can include various curves that meet certain quality criteria, the refinement and addition of which is possible in the near future. Engineering practice shows that quality criteria can change over time, which does not diminish the need to develop multi-criteria methods for assessing the quality of geometric shapes. Technical issues faced during edge rounding in 3D models that affect the quality of industrial design product shape have been reviewed as an example of the imperfection of existing CAD systems.

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Section: Modelling Methodsmentioning

confidence: 99%

Multi-Criteria Assessment of Shape Quality in CAD Systems of the Future

Muftejev

Ziatdinov

Nabiyev

2020

Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2

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“…This family of curves includes the above-described generalized family based on the power average, because if ϕ(x) = x p , Equation (10) transforms to Equation (5).…”

Section: Family Of Generalized Curves Based On the "Kolmogorov Mean" Conceptmentioning

confidence: 99%

“…CAD systems present an essential part of production in almost every industry, which concerns the manufacturing of finished products, preforming for molds, prototypes etc. Design in such systems requires appropriate mathematical software, which enables the high-precision construction of closed curves and surfaces, in particular class A surfaces with high smoothness criteria [5,6].…”

Section: Introductionmentioning

confidence: 99%

Approximation of Generalized Ovals and Lemniscates towards Geometric Modeling

et al. 2021

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This paper considers an approach towards the building of new classes of symmetric closed curves with two or more focal points, which can be obtained by generalizing classical definitions of the ellipse, Cassini, and Cayley ovals. A universal numerical method for creating such curves in mathematical packages is introduced. Specific aspects of the provided numerical data in computer-aided design systems with B-splines for three-dimensional modeling are considered. The applicability of the method is demonstrated, as well as the possibility to provide high smoothness of the curvature profile at the specified accuracy of modeling.

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Line graphics for visualization of surfaces and curves on them

Velickovic

Dolicanin

2023

Filomat

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In this paper, we describe the main principles of our approach for the visualization of surfaces and curves on them in three-dimensional space by the use of line graphics. We also compare our approach with the standard method of polygon mesh. Mainly, we discuss the representation of surfaces, special lines on surfaces and lines of intersections of surfaces. Furthermore, we address the problems of visibility and finding the contour lines of surfaces. Finally we apply our method for visualizing some selected topic in mathematics.

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Universal software platform for visualizing class F curves, log-aesthetic curves and development of applied CAD systems

Cited by 3 publications

References 5 publications

Multi-Criteria Assessment of Shape Quality in CAD Systems of the Future

Multi-Criteria Assessment of Shape Quality in CAD Systems of the Future

Approximation of Generalized Ovals and Lemniscates towards Geometric Modeling

Line graphics for visualization of surfaces and curves on them

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