Abstract
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.
Highlights
Three-dimensional (3D) modeling and 3D printing are rapidly developing computer fields [1,2,3]
(3), the Cayley ovalcase can of be the defined as aoval geometric points the sum Cayley oval can be defined as a geometric location of points with the of distances from two focal points which equals the product of distances to the foci: sum of distances from two focal points which equals the product of distances to the foci: r1 + r2 = r1 ·r2
The generationofofsymmetric symmetric closed curves two or foci more is of particular practical interest
Summary
Three-dimensional (3D) modeling and 3D printing are rapidly developing computer fields [1,2,3]. For example, Cayley ovals, which find application in connection with studies of elementary particle trajectories [26,27,28] Representing such generalized curves in CAD systems is generally carried out by the approximation of parametric curves (Bezier, B-splines, NURBS) [7,8,9,10,11,12,13]. 2 of 17it possible to obtain a large amount of numerical data containing the curve plot coordinates This provides the best approximation in CAD systems. Numerical method makes it possible to obtain a in a similar way A in high the Creo system large amount of numerical data containing the curve plot coordinates.
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