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Technology is proposed for designing curves of class F in an integrated environment - CAD-system + web-app FairCurveModeler + Mathematica: In CAD, geometric determinants or spline curves are prepared using a wide range of editing tools in 2D and 3D graphic environment (using object snaps, manipulation and visualization functions). In the web-application FairCurveModeler NURBS curves of high quality are approximated and improved by the geometric determinants. Creation and editing curves is performed using a variety of editing tools and a large set of types of the geometrical determinants of the form of a base polyline, tangent polyline, Hermite’s scheme, s-polygon of the NURBS curve.
On the basis of Mathematica, I implement the following functions of the integrated system:
- The document Mathematica "Analysis the quality of the NURBS curves.nb" performs a comprehensive analysis of NURBS curves. The document plots the curvature and displays a wide range of quality parameters of NURBS curves (length, number of inflection points, the number of extrema of curvature, maximum and minimum curvature, the rate of change of curvature, the value of the potential energy of curve);
- The Mathematica notebook "Analysis of the quality and editing of the NURBS curves.nb" performs a comprehensive analysis and interactive editing of NURBS curves with online quality control on graphs of the curvature and of the evolute of the curve. The document allows you to edit the spatial configuration by means of controling the NURBS s-polygon on an arbitrary orthogonal projection;
- The document "Analytic curves to NURBS.nb" prepares geometric determinant of Hermite to approximate of analytic curves in the web-application FairCurveModeler.
Provides examples of work in an integrated system: - An example of improving the cubic b-spline curve in the web-application FairCurveModeler, constructed on “edited points” in AutoCAD, and a comparative analysis of the original and the improved curves in the document Mathematica "Analysis the quality of the NURBS curves.nb"; - An example of improving the b-spline curve of seventh degree in the web-application FairCurveModeler, constructed by edited points in the Alias Design, and comparative analysis of the original and the improved curves in Mathematica notebook "Analysis the quality of the NURBS curves.nb"; - An example of improving the b-spline curve of the 10th degree in the web-application FairCurveModeler, created by direct specifying the s-polygon in AutoCAD and comparative analysis of the original and the improved curves in Mathematica "Analysis the quality of the NURBS curves.nb"; - An example of a comprehensive analysis and improvement of b-spline curve seventh degree in the document Mathematica "Analysis of the quality and editing of the NURBS curves.nb", created on “edited points” in the Alias Design; - An example of constructing NURBS template of initial section of clothoid spiral using Mathematica notebook “Analytic curves to NURBS.nb”.
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