Qualitative modification of geometrically oriented methods for constructing spatial curves in C3D FairCurveModeler

Abstract

The article provides a detailed algorithm for improving the C3D FairCurveModeler commands for constructing a class F spatial curve with approximation by a rational cubic spline Bezier curve (NURBzS-curve) and with approximation by a highdegree B-spline curve. The improvement is achieved by optimizing the structure of the Hermite spatial Geometric Determinant when defining it on a spatial virtual curve (V-curve) created on a set of double-tap conical curves. The structure of the Hermite Geometric Determinant is improved by changing the direction of the tangents, taking into account the spatial directions of the tangents at the end points of the conic segments at the step of constructing the set of double-tap conical curves. To demonstrate the modified method, the work shows 1) Improving the quality of a conical spiral modeled by the regular _Helix command
of CAD systems ZWCAD, BricsCAD, AutoCAD by using the C3D FairCurveModeler command for creating a NURBzS-curve. 2) Construction of a B-spline curve of the 8th degree on the points of a conical spiral by the C3D FairCurveModeler command and comparison with similar constructions in the CAD systems 'Rhino Ceros D', 'Alias Design Studio', NX which declare the construction of high quality curves (class A).