Curve Fairing Via Geometric Of Hermite Interpolation

In computer aided geometric design, the shape of the product has manyrequirements, one of which is the shape of fairing. With the increasingly fiercemarket competition, the appearance of new products, flowing lines, surfacesmoothing is particularly important. However, since the calculation and themeasurement data is inevitably error, data obtained by these data curves andsurfaces are generally required for smoothing, to meet the requirements ofdesigners of “good appearance” of curves and surfaces.Constructed based on geometric of Hermite interpolation plane cubic Béziercurve. When the curvature is prescribed at each knot, it has a6-th order accurate.Further constructed space of cubic Bézier curve, when the curvature is prescribed ateach knot, it has a5-th order accurate. Similar to the rational cubic Bézier splinecurve，rational cubic Ball parameter curves also have good conformal nature, and insome respects superior to the rational cubic Bézier spline curve, so according to thetheory of rational Ball parameter curves given two rational cubic Ball parametercurves stitching conditions.