Method for Connection of Two G2 Data Sets by the Use of a Quintic Rational Bézier Curve Defined with Mass Control Points

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The paper deals with the G 2 continuity for planar curves. The G 2 continuity is considered as a superior quality of curvature, which is often sought after in high-precision designs and industrial applications. It ensures a perfectly smooth transition between different parts of a surface or curve, which can improve the functionality, aesthetics, and durability of the finished object. This article describes an algorithm to achieve a G 2 junction between two sets of data –point, tangent, curvature–. The junction is based on a rational Bézier curve defined by control mass points. The control mass points generalize those of classical Bézier curves defined with weighted points with no negative weights. It is necessary as vectors and points with negative weights are coming out while applying homographic parameter change on a curve segment or converting any polynomial function into a rational Bézier representation. Here, from two sets of data –point, tangent and curvature–, a Bézier curve of degree n is built. This curve is described by control mass points. In most situations, the best degree for G 2 connection of those two sets equals 5.