Constrained space curve interpolation with constraint planes

We consider the interpolation of a given set of ordered data points in R3 by a smooth curve in the presence of a set of finite or infinite constraint planes, where the polyline joining consecutive data points does not intersect the constraint planes. A method is presented for the construction of the G2 constrained piecewise rational cubic interpolant which is local. The geometric properties of the Bézier rational cubics are characterized and exploited in the derivation of conditions for the interpolant to avoid crossing the constraint planes.