Constrained Space Curve Interpolation with Constraint Planes.

Abstract

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