On a blossom-based approach for interpolating non-iso-parametric curves by b-spline surfaces

Abstract

Curve interpolation is a problem that has frequently been visited by many authors. However, the proposed solutions rely in a fundamental way on the assumption that the interpolated curve is iso-parametric along one or the other of the parameters of the interpolating surface, in so much that, as soon as this assumption is removed, the level of difficulty of the interpolation problem rises enormously. Ferguson and Grandine are perhaps the first to aim for the construction of B-spline surfaces interpolating non-iso-parametric curves. However, to our knowledge, there was never a follow up to that paper. Most of related research may rather be found in the area of curves on surfaces using blossoming techniques and also in the area of interpolation of arbitrary networks of curves. However, the work of Hu&Sun is directly relevant to the research reported here. Especially so, since the technique proposed here for the solution of the interpolation of non-iso-parametric curves is a slight adaptation of the one reported in that paper and used there for trimmed surface matching.