Analysis and avoidance of singularities for local G~1 surface interpolation of Bezier curve network with 4-valent nodes

摘要

We propose a local method of constructing piecewise G~1 Bezier patches to span a Bezier curve network with odd- and 4-valent node points. We analyze all possible singular cases of the G~1 condition that is to be met by the curve network interpolation and propose a new G continuity condition using linear and quartic scalar weight functions. Using this condition, a curve network can be interpolated without modification at 4-valent nodes with two collinear tangent vectors, even in the presence of singularities. We demonstrate our approach by generating G~1 surfaces over the curve network which includes singularities at its node vertices and edges.