Abstract
We propose a local method of constructing piecewise G 1 Bézier patches to span a Bézier 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 1 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.
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Cho, DY., Lee, KY. & Kim, TW. Analysis and avoidance of singularities for local G 1 surface interpolation of Bézier curve network with 4-valent nodes. Computing 79, 261–279 (2007). https://doi.org/10.1007/s00607-006-0203-1
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DOI: https://doi.org/10.1007/s00607-006-0203-1