Interpolating G1 Bézier surfaces over irregular curve networks for ship hull design

Authors:
Doo-Yeoun Cho;Kyu-Yeul Lee;Tae-Wan Kim
Affiliations:
Department of Naval Architecture and Ocean Engineering, Seoul National University, San 56-1, Shillim-9-dong, Kwanak-gu, Seoul 151-744, South Korea;Department of Naval Architecture and Ocean Engineering, Research Institute of Marine Systems Engineering, Seoul National University, Seoul 151-744, South Korea;Department of Naval Architecture and Ocean Engineering, Research Institute of Marine Systems Engineering, Seoul National University, Seoul 151-744, South Korea
Venue:
Computer-Aided Design
Year:
2006

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Abstract

We propose a local method of constructing piecewise G^1 Bezier patches to span an irregular curve network, without modifying the given curves at odd- and 4-valent node points. Topologically irregular regions of the network are approximated by implicit surfaces, which are used to generate split curves, which subdivide the regions into triangular and/or rectangular sub-regions. The subdivided regions are then interpolated with Bezier patches. We analyze various singular cases of the G^1 condition that is to be met by the 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 in a ship hull.