Constructing G1 Bézier surfaces over a boundary curve network with T-junctions

Authors:
Min-jae Oh;Kittichai Suthunyatanakit;Sung Ha Park;Tae-wan Kim
Affiliations:
Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Republic of Korea;Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Republic of Korea;Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Republic of Korea;Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Republic of Korea and Research Institute of Marine Systems Engineering, Seoul National University, ...
Venue:
Computer-Aided Design
Year:
2012

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Abstract

A T-junction occurs in a boundary curve network when one boundary curve ends in the middle of another. We show how to construct G^1 Bezier surfaces over a boundary curve network with T-junctions. By treating the two micro patches which meet at the edge forming the upright of the 'T' as a single macro patch, we reduce the problem to one of achieving continuity between this composite patch and the third patch which has the crossbar of the 'T' as an edge. Thus we avoid changes to the boundary network, or to any patches except those that meet at the T-junction. Also, we analyze the singularity of the G^1 continuity system with the T-junction, and give the constraint to make a consistent system using free variables of weight functions. This is the first method of surfacing the T-junction. We present examples and verify continuity by drawing reflection lines and checking angles.