Constructing G1G1 Bézier surfaces over a boundary curve network with T-junctions

A T-junction occurs in a boundary curve network when one boundary curve ends in the middle of another. We show how to construct G1G1 Bézier 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 G1G1 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.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights►G1G1 Bézier surfaces are obtained from a boundary curve network with T-junctions. ► The boundary curves remain unchanged. ► Surfacing the T-junction does not affect surrounding patches.