Bézier triangles with \(G^2\) continuity across boundaries (Q2412331)

Summary: PN (point-normal) triangles are cubic Bézier triangles which meet at their edges to surface a triangular mesh, but this only achieves \(G^0\) continuity. We define blending regions that span the edges shared by adjacent pairs of triangular domains and blend the corresponding Bézier triangles using a univariate blending function formulated in terms of barycentric coordinates. This produces \(G^2\) continuity across boundaries while preserving \(G^1\) continuity at vertices. The sharpness of the blends can be controlled locally by varying the extent of these blending regions. We demonstrate the effectiveness of our technique by showing several modeling examples.