Bézier Triangles with G2 Continuity across Boundaries

Abstract

PN (point-normal) triangles are cubic Bézier triangles which meet at their edges to surface a triangular mesh, but this only achieves G0 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 G2 continuity across boundaries while preserving G1 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.

Keywords

• geometric modeling
• PN triangle
• triangular Bézier surface
• Bézier triangle
• blending surface
• barycentric coordinate
• sharp features