Convexity-preserving Bernstein–Bézier quartic scheme

Abstract

A C1 convex surface data interpolation scheme is presented to preserve the shape of scattered data arranged over a triangular grid. Bernstein–Bézier quartic function is used for interpolation. Lower bound of the boundary and inner Bézier ordinates is determined to guarantee convexity of surface. The developed scheme is flexible and involves more relaxed constraints.

Keywords

• Triangular surface patch
• Bernstein–Bézier quartic function
• Boundary Bézier ordinates
• Inner Bézier ordinates
• Convex scattered data