Construction of cubic triangular patches with C¹ continuity around a corner

This paper presents a novel approach for constructing a piecewise triangular cubic polynomial surface with C¹ continuity around a common corner vertex. A C¹ continuity condition between two cubic triangular patches is first derived using mixed directional derivatives. An approach for constructing a surface with C¹ continuity around a corner is then developed. Our approach is easy and fast with the virtue of cubic reproduction, local shape controllability, C² continuous at the corner vertex. Some experimental results are presented to show the applicability and flexibility of the approach.