A note on degenerate triangular Bézier patches

In (Neamtu and Pfluger, 1994) degenerate Bézier patches were used to interpolate irregularly structured spatial data. This very interesting approach is based on the observation that singular parametrizations are no fundamental obstacle to modeling smooth spline surfaces. However, the smoothness conditions on degenerate Bézier patches provided in (Neamtu and Pfluger, 1994) are inaccurate. Moreover, proving tangent plane continuity is not sufficient to guarantee smoothness in the sense of differential geometry. What has to be shown is regularity, i.e. the existence of a regular smooth re-parametrization representing a degenerate patch locally near the singular point. Both correct sufficient smoothness conditions and the proof of regularity are presented in this paper.