The PIA Property of Low Degree Non-uniform Triangular B-B Patches

Progressive-iterative approximation presents an intuitive way to generate a sequence of curves or patches, whose limit interpolates the given data points. It has been shown that the blending curves and tensor product blending patches with normalized totally positive basis have the progressive-iterative approximation property. In this paper, we prove that, the quadratic, cubic, and quartic non-uniform triangular Bernstein-Bezier patches also have the progressive-iterative approximation property. Since the most often employed in geometric design are the low degree curves or patches, especially the cubic curves and patches, the result shown in this paper has practical significance for geometric design.