Table 1.

Analysis of normal vectors in the one-neighborhood of extraordinary vertices as a measure of smoothness. Three quadrature points on the contour bounding two quads were selected within the one-neighborhood, and for each point, unit normals were computed in the two adjoining elements. Last, the dot product was computed for each pair of normals.

	RA-90	RA-360	RA-1440	LA-142	LA-568	LA-2272
Mean dot product	0.925	0.974	0.990	0.928	0.981	0.992
Fraction of points with dot product > 0.99	0.42	0.66	0.83	0.39	0.63	0.84
Fraction of points with dot product > 0.95	0.74	0.86	0.96	0.66	0.89	0.96
Fraction of points with dot product > 0.5	0.96	1.0	1.0	0.98	1.0	1.0