Comparison of CSC method and the B-net method for deducing smoothness condition

Abstract The first author of this paper established an approach to study the multivariate spline over arbitrary partition, and presented the so-called conformality method of smoothing cofactor (the CSC method). Farin introduced the B-net method which is suitable for studying the multivariate spline over simplex partitions. This paper indicates that the smoothness conditions obtained in terms of the B-net method can be derived by the CSC method for the spline spaces over simplex partitions, and the CSC method is more capable in some sense than the B-net method in studying the multivariate spline.