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

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. (C) 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.