Given a finite set of points in three dimensional Euclidean space R³, the subset that forms its surface could be different when observed in different levels of details. In this paper, we introduce a notion called a-surface. We present an algorithm that extracts the a-surface from a finite set of points in R³. We apply the algorithm to extracting the a-surfaces of proteins and discover patterns from these surface structures, using the pattern discovery algorithm we developed earlier. We then use these patterns to classify the proteins. Experimental results show the good performance of the proposed approach.