Since transmitting various files around Internet is one of common activities in everyday life, the compression is important technical issue in these days. Shape models are also frequently transmitted and therefore its compression has also been studied. Considering the large portion of shape model can be normal vectors, a new scheme was recently presented to compress normal vectors using clustering and mixed indexing scheme. Presented in this paper is a mathematical investigation of the scheme to analyze the probability distribution of normal index distances in Normal Index array which is critical for the compression. The probability distribution is formulated so that the values can be easily calculated once the relative probabilities of C, R, E, S, and L op-codes in Edgebreaker are known. It can be shown that the distribution of index distances can be easily transformed into a few measures for the compression performance of the proposed algorithm.

Abstract
 1. 서 론
 2. 관련 연구
 3. 법선 인덱스 배열의 분석
  3.1 모서리 연결 관계
  3.2 꼭지점 연결 관계
  3.3 비연결 관계
 4. 법선 인덱스 거리의 확률 분포
 5. 결 론
 참고문헌

• 조영송(Voronoi Diagram 연구단)
• 임정훈(한양대학교 산업공학과)
• 조철형(한양대학교 산업공학과)
• 김덕수(한양대학교 산업공학과)