3차원 서페이스에 대한 폴리오미노 타일링 = Polyomino Tiling for Three-dimensional Surface

다국어 초록 (Multilingual Abstract)

This paper presents a new polyomino tiling algorithm for three-dimensional surface geometric model. We first apply surface subdivision to the input polygonal mesh or subdivision surface mesh. Then we construct a random Hamiltonian path to connect all subdivided input mesh. This path is used to build initial polyomino tiling on the original input mesh. Finally we apply random polyomino exchanging to the polyomino tiling to get more uniform occurrence of each polyomino types. Our method is applicable to construct three-dimensional puzzle and we show the results of proposed algorithm on three-dimensional mesh data.

목차 (Table of Contents)

• 1. 서론
• 2. 관련 연구
• 3. 3차원 폴리오미노 타일링
• 4. 결 론
• 참고문헌

참고문헌 (Reference)

1 조청운, "테트로미노 타일링을 통한 지뢰찾기 변형 게임의 설계와 구현" (사)한국컴퓨터게임학회 25 (25): 47-53, 2012

2 조청운, "균일 분포 테트로미노 타일링" (사)한국컴퓨터게임학회 26 (26): 43-48, 2013

3 장성갑, "게임등급심의제의 제도적 맥락 연구 -미국, 일본, 한국을 중심으로-" (사)한국컴퓨터게임학회 25 (25): 137-146, 2012

4 Branko Grunbaum., "Tilings and Patterns" 1987

5 Peng Song., "Recursive Interlocking Puzzles" 31 (31): 225-235, 2013

6 Solomon W, "Polyominoes: Puzzles, Patterns, Problems, and Packings, 2nd edition" Princeton University Press 1996

7 George Martin, "Polyominoes : A Guide to Puzzles and Problems in Tiling" The Mathematical Association of America 1996

8 Mario Botsch., "Polygon Mesh Processing" A K Peters, Ltd. 2010

9 Tarini, M., "Polycube-maps" 23 (23): 853-860, 2004

10 Ray, N., "Periodic global parameterization" 25 (25): 1460-1485, 2006

11 Shiqing Xin., "Making Burr Puzzles from 3D Models" 30 (30): 2011

12 T. Asano, "Digital Halftoning Algorithm based on Random Space-Filling Curve" 1 : 545-548, 1996

13 Revital Dafner., "Context-based Space Filling Curves" 19 (19): 209-218, 2000

14 Kui Yip Lo., "3D Polyomino Puzzle" 28 (28): 2009