Shape decompositions and their algebras

Artificial Intelligence for Engineering Design, Analysis and Manufacturing: AIEDAM

Volumn 19, Issue 4, 2005, Pages 261-276

  Krstic, Djordje ^a,b  

^a LUCENT TECHNOLOGIES   (United States)

^b NONE   (United States)

Author keywords

Shape Algebras; Shape Approximations; Shape Decompositions; Shape Decompositions Algebras; Shape Grammars

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; FINITE DIFFERENCE METHOD; STANDARDS;

SHAPE ALGEBRAS; SHAPE APPROXIMATIONS; SHAPE DECOMPOSITIONS; SHAPE DECOMPOSITIONS ALGEBRAS; SHAPE GRAMMARS;

ALGEBRA;

EID: 33744455466     PISSN: 08900604     EISSN: 14691760     Source Type: Journal    
DOI: 10.1017/S0890060405050183     Document Type: Article

References (30)

1. Agrawal, M., & Cagan, J. (1998). A blend of different tastes: the language of coffee makers. Environment and Planning B: Planning and Design 25, 205-226.
2. Birkhoff, G. (1993). Lattice Theory. Providence, RH: American Mathematical Society.
3. Bleicher, M.N., Schneider, H., & Wilson, R.L. (1973). Permanence of identities on algebras. Algebra Universalis 3, 72-93.
4. Carlson, C., Woodbury, R., & McKelvey, R. (1991). An introduction to structure and structure grammars. Environment and Planning B: Planning and Design 18, 417-426.
5. Chase, S.C. (1989). Shapes and shape grammars: from mathematical model to computer implementation. Environment and Planning B: Planning and Design 16, 215-242.
6. Earl, C. (1997). Shape boundaries. Environment and Planning B: Planning and Design 24, 668-687.
7. Flemming, U. (1987). The role of shape grammars in analysis and creation of designs. In Computability of Designs (Kaley, Y.E., Ed.), pp. 245-272. New York: Wiley.
8. Gratzer, G. (1979). Universal Algebra. Providence, RI: American Mathematical Society.
9. Gratzer, G., & Whitney, S. (1978). Infinitary varieties of structures closed under the formation of complex structures [Abstract]. Notices of the American Mathematical Society 25, A224.
10. Guatam, N. (1957). The validity of equations of complex algebras. Archives Mathematic Logik Grundlagenforch 3, 117-124.
11. Knight, T. (1988). Comparing designs. Environment and Planning B: Planning and Design 7, 73-110.
12. Knight, T. (2003a). Computing with emergence. Environment and Planning B: Planning and Design 30, 125-155.
13. Knight, T. (2003b). Computing with ambiguity. Environment and Planning B: Planning and Design 30, 165-180.
14. Krishnamurti, R. (1982). SGI: A Grammar Interpreter [Research Report]. Centre for Configurational Studies, The Open University, Milton Keynes.
15. Krishnamurti, R., & Giraud C. (1986). Towards a shape editor: the implementation of a shape generation system. Environment and Planning B: Planning and Design 13, 391-403.
16. Krstic, D. (1996). Decompositions of shapes. PhD Thesis. University of California, Los Angeles.
17. Krstic, D. (1999). Constructing algebras of design. Environment and Planning B: Planning and Design 26, 45-57.
18. Krstic, D. (2001). Algebras and grammars for shapes and their boundaries. Environment and Planning B: Planning and Design 28, 151-162.
19. Krstic, D. (2004). Computing with analyzed shapes. In Design Computing and Cognition '04 (Gero, J.S., Ed.), pp. 397-416. Dordrecht: Kluwer Academic.
20. Piazzalunga, U., & Fitzhorn, P.I. (1998). Note on three-dimensional shape grammar interpreter. Environment and Planning B: Planning and Design 25, 11-33.
21. Shafaat, A. (1974). On varieties closed under construction of power algebras. Bulletin Australian Mathematical Society 11, 213-218.
22. Stiny, G. (1980). Introduction to shape and shape grammars. Environment and Planning B: Planning and Design 7, 243-251.
23. Stiny, G. (1982). Spatial relations and grammars. Environment and Planning B: Planning and Design 9, 113-114.
24. Stiny, G. (1990). What is a design. Environment and Planning B: Planning and Design 17, 97-103.
25. Stiny, G. (1991). The algebras of design. Research in Engineering Design 2, 171-181.
26. Stiny, G. (1992). Weights. Environment and Planning B: Planning and Design 19, 413-430.
27. Stiny, G. (1994). Shape rules: closure, continuity, and emergence. Environment and Planning B: Planning and Design 21, S49-S78.
28. Stiny, G. (2001). How to calculate with shapes. In Formal Engineering Design Synthesis (Antonson, E.K., & Cagan J., Eds.), pp. 24-60. Cambridge: Cambridge University Press.
29. Tapia, M.A. (1999). A visual implementation of a shape grammar system. Environment and Planning B: Planning and Design 26, 59-73.
30. Vickers, S. (1989). Topology Via Logic. New York: Cambridge University Press.