- 1 BROWN, C. K. PADL-2: A technical summary. IEEE Comput. Graph. Appl. 2, 2 (Mar. 1982), 69-84.Google Scholar
- 2 COLLINS, G.E. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages. Lecture Notes in Computer Science, vol. 33, Springer-Verlag, Berlin, 1975, pp. 134-183. Google Scholar
- 3 COSTE, M., A~O ROY, M. F. Thom's lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets. J. Symbolic Comput. 5, 1 (1988), 121-129. Google Scholar
- 4 DO CARMO, M.P. Differential Geometry of Curves and Surfaces. Prentice-Hall, Englewood Cliffs, N.J., 1976.Google Scholar
- 5 G^RRIT~, T., ^NO WARREN, J. Geometric continuity. Comput. Aided Geom. Des. 8, 1 (Feb. 1991), 51-65. Google Scholar
- 6 Gmcog'~v, D.Y. Complexity of deciding Tarski algebra. J. Symbolic Comput. 5, i (1988), 65-108. Google Scholar
- 7 GUILLEMIN, V., AND POLLACK, A. Topology. Prentice-Hall, Englewood Cliffs, N.J., 1974.Google Scholar
- 8 HEtNTZ, J. Definability and fast quantifier elimination in algebraically closed fields. Theor. Comput. Sci. 24 (1983), 239-277.Google Scholar
- 9 HOFFMANN, C. H. Geometric and Solid Modeling. Morgan Kaufmann, San Mateo, Calif., 1989. Google Scholar
- 10 HOPF, H. Differential Geometry in the Large. 2nd ed. Lecture Notes in Mathematics, vol. 1000. Springer-Verlag, New York, 1989.Google Scholar
- 11 KENI)IG, K. Elementary Algebraic Geometry. Springer-Verlag, New York, 1977.Google Scholar
- 12 KUI~TOWSKI, K., AND MOSTOWSKI, A. Set Theory. North-Holland, Amsterdam, 1976.Google Scholar
- 13 M~, M. An Introduction to Solid Modeling. Computer Science Press, Rockville, Md., 1988. Google Scholar
- 14 M^SSEY, S.W. A Basic Course in Algebraic Topology. Springer-Verlag, New York, 1991.Google Scholar
- 15 McKINsEY, J. C. C,, AND TARSKI, A. On closed elements in closure algebras. Ann. Math. 47, 1 (Jan. 1946), 122-162.Google Scholar
- 16 MmLER, J. R. Architectural issues in solid modelers. IEEE Comput. Graph. Appl. 9, 5 (Sept. 1989) 72-87. Google Scholar
- 17 PATRIKALAg~S, N. M., ANo KRIEZlS, G.A. Representation of piecewise continuous algebraic surfaces in terms of B-splines. Vis. Comput. 5, (1989), 360-374.Google Scholar
- 18 REQUIC~, A. A.G. Mathematical models of rigid solid objects. Tech. Memo 28, Production Automation Project, Univ. of Rochester, Rochester, N.Y., Nov. 1977.Google Scholar
- 19 REQUICHA, A. A. G. Representations for rigid solids: Theory, methods, and systems. Cornput. Surv. (ACM) 12, 4 (Dec. 1980), 437-464. Google Scholar
- 20 REQUICHA, A. A. G., AND TILOVE, R. B. Mathematical foundations of constructive solid geometry: General topology of closed regular sets. Tech. Memo 27a, Production Automation Project, Univ. of Rochester, Rochester, N.Y., June 1978.Google Scholar
- 21 REQWCHA, A. A. G., AND VO~LCKER, H.B. Constructive solid geometry. Tech. Memo 25, Production Automation Project, Univ. of Rochester, Rochester, N.Y., 1977.Google Scholar
- 22 REQUICHA, A. A. G., AND VOELCKER, H.B. Boolean operations in solid modeling: Boundary evaluation and merging algorithms. Proc. IEEE 73, 1 (Jan. 1985), 30-44.Google Scholar
- 23 SEI)ERBERG, T.W. Piecewise algebraic surface patches. Comput. Aided Geom. Des. 2, 1-3 (Sept. 1985), 53-59.Google Scholar
- 24 S~Pmo, V. Representations of semi-algebraic sets in finite algebras generated by space decompositions. Ph.D. thesis, Cornell Programmable Automation, Cornell Univ., Ithaca, N.Y., Feb. 1991.Google Scholar
- 25 SHAPIRO, V., AND VOSSLER, D. L. Construction and optimization of CSG representations. Comput.-Aided Des. 23, 1 (Jam/Feb. 1991), 4-20. Google Scholar
- 26 SHAPIRO, V., AND VOSSLER, D. L. Boundary-based separation for Brep ~ CSG conversion. Tech. Rep. 91-1222, Dept. of Computer Science, Cornell Univ., Aug. 1991.Google Scholar
- 27 SH^mm), V., ANt) VOSSI,ER, D. L. Efficient CSG representations of two-dimensional solids. Trans. ASME, J. Mech. Des. 113, 3 (Sept. 1991), 292-305.Google Scholar
- 28 Sn,v^, C. E. Alternative definitions of faces in boundary representations of solid objects. Tech. Memo 36, Production Automation Project, Univ. of Rochester, Rochester, N.Y., 1981.Google Scholar
- 29 SNYI)ER, V., AND SISAM, C.H. Analytic Geometry of Space. Henry Holt, New York, 1914.Google Scholar
Index Terms
- Separation for boundary to CSG conversion
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