Geometric programming for computer-aided design

Geometric Programming for Computer-Aided Design

Volumn , Issue , 2005, Pages 1-776

  Paoluzzi, Alberto ^a  

^a ROMA TRE UNIVERSITY   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER GRAPHICS; MATHEMATICAL PROGRAMMING; ROBOT PROGRAMMING;

CAD APPLICATIONS; COLLABORATIVE DESIGN ENVIRONMENTS; GEOMETRIC PROGRAMMING; MECHANICAL CAD; MODELING AND ANIMATION; SCIENTIFIC SIMULATIONS; WEB BASED;

COMPUTER AIDED DESIGN;

EID: 85050196926     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/0470013885     Document Type: Book

References (224)

1. C. Armstrong, A.A Bowyer, S. Cameron, J. Coraey, G. Jared, R. Martin, A. Middleditch, M. Sabin, J. Salmon, and J. Woodwark. Djinn: A Geometric Interface for Solid Modeling. Information Geometers, Winchester, UK, 2000.
2. D. Avis, D. Bremner, and R. Seidel. How good are convex hull algorithms? Computational Geometry: Theory and Applications, 7(5-6): 265-301, April 1997.
3. S. Ansaldi, L. De Floriani, and B. Falcidieno. Geometric modeling of solid objects by using a face adjacency graph representation. Computer Graphics, 19(3): 131-140, July 1985.
4. Adobe Systems Inc. PostScript Language Reference Manual. Addison-Wesley, Reading, MA, 1985.
5. D. Avis and K. Fukuda. A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra. Discrete and Computational Geometry, 8(5-6): 295-313, 1992.
6. H. Alt and M. Godau. Measuring the resemblance of polygonal curves. In Proc. 8th Annu. ACM Sympos. Comput. Geom., pages 102-109, 1992.
7. H. Alt and M. Godau. Computing the Frechet distance between two polygonal curves. Internat. J. Comput. Geom. Appl., 5: 75-91, 1995.
8. A. V. Aho, J. E. Hopcroft, and J. D. Ullman. Data Structures and Algorithms. Addison-Wesley, Reading, MA, 1983.
9. Andrea L. Ames, David R. Nadeau, and John L. Moreland. The VRML 2.0 Sourcebook. John Wiley & Sons, New York, 1997.
10. American National Standards Institute. PHIGS+ Functional Description, Revision 2.0. New York, July 1987.
11. T.M. Apostol. Calculus. John Wiley, New York, 1967.
12. H. Arsham. Initialization of the simplex algorithm: An artificial-free approach. SIAM Review, 39(4): 736-744, 1997.
13. M. J. Atallah. A linear time algorithm for the Hausdorff distance between convex polygons. Information Processing Letters, 17(4): 207-209, November 1983.
14. A.V. Aho and J.D. Ullman. Foundations of Computer Science. Computer Science Press, W.H. Freeman and Co., New York, 1992.
15. C. Bajaj and S. Abhyankar. Automatic parameterization of rational curves and surfaces I: Conies and conicoids. Computer Aided Design, 19(1): 11-14, 1987.
16. C. Bajaj and S. Abhyankar. Automatic parameterization of rational curves and surfaces II: Cubics and cubicoids. Computer Aided Desig, 19(9): 499-502, 1987.
17. C. Bajaj and S. Abhyankar. Automatic parameterization of rational curves and surfaces III: Algebraic plane curves. Computer Aided Geometric Design, 5: 309-321, 1988.
18. C. Bajaj and S. Abhyankar. Automatic parameterization of rational curves and surfaces IV: Algebraic space curves. ACM Transactions on Graphics, 8(4): 324-333, 1989.
19. J. Backus. Can programming be liberated from the Von Neuman’s style? A functional style and its algebra of programs. Communications of the ACM, 21(8): 613-641, August 1978. ACM Turing Award Lecture.
20. M.L. Balinski. An algorithm for finding all vertices of convex polyhedral sets. Journal on Industrial Applied Mathematics, 9: 72-78, 1961.
21. A.H. Barr. Superquadrics and angle preserving transformations. Computer Graphics, 15(3): 11,23, August 1981.
22. B.G. Baumgart. Winged-Edge Polyhedron Representation. Technical Report Stan-CS-320, Artificial Intelligence Laboratory, Stanford University, CA, 1972.
23. C. Bajaj, C. Baldazzi, S. Cutchin, A. Paoluzzi, V. Pascucci, and M. Vicentino. A programming approach for complex animations. Part I: Methodology. Computer Aided Design, 31(11): 695-710, November 1999.
24. F. Bernardini, G. Cenciotti, and A. Paoluzzi. Transfinite interpolation of surfaces with integral and differential constraints using a geometric design language. In Proc. of Seventh IFIP Workshop on Geometric Modeling: Fundamentals and Applications, Parma, Italy, 2000. Kluever.
25. R. Bidarra, K.J. de Kraker, and W. Bronsvoort. Representation and management of feature information in a cellular model. Computer-Aided Design, 30(4): 301-313, 1998.
26. F. Bernardini. Integration of polynomials over n-dimensional polyhedra. Computer Aided Design, 23(1): 51-58, February 1991.
27. D. Ba Khang and O. Fujiwara. A new algorithm to find all vertices of a polytope. Operations Research Letters, 8: 261-2640, 1989.
28. M. Bertolotto, L. De Floriani, and P. Marzano. Pyramidal simplicial complexes. In Solid Modeling '95, Third ACM/IEEE Symposium on Solid Modeling and Applications, Salt Lake City, Utah, 1995. ACM Press.
29. D. Bremner, K. Fukuda, and A. Marzetta. Primal-dual methods for vertex and facet enumeration. Discrete and Computational Geometry, 20: 333-357, 1998.
30. nd ACM/IEEE Symposium on Solid Modeling and Applications, pages 43-52. ACM Press, May 1993.
31. H.-P. Bieri. Boolean and topological operations for Nef polyhedra. In CSG '94 Set-Theoretic Solid Modelling Techniques and Applications, pages 35 53, Information Geometers, Winchester, UK, 1994.
32. H.-P. Bieri. Nef polyhedra: A brief introduction. Computing Supplementum, 5(10), 1994.
33. H.-P. Bieri. Nef polyhedra: A brief introduction. In H. Hagen, G.E. Farin, H. Noltemeier, and R. Albrecht, editors, Geometric modelling, Dagstuhl, Germany 1993, volume 10 of Computing. Supplementum, pages 43-60, Springer, New York, 1995.
34. H.-P. Bieri. Representation conversions for Nef polyhedra. In Gerald Farin, Hanspeter Bieri, Guido Brunnett, and Tony DeRose, editors, Geometric Modelling. 3rd Dagstuhl Workshop, Dagstuhl, Germany, 1996, volume 13 sof Computing. Supplementum, pages 27-38, Springer, New York, 1998.
35. F. Bernardini, J. Klosowski, and J. El-Sana. Directional discretized occluders for accelerated occlusion culling. Proc. of Eurographics, 2000.
36. H.-P. Bieri and W. Nef. Elementary set operations with d-dimensional polyhedra. In H. Noltemeier, editor, Computational Geometry and its Applications, number 333 in Lecture Notes in Computer Science, pages 97-112. Springer Verlag, Berlin, 1988.
37. W. Böhm. Inserting new knots into B-spline curves. Computer Aided Design, 12(4): 199-201, July 1980.
38. C. Baldazzi and A. Paoluzzi. Dimension-independent bsp (2): Boundary-to-interior mapping. International Journal of Shape Modeling, 4(1): 107-126, January 1998.
39. I. Braid. The synthesis of solids bounded by many faces. Communications of the ACM, 18(3): 209-216, 1975.
40. I. C. Braid. Notes on a Geometric Modeler. Technical Report 101, CAD Group Document, University of Cambridge, UK, 1979. (revised 1980).
41. E. Brisson. Representing geometric structures in d dimensions: Topology and order. In ACM Symposium on Computational Geometry, pages 218-227, ACM Press, New York, 1989.
42. A. Brondsted. An Introduction to Convex Poly topes. Number 90 in Graduate texts in mathematics. Springer-Verlag, New York, 1983.
43. R. Brown. Topology. Ellis Horwood, Chichester, UK, 1988.
44. C.A. Burdet. Generating all the faces of a polyhedron. SI AM Journal on Applied Mathematics, 26: 479-489, 1974.
45. J. Backus, J.H. Williams, EX. Wimmers, P. Lucas, and A. Aiken. FL Language Manual, Parts 1 and 2. Technical Report RJ 7100, IBM Almaden Research Center, Almaden, CA, October 1989.
46. J. Backus, J.H. Williams, and E.L. Wimmers. An introduction to the programming language FL. In D.A. Turner, editor, Research Topics in Functional Programming, Chapter 9, pages 219-247. Addison-Wesley, Reading, MA, 1990.
47. N.V. Chernikova. Algorithm for finding a general formula for the nonnegative solutions of a system of linear equations. U.S.S.R Computational Mathematics and Mathematical Physics, 5: 228-233, 1965.
48. P. Chen, P. Hansen, and B. Jaumard. On-Line and Off-Line Vertex Enumeration by Adjacency Lists. Technical Report RUTCOR 9-90, Rutgers Center for Operations Research, Rutgers University, New Brunswick, NJ. March 1990.
49. V. Chvatal. Linear Programming. Freeman, New York, 1983.
50. E.T. Cohen, T. Lyche, and R. Riensenfeld. Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics. Computer Grapics and Image Processing, 14(2): 87-111, October 1980.
51. S.A. Coons. Surfaces for Computer-Aided Design of Space Forms. Technical Report MAC-TR-41, MIT, Cambridge, MA, 1967.
52. M.G. Cox. The Numerical Evaluation of B-Splines. Technical Report DNAC 4, National Physical Laboratory, August 1971.
53. I. Carlbom and J. Paciorek. Planar geometric projections and viewing transformations. Computing Surveys, 10(4): 465-502, December 1978.
54. M. Crampin and F.A.E. Pirani. Applicable Differential Geometry. Number 59 in London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, UK, 1986.
55. C. Cattani and A. Paoluzzi. Boundary integration over linear polyhedra. Computer Aided Design, 22(2): 130-135, March 1990.
56. P.R. Cromwell. Polyhedra. Cambridge University Press, Cambridge, UK, 1997.
57. J. Cremer and A. Steward. The architecture of Newton, a general-purpose dynamics simulator. In IEEE International Conference on Robotics and Automation, pages 1806-1811. IEEE Press, 1989.
58. G.B. Dantzig. Maximization of a linear function of variables subject to linear inequalities. In T.C. Koopmans, editor, Activity Analysis of Production and Allocation, Chapter 21, pages 339-347. Wiley, New York, 1951.
59. G.B. Dantzig. Linear Programming and Extensions. Princeton University Press, Princeton, 1963.
60. C.J. Date. An Introduction to Database Systems. The Systems Programming Series. Addison-Wesley, seventh edition edition, 1997.
61. C. de Boor. On calculating with B-splines. Journal of Approximation Theory, 6: 50-62, 1972.
62. G. Di Battista, P. Eades, R. Tamassia, and I.G. Tollis. Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall, Upper Saddle River, New Jersey, 1999.
63. G.B. Dantzig and B. Curtis Eaves. Fourier-motzkin elimination and its dual. Journal of Combinatorial Theory, 14: 288-297, 1973.
64. C.T.J. Dodson and T. Poston. Graphs, Surfaces and Homology. Pitman Publ., London, 1977.
65. M.E. Dyer and L.G. Proll. An algorithm for determining all extreme points of a convex polytope. Mathematical Programming, 12: 81-96, 1977.
66. M.E. Dyer. The complexity of vertex enumeration methods. Mathematics of Operation Research, 8(3): 381-402, 1983.
67. H. Edelsbrunner. Algorithms in Combinatorial Geometry. Number 10 in EATCS Monographs on Th. Comp. Sci. Springer-Verlag, New York. 1987.
68. H. Edelsbrunner. Algebraic decomposition of nonconvex polyhedra. In Procs. of 36th Symposium on Foundations of Computer Science, pages 248-257, October 1995.
69. G. Enderle, K. Kansy, and G. Pfaff. Computer Graphics Programming. GKS - The Graphics Standard. Springer-Verlag, New York, second edition, 1987.
70. R. Egli and N.F. Stewart. A framework for system specification using chains on cell complexes. Computer-Aided Design, 32(9): 447-459, 2000.
71. G. Farin. Curves and Surfaces for Computer Aided Geometric Design. Academic Press, San Diego, CA, 1988.
72. V. Ferrucci. Dimension-independent solid modeling. PhD thesis, Dip. di Informatica e Sistemistica, Universita “La Sapienza”, Rome, June 1995.
73. V. Ferrucci. Representing Nef polyhedra. In Pacific Graphic Conference, 1995.
74. M. Felleisen, R.B. Findler, M. Flatt, and S. Krishnamurthi. The DrScheme project: An overview. ACM Sigplan Notices, 33(6), 1998.
75. M. Friedman, D.P. Wand and C.T. Haynes. Essentials of Programming Languages. The MIT Press and McGraw-Hill, Cambridge, MA, 1992.
76. R.C. Fu, K.S. Gonzales and C.S.G. Lee. Robotics: Control, Sensing, Vison and Intelligence. McGraw-Hill, New York, 1987.
77. I.D. Faux and M.J. Pratt. Computational Geometry for Design and Manufacture. Halsted, Chichester, England, 1980.
78. V. Ferrucci and A. Paoluzzi. Extrusion and boundary evaluation for multidimensional polyhedra. Computer Aided Design, 23(1): 40-50, February 1991. Special issue entitled ‘Beyond Solid Modeling’.
79. J.D. Foley and A. van Dam. Fundamentals of Interactive Computer Graphics. Addison-Wesley, Reading, MA, 1982.
80. J.D. Foley, A. van Dam, S.K. Feiner, and J.F. Hughes. Computer Graphics, Principles and Practice. Addison-Wesley, Reading, MA, 1990. Second edition.
81. T. Gaskins. PHIGS Programming Manual: 3D Programming in X. O’Reilly, Sebastopol, CA, 1992.
82. W. A. Garnan and W.A. Giovinazzo. PHIGS by Example. Springer-Verlag, New York, 1991.
83. P.J. Giblin. Graphs, Surfaces and Homology. Chapman and Hall, London, 1977.
84. M. Grötschel, L. Lovász, and A. Schrijver. Geometric Algorithms and Combinatorial Optimization. Springer-Verlag, Berlin and Heidelberg, 1988.
85. R.N. Goldman. The role of surfaces in solid modeling. In G.E. Farin, editor, Geometric Modeling: Algorithms and New Trends. SIAM Publications, Philadelphia, Pennsylvania, 1987.
86. W.J. Gordon. Blending Function Methods of Bivariate and Multivariate Interpolation and Approximation. Technical Report GMR-834, General Motors, Warren, Michigan, 1968.
87. W.J. Gordon. Spline-blended surface interpolation through curve networks. Journal of Mathematical Mechanics, 18: 931-952, 1969.
88. W.J. Gordon and R.F. Riesenfeld. Bernstein-Bezier methods for the computer-aided design of free form curves and surfaces. Journal of the ACM, 21: 293-310, 1974.
89. B. Grünbaum. Convex polytopes. J. Wiley, London, UK, 1967.
90. L. Guibas and J. Stolfi. Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Transactions on Graphics, 4(2): 74-123, 1985.
91. J.L. Gross and T.W. Tucker. Topological Graph Theory. John Wiley, New York, 1987.
92. O. Günther and E. Wong. Convex polyhedral chains: a representation for geometric data. Computer Aided Design, 21(3): 157-164, March 1989.
93. R. Horst, J. de Vries, and N.V. Thoai. On finding new vertices and redundant constraints in cutting plane algorithms for global optimization. Operations Research Letters, 7: 85-90, 1988.
94. T.L.J. Howard, W.T. Hewitt, R.J. Hubbold, and K.M. Wyrwas. A Practical Introduction to PHIGS and PHIGS PLUS. Addison-Wesley, Wokingham, UK, 1991.
95. CM Hoffmann, J.E. Hopcroft, and M. Karasick. Towards implementing robust geometric computations. In Fourth A CM Symposium on Computational Geometry, pages 106-117, ACM Press, New York, 1988.
96. CM. Hoffmann. Geometric and Solid modeling. Morgan Kaufman, New York, 1989.
97. H. Hopf. Differential Geometry in the Large. Springer-Verlag, Berlin, 1983.
98. B. Horn. Robot Vision. McGraw-Hill, New York, 1989, seventh edition.
99. J.E. Hopcroft, J.T. Schwartz, and M. Sharir. On the complexity of motion planning for multiple independent objects; pspace hardness of “warehouseman’s problem”. Intemat. J. Robotics Res., 3(4): 76-88, 1984.
100. H. Hies and V. Shapiro. The dual of sweep. Computer Aided Design, 31(3): 185-201, 1999.
101. International Organization for Standardization. The Graphical Kernel System (GKS): ISO 7942. International Organization for Standardization, Geneva, Switzerland, 1985.
102. International Organization for Standardization. The Programmer’s Hierarchical Interactive Graphics System (PHIGS): ISO 9592. International Organization for Standardization, Geneva, Switzerland, 1989.
103. International Organization for Standardization. The Virtual Reality Modeling Language: ISO/IEC 14772-1. International Organization for Standardization, Geneva, Switzerland, 1997.
104. A. Jones, A. Gray, and R. Hutton. Manifolds and Mechanics. Number 2 in Australian Mathematical Society Lecture Series. Cambridge University Press, Cambridge, UK, 1987.
105. A.C. Jeffrey and V. Shapiro. A multivector data structure for differential forms and equations. IMACS Transactions Journal, Mathematics and Computers in Simulation, 54(1): 33-64, 2000.
106. J.C. Latombe. Robot Motion Planning. Kluwer Academic Publishers, Boston, MA, 1991.
107. T. Levi-Civita and U. Amaldi. Lezioni di meccanica razionale. Zanichelli, Bologna, 1926.
108. J. Loustau and M. Dillon. Linear Geometry with Computer Graphics, volume 170 of Pure and Applied Mathematics Series. Marcel Dekker, New York, 1993.
109. S. Lefschetz. Introduction to Topology. Princeton University Press, Princeton, N.J. 1949.
110. R. Light and D.C. Gossard. Modification of geometric models through variational geometry. Computer-Aided Design, 14(4): 209-214, 1982.
111. K.W. Lee and D.C. Gossard. A hierarchical data structure for representing assemblies: Part 1. Computer Aided Design, 17(1): 15-19, 1985.
112. J. Lammers and L. Gooding. Maya 4 Fundamentals. New Riders, Indianapolis, Indiana, 2002.
113. P. Lienhardt. Subdivisions of n-dimensional spaces and n-dimensional generalized maps. In ACM Symposium on Computational Geometry, pages 228-236, New York, 1989. ACM Press.
114. S. Ling Lien and J.T. Kajiya. Symbolic method for calculating the integral properties of arbitrary nonconvex polyhedra. IEEE Computer Graphics and Applica- Hons, 4(10): 35-41, 1984.
115. T. Lozano-Perez and M. Wesley. An algorithm for planning collision-free paths among polyhedral obstacles. Communications of the ACM, 22: 560-570, 1979.
116. Y.T. Lee and A.A.G. Requicha. Algorithms for computing the volume and other integral properties of solids i: known methods and open issues. Communications of the ACM, 25(9): 635-641, 1982.
117. P. Lancaster and K. Salkauskas. Curve and Surface Fitting. An Introduction. Academic Press, London, UK, 1986.
118. D.H. Laidlaw, W.B. Trumbore, and J.F. Hughes. Constructive solid geometry for polyhedral objects. ACM Siggraph '86, Computer Graphics, 20(4): 161-170, August 1986.
119. D.G. Luenberger. Linear and Nonlinear Programming. Addison-Wesley, Reading, MA, 1984.
120. A.T. Lundell and S. Weingram. The Topology of CW Complexes. Van Nostrand Reinhold, New York, 1969.
121. P. Lucas and S.N. Zilles. Applicative Graphics Using Abstract Data Types. Technical Report RJ 6198, IBM Almaden Research Center, February 1988.
122. M. Mäntylä. Boolean operation of 2-manifold trough vertex neighborhood classification. ACM Transactions on Graphics, 5(1): 1-29, 1986.
123. M. Mäntylä. An Introduction to Solid Modeling. Computer Science Press, Rockville, Maryland, 1988.
124. Benoit B. Mandelbrot. Fractal Geometry of Nature. W.H. Freeman & Co., 1988.
125. A. Maulik. An efficient intersection algorithm for polyhedral cellular decompositions. In J. Rossignac and J. Turner, editors, ACM Symposium on Solid Modeling Foundations and CAD/CAM Applications, pages 109-118, Austin, TX, 1991. ACM Press.
126. M. McKenna. Worst-case optimal hidden-surface removal. ACM Transactions on Graphics, 6(1): 19-28, January 1987.
127. W.J. Mitchell. Computer-Aided Architectural Design. Van Nostrand Reinhold, New York, 1977.
128. M. Cialdea Mayer, G. Marzano, A. Paoluzzi, and S. Portuesi. Representing and exporting design knowledge. Submitted paper, November 2002.
129. M. Manas and J. Nedoma. Finding all vertices of the convex polyhedron. Numerische Mathematik, 12: 226-229, 1968.
130. M.E. Morteson. Geometric Modeling. John Wiley & Sons, New York, 1985.
131. T.H. Matheiss and D.S. Rubin. Comments on Dyer and Proll’s Vertex Generating Algorithm. Technical Report 11, Curriculum in Operations Research, University of North Carolina at Chapel Hill, September 1977.
132. T.H. Matheiss and D.S. Rubin. A survey and comparison of methods for finding all vertices of convex polyhedral sets. Mathematics of Operation Research, 5(2): 167-185, 1980.
133. J.R. Munkres. Elements of Algebraic Topology. Addison Wesley, Reading, MA. 1984.
134. K.G. Murty. Linear Programming. Wiley & Sons, New York, 1983.
135. J. Menon and H. Voelcker. Toward a comprehensive formulation of nc verification as a mathematical and computational problem. In 1992 Winter Annual Meeting of ASME, volume 59, pages 147-164, Anaheim, CA, 1992.
136. M. Nakahara. Geometry, Topology and Physics. Graduate Student Series in Physics. Adam Hilger, Bristol, UK, 1990.
137. M. Nakahara. Geometry, Topology and Physiscs. Graduate Student Series in Physiscs. Adam Hilger, Bristol, UK, 1991.
138. B.F. Naylor, J. Amanatides, and W. Thibault. Merging BSP trees yields polyhedral set operations. Computer Graphics, 24(4): 115-124, August 1990. Proc. of ACM Siggraph’90.
139. J. Neider, T. Davis, and M. Woo. OpenGL Programming Guide. Addison-Wesley, Reading, MA, 1992.
140. W. Nef. Beitrage zur Theorie der Polyeder - mit Anwendungen in der Computergrafik. Herbert Lang, Bern, 1978. In German.
141. N. Negroponte. The Architecture Machine: Towards a More Human Environment. MIT Press, Cambridge, MA, 1970.
142. G.L. Nemhauser. Branch-and-price for solving integer programs with a huge number of variables: Methods and applications. Number 1118 of Lecture Notes in Computer Science, Springer Verlag, Berlin, 1996.
143. M.E. Newell, R.G. Newell, and T.L. Sancha. A solution to the hidden surface problem. In Proceeedings of the ACM National Conference, pages 443-450, 1972.
144. OpenGL Architecture Review Board. OpenGL Reference Manual. Addison-Wesley, Reading, MA, 1992.
145. E. Panofsky. The Life and Art of Albrecht Durer. Princeton University Press, Princeton, NJ, 1971.
146. E. Panofsky. Perspective as Symbolic Form. Zone Books, New York, 1991. (1927).
147. A. Paoluzzi. Disegno Automatico di Solidi Poliedrici. Quaderni di Architettura Tecnica 16, Istituto di Architettura, Edilizia e Tecnica Urbanistica, Universita “La Sapienza”, Rome, May 1978. In Italian.
148. A. Paoluzzi. Integration Constraints in Parametric Design of Physical Objects. Teehn. Rep. 87-804, Dept. of Computer Science, Cornell University, Ithaca, NY, January 1987.
149. A. Paoluzzi. Motion Planning + Solid Modeling = Motion Modeling. Techn. Rep. 17.89, Dip. di Informatica e Sistemistica, Universita “La Sapienza”, Rome, November 1989.
150. A. Paoluzzi. Bilinear matrix forms for the area of polygons. Computer Aided Design, 28(4): 301-306, 1996.
151. A. Paoluzzi, F. Bernardini, C. Cattani, and V. Ferrucci. Dimension-independent modeling with simplicial complexes. ACM Transactions on Graphics, 12(1): 56-102, January 1993.
152. M. Pesce. VRML Browsing and Building Cyberspace. New Riders, London, UK, 1992.
153. V. Pascucci, V. Ferrucci, and A. Paoluzzi. Dimension-indipendent convex-cell based hpc: Skeletons and product. International Journal of Shape Modeling, 2(1): 37-67, January 1996.
154. B.T. Phong. Illumination for computer generated pictures. Communications of the ACM, 18(6): 311-317, June 1975.
155. A. Paoluzzi and M. Masia. The geometric modeler Minerva. Wheels for the Mind, Apple Europe, 3(2): 14-32, April 1989.
156. H. Poincaré. Oeuvres, volume 6. Gauthier-Villars, Paris, 1953.
157. A. Paoluzzi, V. Pascucci, and M. Vicentino. Geometric programming: a programming approach to geometric design. ACM Transactions on Graphics, 14(3): 266-306, July 1995.
158. A. Paoluzzi, M. Ramella, and A. Santarelli. Boolean algebra over linear polyhedra. Computer Aided Design, 21(8): 474-484, October 1989.
159. F.P. Preparata and M.I. Shamos. Computational Geometry. Springer-Verlag, Berlin, 1985.
160. A. Paoluzzi and C. Sansoni. Programming language for solid variational geometry. Computer Aided Design, 24(7): 349-366, July 1992.
161. Michael S. Paterson and F. Frances Yao. Efficient binary space partitions for hidden-surface removal and solid modeling. Discrete and Computational Geometry, 5: 485-503, 1990.
162. D.F. Rogers and J.A. Adams. Mathematical Elements for Computer Graphics. McGraw-Hill, New York, 1976.
163. S. Raghothama. Models and representations for parametric family of parts. PhD thesis, Department of Mechanical Engineering, Univeristy of Wisconsin-Madison, September 2000.
164. A. Rappoport. Geometric modeling: a new fundamental framework and its practical implications. In Solid Modeling '95, Third ACM/IEEE Symposium on Solid Modeling and Applications, Salt Lake City, Utah, 1995. ACM Press.
165. A.A.G. Requicha. Mathematical Models of Rigid Solid Objects. Technical Report 28, Production Automation Project, Univ. of Rochester, NY, November 1977.
166. A.A.G. Requicha. Representations for rigid solids: theory, methods and systems. ACM Computing Surveys, 12(4): 437 464, December 1980.
167. A.A.G. Requicha. Solid modeling: A 1988 update. In B. Ravani, editor, CAD Based Programming for Sensory Robots, number 50 in Nato ASI Series, pages 3-22. Springer-Verlag, Berlin, 1988.
168. R.F. Riesenfeld. Application of B-Spline Approximation to Geometric problems of Computer Aided Design. Technical Report 126, University of Utah, 1973.
169. J. Rossignac and M. O’Connor. SGC: A dimension-independent model for pointsets with internal structures and incomplete boundaries. In M.J. Wozny, J. Turner, and K. Preiss, editors, Geometric Modeling for Product Engineering, pages 145-180, Rensselaerville, NY, 1990. North Holland.
170. F.D. Robinson. The background of the PERT algorithm. The Computer Journal, 5(4): 297-300, January 1963.
171. David F. Rogers. Procedural Elements for Computer Graphics. McGraw-Hill. New York, 1997, second edition.
172. J.R. Rossignac. Through the cracks of the solid modeling. In S. Coquillart, W. Strasser, and P. Stucki, editors, From Object Modelling to Advanced Visualization. Springer-Verlag, 1994.
173. J.R. Rossignac and A.A.G. Requicha. Offsetting operations in solid modeling. Computer Aided Geometric Design, 26(2): 129-148, 1986.
174. A.A.G. Requicha and J.R. Rossignac. Constructive non-regularized geometry. Computer-Aided Design, 23(1), 1991.
175. A.A.G. Requicha and J.R. Rossignac. Solid modeling and beyond. IEEE Computer Graphics and Applications, 12(9): 31-44, September 1992.
176. A.A.G. Requicha and J.R. Rossignac. Solid modeling. In J. Webster, editor, Encyclopedia of Electrical and Electronics Engineering. John Wiley &: Sons, New York, 1999.
177. CP. Rourke and B.J. Sanderson. Introduction to Pieceurise-Linear Topology. Springer Verlag, Berlin, 1972.
178. J. Ruppert and R. Seidel. On the difficulty of tetrahedralizing 3-dimensional non-convex polyhedra. In ACM Symposium on Computational Geometry, New York, 1989. ACM Press.
179. S. Raghothama and V. Shapiro. Topological framework fo part families. In K. Lee and N.M. Patrikalakis, editors, Seventh ACM Symposium on Solid Modeling and Applications, pages 1-12, Saarbriicken, Germany, 2002. ACM Press.
180. V.L. Rvachev, T.I. Sheiko, V. Shapiro, and I. Tsukanov. Transfinite interpolation over implicitly defined sets. Computer Aided Geometric Design, 18: 195-220, 2001.
181. A.A.G. Requicha and H.B. Voelcker. Constructive Solid Geometry. Technical Report TM-25, PAP, University of Rochester, Rochester, NY, November 1977.
182. A.A.G. Requicha and H.B. Voelcker. Solid modeling: Current status and research directions. IEEE Computer Graphics and Applications, 3(7): 25-37. October 1983.
183. H.S. Samet. An overview of quadtrees, octrees, and related hierarchical data structures. In R.A. Earnshaw, editor, Theoretical Foundations of Computer Graphics and CAD, Nato ASI Series, pages 51-68. Springer-Verlag, Berlin, 1988.
184. H.S. Samet. Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS. Addison Wesley, Reading, MA, 1990.
185. H.S. Samet. The Design and Analysis of Spatial Data Structures. Addison Wesley, Reading, MA, 1990.
186. R.J. Sandor Ritz. The temple of Santo Stefano Rotondo in Rome, the new Jerusal of Revelation. Tipografia PUG, Rome, 1970. in Italian.
187. A. Schrijver. Theory of Linear and Integer Programming. John Wiley, London, 1986.
188. R. Schneider. Convex Bodies: The Brunn-Minkowski Theory. Cambridge University Press, Cambridge, UK, 1993.
189. R. Seidel. A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions. Technical report, University of British Columbia, Dept. of Computer Science, 1981.
190. J. Springer and D.P. Friedman. Scheme and the Art of Programming. The MIT Press and McGraw-Hill, New York, 1997.
191. V. Shapiro. Solid modeling. In G. Farin, J. Hoschek, and M.S. Kim, editors, Handbook of Computer Aided Design. Elsevier Science Publishers, Oxford, 2001.
192. J.M. Snyder and J.T. Kajiya. Generative modeling: a symbolic system for geometric modeling. Computer Graphics, 26: 369-378, 1992. SIGGRAPH '92 Proceedings.
193. H.A. Sowizral and D.R. Nadeau. An Introduction to Programming AR and VR Applications in JavaSD. ACM Siggraph Tutorial, 1999.
194. J.M. Snyder. Generative Modeling for Computer Graphics and CAD. Academic Press, San Diego, CA, 1992.
195. C. Sobhanpanah. Extension of a boundary representation technique for the description of n dimensional polytopes. Computers & Graphics, 13(1): 17-23, 1989.
196. S. Scopigno, A. Paoluzzi, S. Guerrini, and G. Rumolo. Parallel depth merge: A paradigm for hidden surface removal. Computers & Graphics, 14(2), 1993.
197. H.A. Sowizral, K. Rushforth, and M. Deering. The Java 3D API Specification. Addison-Wesley, Reading, MA, 2000.
198. J.T. Schwartz and M. Sharir. Algorithmic motion planning in robotics. In Jan Van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A, Algorithms and Complexity. Elsevier and The MIT Press, Amsterdam, 1990.
199. I.E. Sutherland, R.F. Sproull, and R.A. Schumacker. A characterization of ten hidden-surface algorithms. ACM Computing Surveys, 6(1): 1-55, March 1974.
200. K.A. Steele. CPM/PERT. In Second Canadian Man-Computer Communications Conference, pages 81-84, May 1971.
201. K. Sugihara. Resolvable representation of polyhedra. In J. Turner, J. Rossignac, and G. Allen, editors, Second ACM/IEEE Symposium on Solid Modeling and Applications, pages 127-135, Montreal, CA, 1993. ACM Press.
202. V. Shapiro and D.L. Vossler. Construction and optimization of CSG representations. Computer-Aided Design, 23(1): 4-20, 1991.
203. V. Shapiro and D.L. Vossler. Separation for boundary to csg conversion. ACM Transactions on Graphics, 12(1): 35-55, 1993.
204. SVG Working Group. Scalable Vector Graphics (SVG) 1.1 Specification. Technical report, W3 Consortium, 2002. URL http://www.w3.org/TR/2002/PR-SVG11-20021115/.
205. T. Takala. Geometric boundary modeling without topological data structures. In A.A.G. Requicha, editor, Eurographics '86. North-Holland, Amsterdam, 1986.
206. T. Takala. A taxonomy of geometric and topological models. In Proc. Eurographics Workshop on Mathematics and Computer Graphics. S. Margherita, Genova, Italy, October 1991.
207. M.N. Thapa and G.B. Dantzig. Linear Programming 1: Introduction. Springer series in Operation Research. Springer-Verlag, Berlin, 1997.
208. Godfried T. Toussaint. Computational Morphology. North Holland. Amsterdam, 1988.
209. G.H. Timmer and J.M. Stern. Computation of global geometric properties of solid objects. Computer Aided Design, 12(6), 1980.
210. G. Vanĕček, Jr. Brep-index: A multidimensional space partitioning tree. International Journal of Computational Geometry and Applications, 1(3): 243-261, 1991.
211. T. Varady, R. Martin, and J. Cox. Reverse engineering of geometric models: an introduction. Computer-Aided Design, 29(6): 255-268, 1997.
212. H.B. Voelcker. The current state of affairs in dimensional tolerancing: 1997. Integrated Manufacturing Systems, 9(4): 205-217, 1998.
213. B. Von Hohenbalken. Least distance methods for the scheme of polytopes. Mathematical Programming, 15: 1-11, 1978.
214. B. Von Hohenbalken. Finding simplicial subdivisions of polytopes. Mathematical Programming, 21: 233-234, 1981.
215. K.J. Weiler. Topological structures for geometric modeling. PhD thesis. Rensselaer Polytechnic Institute, Albany, NY, 86.
216. M.J. Wenninger. Polyhedron Models. Cambridge University Press, Cambridge, UK, 1971.
217. J.H. Williams. Notes on the FP style of functional programming. In P. Henderson, J. Darlington, and D.A. Turner, editors, Functional Programming and its Applications, pages 219-247. Cambridge University Press, Cambridge. UK, 1982.
218. J. Wernecke and Open Inventor Architecture Group. The Inventor Mentor. Addison-Wesley, Reading, MA, 1994.
219. T. Woo. A combinatorial analysis of boundary data structure schemata. IEEE Computer Gaphics & Applications, 5(3): 19-27, March 1985.
220. J.H. Williams and E.L. Wimmers. An Optimizing Compiler Based on Program Transformation. Technical report, IBM Almaden Research Center, March 1991. Internal IBM report.
221. F.F. Yao. Computational geometry. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science, Chapter 7, pages 364-374. Elsevier, Amsterdam. 1990.
222. F. Yamaguchi and T. Tokieda. Bridge edge and triangulation approach in solid modeling. In T.L. Kunii, editor, Frontiers in Computer Graphics. Springer Verlag, Berlin, 1985.
223. G.M. Ziegler. Lectures on Polytopes. Number 152 in Graduate texts in mathematics. Springer-Verlag, New York, 1995.
224. S.N. Zilles, P. Lucas, T.M. Linden, J.B. Lotspiech, and A.R. Harbury. The Escher document imaging model. In ACM Conference on Document Processing Systems, 1988.