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7. References
Aho, A.V., Hopcroft, J.E., Ullman, J.D.: Data structures and algorithms. Reading: Addison-Wesley 1983.
Bentley, J.L., Ottmann, T.A.: Algorithms for reporting and counting geometric intersections. IEEE Trans. Comput. C-28, 643–647 (1979).
Bieri, H.: Eine Charakterisierung der Polyeder. Elemente Math. 35, 143–144 (1980).
Bieri, H., Nef, W.: A recursive sweep-plane algorithm, determining all cells of a finite division of Rd. Computing 28, 189–198 (1982).
Bieri, H., Nef, W.: A sweep-plane algorithm for computing the volume of polyhedra represented in Boolean form. Linear Algebra Appl. 52/53, 69–97 (1983).
Bieri, H., Nef, W.: A sweep-plane algorithm for computing the Euler-characteristic of polyhedra represented in Boolean form. Computing 34, 287–302 (1985).
Bieri, H.: Wechselwirkung zwischen der Computergrafik und der Theorie der Polyeder. Informatik-Fachberichte 126, 441–455. Berlin: Springer 1986.
Brüderlin, B.D.: Rule-based geometric modelling. Dissertation, ETH Zürich. Zürich: Verlag der Fachvereine 1988.
Bruggesser, H.: Ein Programmsystem für die graphische Darstellung von Polyedern. Dissertation, Universität Bern 1975.
Chazelle, B., Dobkin, D.P.: Intersection of convex objects in two and three dimensions. J.ACM 34, 1–27 (1987).
Edelsbrunner, H.: O'Rourke, J., Seidel, R.: Constructing arrangements of lines and hyperplanes with applications. SIAM J. Comput. 15, 341–363 (1986).
Edelsbrunner, H.: Algorithms in combinatorial geometry. Berlin: Springer 1987.
Hertel, S., Mäntylä, M., Mehlhorn, K., Nievergelt, J.: Space sweep solves intersection of convex polyhedra. Acta Informatica 21, 501–519 (1984).
Laidlaw, D.H., Trumbore, W.B., Hughes, J.F.: Constructive solid geometry for polyhedral objects. ACM SIGGRAPH'86 Proc., 161–170.
Maibach, B.: MATIP — Eine Benutzersprache und ein Interpreter für mathematische Anwendungen. Dissertation, Universität Bern 1982.
Mehlhorn, K., Simon, K.: Intersecting two polyhedra one of which is convex. Lecture Notes in Computer Science 199, 534–542. Berlin: Springer 1985.
Meier, A.: Methoden der grafischen und geometrischen Datenverarbeitung. Stuttgart: Teubner 1986.
Muller, D.E., Preparata, F.P.: Finding the intersection of two convex polyhedra. Theor. Comput. Sci. 7, 217–236 (1978).
Nef, W.: Beiträge zur Theorie der Polyeder, mit Anwendungen in der Computergraphik. Bern: Herbert Lang 1978.
Preparata, F.P., Shamos, M.I.: Computational geometry — An introduction. Berlin: Springer 1985.
Requicha, A.A.G.: Representations for rigid solids: Theory, methods, and systems. ACM Comput.Surv. 12, 437–464 (1980).
Schmidt, P.M.: Algorithm for constructing a sweep-plane which is in general position to a given point set. Manuskript, Friedrich-Schiller-Universität Jena 1987.
Shamos, M.I., Hoey, D.: Geometric intersection problems. 17th Annual IEEE Symp. Foundations of Comput Sci. 1976, 208–215.
Six, H.W., Wood, D.: Counting and reporting intersections of d-ranges. IEEE Trans. Comput. C-31, 181–187 (1982).
Vogel, V.: Mathematische Modelle für die Geometrieverarbeitung — mengentheoretisch-algebraische Grundlagen und ein (Fleisch, Haut)-Modell. Technische Universität Dresden, Sektion Mathematik, Nr. 07-07-84.
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Bieri, H., Nef, W. (1988). Elementary set operations with d-dimensional polyhedra. In: Noltemeier, H. (eds) Computational Geometry and its Applications. CG 1988. Lecture Notes in Computer Science, vol 333. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50335-8_28
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DOI: https://doi.org/10.1007/3-540-50335-8_28
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