N. Amenta, Computational geometry software, In Goodman and O'Rourke [19], pp. 951{ 960.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and many more. The purpose of polymake is to combine the features of these (and other) programs and to go beyond. Many features of the polymake system are realized by interfacing to these programs. For an overview over existing software systems in the area of Computational Geometry see Amenta [2]. Here we describe polymake Version 1.3, released Feb 12, 1999. 1 2 Exploring polymake 2.1 First Steps Suppose you have a nite set of points in some vector space R d . Their convex hull is a polytope P . Now you want to know how many facets the polytope P has. As an example let the set S ....

....subtle. Successfully written data must be acknowledged by the client. This is the code of the client rank already discussed above, cf. Section 5.5. We stripped some #include statements plus the parameter checks. int main (int argc, char argv[ Poly p (argv[1] ios: in ios: out) p. read(argv[2], 0) p.write(argv[3] 0) Matrix Rational M(p) p rank(M) argc= 5 atoi(argv[4] 0) n endl; return 0; The code uses the template class Matrix which is part of the PTL, cf. Section 5.6. The function rank( is a friend function of this class. The Rational class is a ....

N. Amenta, Computational geometry software, In Goodman and O'Rourke [19], pp. 951{ 960.

....construct the planar map induced by a set of (possibly intersecting) segments. LEDA also supports a subdivision class for planar maps of non intersecting segments with point location queries. Both implementations are restricted to dealing with linear objects line segments or polygons. Amenta [1, 2] also points to the pploc package for answering vertical ray shooting queries in a set of non intersecting line segments (which seems much more restricted than the other packages) The MAPC library [17] is a software package for manipulating algebraic points and curves. It has been used to ....

N. Amenta. Computational geometry software. In J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, chapter 52, pages 951--

....with the C programming language [10] and the basics of its Standard Template Library. Copyright c # 1999 John Wiley Sons, Ltd. Softw. Pract. Exper. 29(00) 1 38 (1999) Prepared using speauth.cls 4 A. FABRI, G. J. GIEZEMAN, L. KETTNER, S. SCHIRRA, S. SCH ONHERR RELATED WORK Amenta [11] gives an overview on the state of the art of computational geometry software before CGAL and provides many references. Computational geometry software was intensively discussed at the First ACM Workshop on Applied Computational Geometry [12, 13, 14] The design of the CGAL kernel at that time is ....

N. Amenta, `Computational geometry software', Handbook of Discrete and Computational Geometry, CRC Press, 1997, pp. 951--960.

....of the library and a brief description of its various parts. Cgal is de nitely not the only software development e ort of computational geometry algorithms. Implementations of geometric algorithms have been reported in the literature and were made available for various problems; see [7] and [8]. These include libraries and workbench e orts. Schirra [69] comments that as far as libraries workbenches are concerned, two have paid special attention to robustness issues: The XYZ workbench and Leda. This paper concentrates on arrangements and motion planning. Arrangements are space ....

N. Amenta. Computational geometry software. In J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, chapter 52, pages 951-960. CRC Press LLC, Boca Raton, FL, 1997.

....with size functions is available via http: www. dm.unibo.it ferri vismath sizefcts sizehom2.htm. No matching software is available via Netlib (http: netlib.bell labs.com netlib index.html) and no matching software at all is mentioned in the overview of computational geometry software of [Ame97] For implementing geometric algorithms, CGAL, the Computational Geometry Algorithms Library is available via http: www.cs.uu.nl CGAL . The library provides geometric primitives such as points, lines, and triangles, basic operations such as distance and intersection calculations, as well as ....

Nina Amenta. Computational Geometry Software, chapter 52, pages 951-960. In Goodman and O'Rourke [GO97], 1997.

....and testing. These are discussed in Section 9. We conclude with an evaluation of the design. In the more technical parts of the paper we assume that the reader is familiar with the C programming language and the basics of its Standard Template Library, see e.g. Str97] 2 Related Work Amenta [Ame97] gives an overview on the state of the art of computational geometry software before Cgal and provides many references. Computational geometry software was intensively discussed at the First ACM Workshop on Applied Computational Geometry, cf. Lee96, Meh96, Ove96] The design of the Cgal kernel ....

N. Amenta. Computational geometry software. In Handbook of Discrete and Computational Geometry, pages 951--960. CRC Press, 1997.

.... the geometry part of the Library of Efficient Data types and Algorithms LEDA 3 [MN95, Meh 97] the Computational Geometry Algorithms Library CGAL 4 [Fab 98] the GEOMLIB 5 project [Bak 97] or the rich collection of geometric programs in the Directory of Computational Geometry Software 6 [Ame97]. As mentioned before, the numerical problems can usually be circumvented by simulating infinite precision. Several successful techniques have recently been proposed in order to keep the slowdown small see [Bur 95, FW96, She97, Avn 97] but some penalty in running time has to be accepted. ....

N. AMENTA, Computational geometry software. In [GO97] (1997) 951--960.

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