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Abstract: Implicitly defined surface arise in many different contexts, from physical simulation to CAD and visualization. We describe a continuation algorithm for computing implitily defined surfaces. It is similar to analytic continuation, without the drawbacks of that algorithm. It is well suited to surfaces embedded in high dimensional spaces, has a natural step-size selection, and has no difficulties with global topologies which are not planar (i.e. spheres, tori etc.). Keywords: Surface... (Update)
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...or singularity manifolds. See Allgower Georg for a survey of some basic numerical techniques. A global scheme was developed by Henderson (1993), and a current software project (Pisces) for computing manifolds and their singularities is in progress (Wicklin (1995) 5.3.2...
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BibTeX entry: (Update)
Henderson, M. (1993), Computing implicitly defined surfaces: two parameter continuation, Technical report, IBM Thomas Watson Research Center, Yorktown Heights, N.Y. (IBM Research Report RC 18777). http://citeseer.ist.psu.edu/henderson93computing.html More
@techreport{ defined-research,
author = "Michael E. Henderson",
title = "Computing Implicitly Defined Surfaces: Two Parameter Continuation",
year = "1993",
number = "18777",
institution = "IBM Research",
url = "citeseer.ist.psu.edu/henderson93computing.html" }
Citations (may not include all citations):100 Polygonization of implicit surfaces - Bloomenthal - 1988
91 PLTMG: A Software Package for Solving Elliptic Partial Diffe.. (context) - Bank - 1990
52 An algorithm for piecewise-linear approximation of an implic.. (context) - Allgower, Schmidt - 1985
7 Functions of a Complex Variable (context) - Carrier, Krook et al. - 1966
2 On steplength algorithms for a class of continuation methods (context) - den Heijer, Rheinboldt - 1981
1 fixed points and solutions to systems of equations (context) - Allgower, Georg et al. - 1980
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