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32
Mesh Generation
 HANDBOOK OF COMPUTATIONAL GEOMETRY. ELSEVIER SCIENCE
, 2000
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Dense Point Sets Have Sparse Delaunay Triangulations
"... Delaunay triangulations and Voronoi diagrams are one of the most thoroughly studies objects in computational geometry, with numerous applications including nearestneighbor searching, clustering, finiteelement mesh generation, deformable surface modeling, and surface reconstruction. Many algorithms ..."
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Delaunay triangulations and Voronoi diagrams are one of the most thoroughly studies objects in computational geometry, with numerous applications including nearestneighbor searching, clustering, finiteelement mesh generation, deformable surface modeling, and surface reconstruction. Many algorithms in these application domains begin by constructing the Delaunay triangulation or Voronoi diagram of a set of points in R³. Since threedimensional Delaunay triangulations can have complexity Ω(n²) in the worst case, these algorithms have worstcase running time \Omega (n2). However, this behavior is almost never observed in practice except for highlycontrived inputs. For all practical purposes, threedimensional Delaunay triangulations appear to have linear complexity. This frustrating
Optimal Möbius Transformations for Information Visualization and Meshing
 Meshing, WADS 2001, Lecture Notes in Computer Science 2125
, 2001
"... . We give lineartime quasiconvex programming algorithms for ..."
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. We give lineartime quasiconvex programming algorithms for
Conformal mapping in linear time
, 2006
"... Abstract. Given any ɛ> 0 and any planar region Ω bounded by a simple ngon P we construct a (1 + ɛ)quasiconformal map between Ω and the unit disk in time C(ɛ)n. One can take C(ɛ) = C + C log 1 ɛ log log ..."
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Abstract. Given any ɛ> 0 and any planar region Ω bounded by a simple ngon P we construct a (1 + ɛ)quasiconformal map between Ω and the unit disk in time C(ɛ)n. One can take C(ɛ) = C + C log 1 ɛ log log
SchwarzChristoffel Mapping in the Computer Era
"... . Thanks to powerful algorithms and computers, Schwarz Christoffel mapping is a practical reality. With the ability to compute have come new mathematical ideas. The state of the art is surveyed. 1991 Mathematics Subject Classification: 30C30, 31A05 Keywords and Phrases: conformal mapping, Schw ..."
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Cited by 15 (1 self)
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. Thanks to powerful algorithms and computers, Schwarz Christoffel mapping is a practical reality. With the ability to compute have come new mathematical ideas. The state of the art is surveyed. 1991 Mathematics Subject Classification: 30C30, 31A05 Keywords and Phrases: conformal mapping, SchwarzChristoffel formula 1. Introduction. In the past twenty years, because of new algorithms and new computers, SchwarzChristoffel conformal mapping of polygons has matured to a technology that can be used at the touch of a button. Many authors have contributed to this progress, including Dappen, Davis, Dias, Elcrat, Floryan, Henrici, Hoekstra, Howell, Hu, Reppe, Zemach, and ourselves. The principal SC software tools are the Fortran package SCPACK [15] and its more capable Matlab successor, the SchwarzChristoffel Toolbox [3]. It is now a routine matter to compute an SC map involving a dozen vertices to ten digits of accuracy in a few seconds on a workstation. With the power to compute...
A multipole method for SchwarzChristoffel mapping of polygons with thousands of sides
 SIAM J. Sci. Comput
"... Abstract. A method is presented for the computation of Schwarz–Christoffel maps to polygons with tens of thousands of vertices. Previously published algorithms have CPU time estimates of the order O(N 3) for the computation of a conformal map of a polygon with N vertices. This has been reduced to O( ..."
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Abstract. A method is presented for the computation of Schwarz–Christoffel maps to polygons with tens of thousands of vertices. Previously published algorithms have CPU time estimates of the order O(N 3) for the computation of a conformal map of a polygon with N vertices. This has been reduced to O(N log N) by the use of the fast multipole method and Davis’s method for solving the parameter problem. The method is illustrated by a number of examples, the largest of which has N ≈ 2 × 10 5. Key words. snowflake conformal mapping, fast multipole method, Schwarz–Christoffel mapping, Koch
History and Recent Developments in Techniques for Numerical Conformal Mapping
 PROCEEDINGS OF THE INTERNATIONAL WORKSHOP ON QUASICONFORMAL MAPPINGS AND THEIR APPLICATIONS (IWQCMA05)
, 2005
"... A brief outline is given of some of the main historical developments in the theory and practice of conformal mappings. Originating with the science of cartography, conformal mappings has given rise to many highly sophisticated methods. We emphasize the principles of mathematical discovery involved i ..."
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Cited by 6 (0 self)
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A brief outline is given of some of the main historical developments in the theory and practice of conformal mappings. Originating with the science of cartography, conformal mappings has given rise to many highly sophisticated methods. We emphasize the principles of mathematical discovery involved in
A General ConformalMapping Approach to the Optimum Electrode Design of Coplanar Waveguides With Arbitrary Cross Section
"... The SchwarzChristoffel toolbox, a free MATLAB package for the computation of conformal maps, is applied to the quasistatic analysis of coplanar waveguides (CPWs) of arbitrary cross section in order to provide computationally efficient and very accurate estimates of their capacitance, inductance, ..."
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The SchwarzChristoffel toolbox, a free MATLAB package for the computation of conformal maps, is applied to the quasistatic analysis of coplanar waveguides (CPWs) of arbitrary cross section in order to provide computationally efficient and very accurate estimates of their capacitance, inductance, characteristic impedance, and skineffect attenuation. A few examples of manysided polygonal waveguides are discussed, and the trapezoidal CPW, important, for example, for electrooptic modulators, is described in full detail, providing general guidelines for the electrode geometry optimization. The technique is validated through a comparison with the results of a fullwave finiteelement method, and excellent agreement is demonstrated both in vacuo and with twolayer dielectric substrates.