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00047894 contributor B40987.
00047894 created "2002.".
00047894 date "2002".
00047894 date "2002.".
00047894 dateCopyrighted "2002.".
00047894 description "Includes bibliographical references (p. 581-594) and index.".
00047894 description "Machine generated contents note: 1 Discrete Modeling for Natural Objects 1 -- 1.1 Introduction1 -- 1.2 Discrete modeling5 -- 1.3 Interpolation12 -- 1.4 Examples of applications19 -- 1.5 Conclusions26 -- 2 Cellular Partitions 27 -- 2.1 Introduction27 -- 2.2 Elements of topology28 -- 2.3 Cellular partition of an n-manifold object36 -- 2.4 Generalized Maps57 -- 2.5 Implementing GMap-based models81 -- 2.6 Conclusions93 -- 3 Tessellations 97 -- 3.1 Introduction97 -- 3.2 Delaunay's tessellation98 -- 3.3 Non-Delaunay triangulated surfaces109 -- 3.4 Notion of a regular n-grid122 -- 3.5 Notion of an irregular n-grid132 -- 3.6 Implicit surfaces134 -- 3.7 Conclusions137 -- 4 Discrete Smooth Interpolation 139 -- 4.1 Introduction139 -- 4.2 The DSI problem147 -- 4.3 Uniqueness of the DSI solution153 -- 4.4 The local DSI equation160 -- 4.5 Accounting for hard constraints170 -- 4.6 Accelerating the convergence174 -- 4.7 The fuzzy Control-Point paradigm182 -- 4.8 The fuzzy Control-Node paradigm190 -- 4.9 From a discrete to a continuous model193 -- 4.10 Conclusions196 -- 5 Elements of Differential Geometry 199 -- 5.1 Parametric curves199 -- 5.2 Parametric surfaces203 -- 5.3 Curvature of curves drawn on a surface 211 -- 5.4 Miscellaneous 218 -- 5.5 Discrete modeling 226 -- 5.6 Examples of applications to geology 233 -- 5.7 Conclusions 244 -- 6 Piecewise Linear Triangulated Surfaces 245 -- 6.1 Introduction245 -- 6.2 Basic DSI constraints256 -- 6.3 Modeling a faulted surface272 -- 6.4 Continuity through faults278 -- 6.5 Global parameterization 287 -- 6.6 Modifying the topology305 -- 6.7 Conclusions 315 -- 7 Curvilinear Triangulated Surfaces 317 -- 7.1 Introduction317 -- 7.2 Building a smooth curvilinear triangle318 -- 7.3 Gregory G1 patchwork336 -- 7.4 Recursive subdivisions 3350 -- 7.5 Conclusions369 -- 8 Elements of Structural Geology 371 -- 8.1 Geometry of faults and horizons371 -- 8.2 Modeling stratified media379 -- 8.3 Merging seismic data with well data390 -- 8.4 Deformation analysis 392 -- 8.5 Unfolding a horizon405 -- 8.6 Unfolding a stack of layers418 -- 8.7 Conclusions 441 -- 9 Stochastic Modeling 443 -- 9.1 Simulation versus interpolation443 -- 9.2 Probabilities in a nutshell 445 -- 9.3 Random Functions 459 -- 9.4 Random Fourier Series474 -- 9.5 Uniform Random Functions and P-fields488 -- 9.6 Stochastic simulators 492 -- 9.7 Kriging-based methods 5502 -- 9.8 Blending-based method519 -- 9.9 Assessing geometric uncertainties528 -- 9.10 Conclusions532 -- 10 Discrete Smooth Partition 533 -- 10.1 Introduction533 -- 10.2 The probabilistic approach538 -- 10.3 Structural constraints548 -- 10.4 Moving-Centers-based methods559 -- 10.5 A tutorial example572 -- 10.6 Conclusions579.".
00047894 extent "viii, 599 p. :".
00047894 identifier "0195144600 (acid-free paper)".
00047894 identifier 00047894-d.html.
00047894 identifier 00047894.html.
00047894 isPartOf "Applied geostatistics series".
00047894 issued "2002".
00047894 issued "2002.".
00047894 language "eng".
00047894 publisher "Oxford ; New York : Oxford University Press,".
00047894 subject "550/.1/13 21".
00047894 subject "Computer-aided design.".
00047894 subject "Geology Computer simulation.".
00047894 subject "QE48.8 .M34 2002".
00047894 tableOfContents "Machine generated contents note: 1 Discrete Modeling for Natural Objects 1 -- 1.1 Introduction1 -- 1.2 Discrete modeling5 -- 1.3 Interpolation12 -- 1.4 Examples of applications19 -- 1.5 Conclusions26 -- 2 Cellular Partitions 27 -- 2.1 Introduction27 -- 2.2 Elements of topology28 -- 2.3 Cellular partition of an n-manifold object36 -- 2.4 Generalized Maps57 -- 2.5 Implementing GMap-based models81 -- 2.6 Conclusions93 -- 3 Tessellations 97 -- 3.1 Introduction97 -- 3.2 Delaunay's tessellation98 -- 3.3 Non-Delaunay triangulated surfaces109 -- 3.4 Notion of a regular n-grid122 -- 3.5 Notion of an irregular n-grid132 -- 3.6 Implicit surfaces134 -- 3.7 Conclusions137 -- 4 Discrete Smooth Interpolation 139 -- 4.1 Introduction139 -- 4.2 The DSI problem147 -- 4.3 Uniqueness of the DSI solution153 -- 4.4 The local DSI equation160 -- 4.5 Accounting for hard constraints170 -- 4.6 Accelerating the convergence174 -- 4.7 The fuzzy Control-Point paradigm182 -- 4.8 The fuzzy Control-Node paradigm190 -- 4.9 From a discrete to a continuous model193 -- 4.10 Conclusions196 -- 5 Elements of Differential Geometry 199 -- 5.1 Parametric curves199 -- 5.2 Parametric surfaces203 -- 5.3 Curvature of curves drawn on a surface 211 -- 5.4 Miscellaneous 218 -- 5.5 Discrete modeling 226 -- 5.6 Examples of applications to geology 233 -- 5.7 Conclusions 244 -- 6 Piecewise Linear Triangulated Surfaces 245 -- 6.1 Introduction245 -- 6.2 Basic DSI constraints256 -- 6.3 Modeling a faulted surface272 -- 6.4 Continuity through faults278 -- 6.5 Global parameterization 287 -- 6.6 Modifying the topology305 -- 6.7 Conclusions 315 -- 7 Curvilinear Triangulated Surfaces 317 -- 7.1 Introduction317 -- 7.2 Building a smooth curvilinear triangle318 -- 7.3 Gregory G1 patchwork336 -- 7.4 Recursive subdivisions 3350 -- 7.5 Conclusions369 -- 8 Elements of Structural Geology 371 -- 8.1 Geometry of faults and horizons371 -- 8.2 Modeling stratified media379 -- 8.3 Merging seismic data with well data390 -- 8.4 Deformation analysis 392 -- 8.5 Unfolding a horizon405 -- 8.6 Unfolding a stack of layers418 -- 8.7 Conclusions 441 -- 9 Stochastic Modeling 443 -- 9.1 Simulation versus interpolation443 -- 9.2 Probabilities in a nutshell 445 -- 9.3 Random Functions 459 -- 9.4 Random Fourier Series474 -- 9.5 Uniform Random Functions and P-fields488 -- 9.6 Stochastic simulators 492 -- 9.7 Kriging-based methods 5502 -- 9.8 Blending-based method519 -- 9.9 Assessing geometric uncertainties528 -- 9.10 Conclusions532 -- 10 Discrete Smooth Partition 533 -- 10.1 Introduction533 -- 10.2 The probabilistic approach538 -- 10.3 Structural constraints548 -- 10.4 Moving-Centers-based methods559 -- 10.5 A tutorial example572 -- 10.6 Conclusions579.".
00047894 title "Geomodeling / Jean-Laurent Mallet.".
00047894 type "text".