Generalized barycentric coordinates in computer graphics and computational mechanics / edited by Kai Hormann, N. Sukumar
- Published:
- Boca Raton, FL : CRC Press, [2018]
- Physical Description:
- xx, 314 pages ; 25 cm
- Additional Creators:
- Hormann, Kai and Sukumar, N.
- Contents:
- Machine generated contents note: ch. 1 Barycentric Coordinates and Their Properties -- 1.1.Introduction / Dmitry Anisimov -- 1.1.1.Barycentric coordinates for simplices / Dmitry Anisimov -- 1.1.2.Generalized barycentric coordinates / Dmitry Anisimov -- 1.2.2D Coordinates / Dmitry Anisimov -- 1.2.1.Wachspress coordinates / Dmitry Anisimov -- 1.2.2.Discrete harmonic coordinates / Dmitry Anisimov -- 1.2.3.Mean value coordinates / Dmitry Anisimov -- 1.2.4.Complete family of coordinates / Dmitry Anisimov -- 1.2.5.Metric coordinates / Dmitry Anisimov -- 1.2.6.Poisson coordinates / Dmitry Anisimov -- 1.2.7.Gordon-Wixom coordinates / Dmitry Anisimov -- 1.2.8.Harmonic coordinates / Dmitry Anisimov -- 1.2.9.Maximum entropy coordinates / Dmitry Anisimov -- 1.2.10.Local coordinates / Dmitry Anisimov -- 1.2.11.Affine coordinates / Dmitry Anisimov -- 1.2.12.Sibson coordinates / Dmitry Anisimov -- 1.2.13.Laplace coordinates / Dmitry Anisimov -- 1.2.14.Hermite coordinates / Dmitry Anisimov -- 1.2.15.Complex coordinates / Dmitry Anisimov -- 1.2.16.Comparison / Dmitry Anisimov -- 1.3.3D Coordinates / Dmitry Anisimov -- 1.3.1.Wachspress coordinates / Dmitry Anisimov -- 1.3.2.Discrete harmonic coordinates / Dmitry Anisimov -- 1.3.3.Mean value coordinates / Dmitry Anisimov -- 1.3.4.Complete family of coordinates / Dmitry Anisimov -- 1.3.5.Other coordinates / Dmitry Anisimov -- ch. 2 Shape Quality for Generalized Barycentric Interpolation / Dmitry Anisimov -- 2.1.Introduction / Alexander Rand / Andrew Gillette -- 2.2.Deconstructing The A Priori Error Estimate / Alexander Rand / Andrew Gillette -- 2.3.Shape Quality Metrics For Simplices / Alexander Rand / Andrew Gillette -- 2.4.Shape Quality Metrics For Polygons And Polyhedra / Alexander Rand / Andrew Gillette -- 2.5.Interpolation Error Estimates On Polygons / Alexander Rand / Andrew Gillette -- 2.5.1.Triangulation coordinates / Alexander Rand / Andrew Gillette -- 2.5.2.Harmonic coordinates / Alexander Rand / Andrew Gillette -- 2.5.3.Wachspress coordinates / Alexander Rand / Andrew Gillette -- 2.5.4.Mean value coordinates / Alexander Rand / Andrew Gillette -- 2.6.Interpolation Error Estimates On Polyhedra And Polytopes / Alexander Rand / Andrew Gillette -- 2.6.1.Harmonic coordinates in 3D and higher / Alexander Rand / Andrew Gillette -- 2.6.2.Wachspress coordinates in 3D and higher / Alexander Rand / Andrew Gillette -- 2.7.Extensions And Future Directions / Alexander Rand / Andrew Gillette -- ch. 3 Transfinite Barycentric Coordinates / Alexander Rand / Andrew Gillette -- 3.1.Introduction / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.2.Weighted Mean Value Interpolation / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.2.1.General construction / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.2.2.Transfinite three-point coordinates / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.2.3.Transfinite Laplace coordinates / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.2.4.Transfinite Wachspress coordinates / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.2.5.Transfinite Laplace and Wachspress coordinates coincide for a disk / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.3.Gordon-Wixom Interpolation / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.3.1.Lagrange-type Gordon-Wixom interpolation / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.3.2.Hermite-type Gordon-Wixom interpolation / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.3.3.Modified Hermite-type Gordon-Wixom interpolation / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.3.4.Modified Gordon-Wixom for polyharmonic interpolation / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.4.Generalized Mean Value Potentials And Distance Function Approximations / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.4.1.Generalized mean value potentials for smooth domains / Pierre-Alain Fayolle / Alexander G. Belyaev -- 3.4.2.Generalized potentials for polygons / Pierre-Alain Fayolle / Alexander G. Belyaev -- ch. 4 Barycentric Mappings / Pierre-Alain Fayolle / Alexander G. Belyaev -- 4.1.Introduction / Teseo Schneider -- 4.1.1.Convex polygons / Teseo Schneider -- 4.1.2.Arbitrary polygons / Teseo Schneider -- 4.2.Bijective Barycentric Mapping / Teseo Schneider -- 4.2.1.Perturbed target polygons / Teseo Schneider -- 4.3.Bijective Composite Barycentric Mapping / Teseo Schneider -- 4.3.1.Limit of composite barycentric mappings / Teseo Schneider -- 4.4.Extensions / Teseo Schneider -- 4.4.1.Closed planar curves / Teseo Schneider -- 4.4.2.Polyhedra / Teseo Schneider -- 4.5.Practical Considerations / Teseo Schneider -- 4.5.1.Choosing the coordinates / Teseo Schneider -- 4.5.2.Choosing the vertex paths / Teseo Schneider -- ch. 5 A Primer on Laplacians / Teseo Schneider -- 5.1.Introduction / Max Wardetzky -- 5.1.1.Basic properties / Max Wardetzky -- 5.2.Laplacians On Riemannian Manifolds / Max Wardetzky -- 5.2.1.Exterior calculus / Max Wardetzky -- 5.2.2.Hodge decomposition / Max Wardetzky -- 5.2.3.The spectrum / Max Wardetzky -- 5.3.Discrete Laplacians / Max Wardetzky -- 5.3.1.Laplacians on graphs / Max Wardetzky -- 5.3.2.The spectrum / Max Wardetzky -- 5.3.3.Laplacians on simplicial manifolds / Max Wardetzky -- 5.3.4.Strongly and weakly defined Laplacians / Max Wardetzky -- 5.3.5.Hodge decomposition / Max Wardetzky -- 5.3.6.The cotan Laplacian and beyond / Max Wardetzky -- 5.3.7.Discrete versus smooth Laplacians / Max Wardetzky -- ch. 6 Mesh Parameterization / Max Wardetzky -- 6.1.Introduction / Bruno Levy -- 6.2.Applications Of Mesh Parameterization / Bruno Levy -- 6.3.Notions Of Topology / Bruno Levy -- 6.4.Tutte's Barycentric Mapping Theorem / Bruno Levy -- 6.5.Solving The Linear Systems / Bruno Levy -- 6.6.Choosing The Weights / Bruno Levy -- ch. 7 Planar Shape Deformation / Bruno Levy -- 7.1.Introduction / Ofir Weber -- 7.2.Complex Barycentric Coordinates / Ofir Weber -- 7.2.1.Holomorphic functions / Ofir Weber -- 7.2.2.General construction of complex barycentric coordinates / Ofir Weber -- 7.2.3.Magic coordinates / Ofir Weber -- 7.3.Variational Barycentric Coordinates / Ofir Weber -- 7.3.1.Point-based barycentric maps / Ofir Weber -- 7.3.2.Point-to-point barycentric coordinates / Ofir Weber -- 7.4.Conformal Maps / Ofir Weber -- 7.4.1.Log derivative construction / Ofir Weber -- 7.4.2.Shape interpolation / Ofir Weber -- 7.4.3.Variational conformal maps / Ofir Weber -- 7.5.Implementation Details / Ofir Weber -- 7.5.1.Visualizing planar maps / Ofir Weber -- ch. 8 Multi-Sided Patches via Barycentric Coordinates / Ofir Weber -- 8.1.Introduction / Scott Schaefer -- 8.1.1.Bezier form of curves / Scott Schaefer -- 8.1.2.Evaluation / Scott Schaefer -- 8.1.3.Degree elevation / Scott Schaefer -- 8.2.Multisided Bezier Patches In Higher Dimensions / Scott Schaefer -- 8.2.1.Indexing for S-patches / Scott Schaefer -- 8.2.2.Evaluation / Scott Schaefer -- 8.2.3.Degree elevation / Scott Schaefer -- 8.3.Applications / Scott Schaefer -- 8.3.1.Surface patches / Scott Schaefer -- 8.3.2.Spatial deformation / Scott Schaefer -- ch. 9 Generalized Triangulations / Scott Schaefer -- 9.1.Introduction / Pooran Memari -- 9.2.Generalized Primal-Dual Triangulations / Pooran Memari -- 9.2.1.Some classical examples / Pooran Memari -- 9.2.2.Primal-dual triangulations (PDT) / Pooran Memari -- 9.3.A Characterization Theorem / Pooran Memari -- 9.3.1.Combinatorially regular triangulations (CRT) / Pooran Memari -- 9.3.2.Equivalence between PDT and CRT / Pooran Memari -- 9.3.3.Parametrization of primal-dual triangulations / Pooran Memari -- 9.4.Discrete Representation Using Generalized Triangulations / Pooran Memari -- 9.4.1.Discrete exterior calculus framework / Pooran Memari -- 9.4.2.Applications in mesh optimization / Pooran Memari -- ch. 10 Self-Supporting Surfaces / Pooran Memari -- 10.1.Introduction And Historical Overview / Etienne Vouga -- 10.1.1.What is a masonry structure? / Etienne Vouga -- 10.1.2.Heyman's safe theorem / Etienne Vouga -- 10.1.3.Gaudi and hanging nets / Etienne Vouga -- 10.1.4.Maxwell's reciprocal diagrams / Etienne Vouga -- 10.2.Smooth Theory / Etienne Vouga -- 10.2.1.Equilibrium equations / Etienne Vouga -- 10.2.2.Airy stress potential / Etienne Vouga -- 10.2.3.Relative curvatures / Etienne Vouga -- 10.2.4.Curvature interpretation of equilibrium / Etienne Vouga -- 10.3.Discrete Theory / Etienne Vouga -- 10.3.1.Thrust network analysis / Etienne Vouga -- 10.3.2.Thrust networks as block networks / Etienne Vouga -- 10.3.3.Discrete Airy stress potential / Etienne Vouga -- 10.3.4.FEM discretization of Airy stress / Etienne Vouga -- 10.3.5.Discrete curvature interpretation of equilibrium / Etienne Vouga -- 10.4.Optimizing For Stability / Etienne Vouga -- 10.4.1.Alternating optimization / Etienne Vouga -- 10.4.2.Dual formulation as vertex weights / Etienne Vouga -- 10.4.3.Perfect Laplacian optimization / Etienne Vouga -- 10.4.4.Relative-curvature-based smoothing / Etienne Vouga -- 10.4.5.Steel-glass structures and PQ faces / Etienne Vouga -- 10.4.6.Block layouts from stable surfaces / Etienne Vouga -- 10.5.Conclusion And Open Problems / Etienne Vouga -- 10.5.1.Sensitivity analysis of masonry structures / Etienne Vouga -- 10.5.2.Progressive stable structures / Etienne Vouga -- ch. 11 Applications of Polyhedral Finite Elements in Solid Mechanics / Etienne Vouga -- 11.1.Introduction / Joseph E. Bishop -- 11.2.Governing Equations Of Solid Mechanics / Joseph E. Bishop -- 11.3.Polyhedral Finite Element Formulation / Joseph E. Bishop -- 11.3.1.Weak form of governing equations / Joseph E. Bishop -- 11.3.2.Shape functions / Joseph E. Bishop -- 11.3.3.Element integration / Joseph E. Bishop -- 11.4.Rapid Engineering Analysis / Joseph E. Bishop -- 11.5.Fragmentation Modeling / Joseph E. Bishop -- 11.5.1.Fracture methodology / Joseph E. Bishop -- 11.5.2.Random Voronoi meshes / Joseph E. Bishop -- 11.5.3.Fragmentation / Joseph E. Bishop -- 11.6.Summary And Outlook / Joseph E. Bishop -- and Contents note continued: ch. 12 Extremely Large Deformation with Polygonal and Polyhedral Elements / Joseph E. Bishop -- 12.1.Introduction / Glaucio H. Paulino / Heno Chi / Cameron Talischi / Oscar Lopez-Pamies -- 12.2.Finite Elasticity Formulations / Glaucio H. Paulino / Oscar Lopez-Pamies / Cameron Talischi / Heno Chi -- 12.2.1.Displacement-based formulation / Glaucio H. Paulino / Heno Chi / Cameron Talischi / Oscar Lopez-Pamies -- 12.2.2.A general two-field mixed variational formulation / Glaucio H. Paulino / Heno Chi / Oscar Lopez-Pamies / Cameron Talischi -- 12.3.Polygonal And Polyhedral Approximations / Glaucio H. Paulino / Cameron Talischi / Heno Chi / Oscar Lopez-Pamies -- 12.3.1.Displacement space on polygons in 2D / Glaucio H. Paulino / Heno Chi / Oscar Lopez-Pamies / Cameron Talischi -- 12.3.2.Displacement space on polyhedra in 3D / Glaucio H. Paulino / Heno Chi / Cameron Talischi / Oscar Lopez-Pamies -- 12.3.3.Pressure space on polygons in 2D / Glaucio H. Paulino / Heno Chi / Oscar Lopez-Pamies / Cameron Talischi -- 12.4.Quadrature Rules And Accuracy Requirements / Cameron Talischi / Heno Chi / Glaucio H. Paulino / Oscar Lopez-Pamies -- 12.5.Gradient Correction Scheme And Its Properties / Heno Chi / Cameron Talischi / Oscar Lopez-Pamies / Glaucio H. Paulino -- 12.5.1.Gradient correction for scalar problems / Glaucio H. Paulino / Heno Chi / Cameron Talischi / Oscar Lopez-Pamies -- 12.5.2.Gradient correction for vectorial problems / Glaucio H. Paulino / Heno Chi / Cameron Talischi / Oscar Lopez-Pamies -- 12.6.Conforming Galerkin Approximations / Glaucio H. Paulino / Heno Chi / Oscar Lopez-Pamies / Cameron Talischi -- 12.7.Numerical Examples / Glaucio H. Paulino / Heno Chi / Cameron Talischi / Oscar Lopez-Pamies -- 12.7.1.Displacement-based polygonal and polyhedral elements / Glaucio H. Paulino / Cameron Talischi / Heno Chi / Oscar Lopez-Pamies -- 12.7.2.Two-field mixed polygonal elements / Glaucio H. Paulino / Oscar Lopez-Pamies / Cameron Talischi / Heno Chi -- 12.8.Application To The Study Of Filled Elastomers / Glaucio H. Paulino / Heno Chi / Cameron Talischi / Oscar Lopez-Pamies -- 12.8.1.Results for filled neo-Hookean elastomers / Glaucio H. Paulino / Heno Chi / Cameron Talischi / Oscar Lopez-Pamies -- 12.8.2.Results for a filled silicone elastomer / Glaucio H. Paulino / Oscar Lopez-Pamies / Cameron Talischi / Heno Chi -- ch. 13 Maximum-Entropy Meshfree Coordinates in Computational Mechanics / Glaucio H. Paulino / Heno Chi / Cameron Talischi / Oscar Lopez-Pamies -- 13.1.Introduction / Marino Arroyo -- 13.2.Selecting Barycentric Coordinates Through Entropy Maximization / Marino Arroyo -- 13.3.Introducing Locality: Local Maximum-Entropy Approximants / Marino Arroyo -- 13.4.Further Extensions / Marino Arroyo -- 13.5.Applications / Marino Arroyo -- 13.5.1.High-order partial differential equations / Marino Arroyo -- 13.5.2.Manifold approximation / Marino Arroyo -- 13.6.Outlook / Marino Arroyo -- ch. 14 BEM-Based FEM / Marino Arroyo -- 14.1.Introduction / Steffen Weiber -- 14.2.High-Order BEM-Based FEM In 2D / Steffen Weiber -- 14.2.1.Construction of basis functions / Steffen Weiber -- 14.2.2.Finite element method / Steffen Weiber -- 14.2.3.Introduction to boundary element methods / Steffen Weiber -- 14.2.4.Numerical examples / Steffen Weiber -- 14.3.Adaptive BEM-Based FEM In 2D / Steffen Weiber -- 14.3.1.Adaptive FEM strategy / Steffen Weiber -- 14.3.2.Residual-based error estimate for polygonal meshes / Steffen Weiber -- 14.3.3.Numerical examples / Steffen Weiber -- 14.4.Developments And Outlook / Steffen Weiber -- 14.4.1.Hierarchical construction for 3D problems / Steffen Weiber -- 14.4.2.Convection-adapted basis functions in 3D / Steffen Weiber -- ch. 15 Virtual Element Methods for Elliptic Problems on Polygonal Meshes / Steffen Weiber -- 15.1.Introduction / Andrea Cangiani / Oliver J. Sutton / Vitaliy Gyrya / Gianmarco Manzini -- 15.2.Virtual Element Spaces And GBC / Andrea Cangiani / Oliver J. Sutton / Gianmarco Manzini / Vitaliy Gyrya -- 15.2.1.Generalities / Vitaliy Gyrya / Oliver J. Sutton / Andrea Cangiani / Gianmarco Manzini -- 15.2.2.Lowest order discrete space / Andrea Cangiani / Oliver J. Sutton / Vitaliy Gyrya / Gianmarco Manzini -- 15.2.3.Generalization to arbitrary order discrete spaces / Vitaliy Gyrya / Oliver J. Sutton / Andrea Cangiani / Gianmarco Manzini -- 15.2.4.The natural basis / Andrea Cangiani / Oliver J. Sutton / Vitaliy Gyrya / Gianmarco Manzini -- 15.2.5.A convenient basis / Andrea Cangiani / Oliver J. Sutton / Gianmarco Manzini / Vitaliy Gyrya -- 15.2.6.A link between the bases / Andrea Cangiani / Oliver J. Sutton / Vitaliy Gyrya / Gianmarco Manzini -- 15.2.7.Extension to three dimensions / Gianmarco Manzini / Andrea Cangiani / Oliver J. Sutton / Vitaliy Gyrya -- 15.3.Virtual Element Method For Elliptic PDES / Vitaliy Gyrya / Oliver J. Sutton / Andrea Cangiani / Gianmarco Manzini -- 15.3.1.Model problem / Vitaliy Gyrya / Oliver J. Sutton / Andrea Cangiani / Gianmarco Manzini -- 15.3.2.Overview of the conforming VEM / Andrea Cangiani / Oliver J. Sutton / Vitaliy Gyrya / Gianmarco Manzini -- 15.4.Connection With Other Methods / Andrea Cangiani / Oliver J. Sutton / Vitaliy Gyrya / Gianmarco Manzini -- 15.4.1.Polygonal and polyhedral finite element method / Andrea Cangiani / Oliver J. Sutton / Gianmarco Manzini / Vitaliy Gyrya -- 15.4.2.Nodal MFD method / Vitaliy Gyrya / Oliver J. Sutton / Andrea Cangiani / Gianmarco Manzini -- 15.4.3.BEM-based FEM / Vitaliy Gyrya / Oliver J. Sutton / Andrea Cangiani / Gianmarco Manzini.
- Subject(s):
- ISBN:
- 9781498763592 hardcover ; alkaline paper
1498763596 hardcover ; alkaline paper - Bibliography Note:
- Includes bibliographical references and index.
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