Classical and Discrete Differential Geometry: Theory, Applications and Algorithms

ISBN-13: 9781032390178 / Angielski / Twarda / 2023 / 608 str.

Emil Saucan

Opis

This book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks.

Spis treści

Section I Differential Geometry, Classical and Discrete  1. Curves  2. Surfaces: Gauss Curvature – First Definition  3. Metrization of Gauss Curvature  4. Gauss Curvature and Theorema Egregium  5. The Mean and Gauss Curvature Flows  6. Geodesics  7. Geodesics and Curvature  8. The Equations of Compatibility  9. The Gauss-Bonnet Theorem and the Poincare Index Theorem  10. Higher Dimensional Curvatures  11. Higher Dimensional Curvatures  12. Discrete Ricci Curvature and Flow  13. Weighted Manifolds and Ricci Curvature Revisited  Section II Differential Geometry, Computational Aspects  14. Algebraic Topology  15. Homology and Cohomology Group  16. Exterior Calculus and Hodge Decomposition 17. Harmonic Map  18. Riemann Surface  19. Conformal Mapping  20. Discrete Surface Curvature Flows  21. Mesh Generation Based on Abel-Jacobi Theorem  Section III Appendices  22. Appendix A  23. Appendix B  24. Appendix C