CIS 610, Spring 2006

Advanced Geometric Methods in Computer Science

Textbook:

• Geometric Methods and Applications

  
  Home page for book  

  and some class notes

• Convex sets, Polytopes, Combinatorial Topology, Voronoi Diagrams and Delaunay Triangulations (see below)
• The Classification Theorem for Compact Surfaces And a Detour on Fractals   (book home page)   (pdf)

Some Slides and Notes

• Preface and Chapter 1 of GMA (ps)   |  (pdf)
• Chapter 2 of GMA (ps)   |  (pdf)
• Chapter 3 of GMA (ps)   |  (pdf)
• Chapter 6 of GMA (ps)   |  (pdf)
• Basics on Affine spaces I (slides) (ps)   |  (pdf)
• Basics on Affine spaces II, Convex Sets, a first look (slides) (ps)   |  (pdf)
• Convex sets: A deeper look (slides) (ps)   |  (pdf)
• Euclidean Geometry (Gram-Schmidt) I (slides) (ps)   |  (pdf)
• Euclidean Geometry (Linear isometries, The Groups O(n), SO(n), QR-decomposition, the Cartan-Dieudonne' Theorem) II (slides) (ps)   |  (pdf)
• Euclidean Geometry (Affine isometries, The Groups Is(n), SE(n), Fixed Points of Affine Isometries, Cartan-Dieudonne', Orientation of a Euclidean space, Generalized Cross-product) III (slides) (ps)   |  (pdf)
• Polyhedra and Polytopes: A deeper look (slides) (ps)   |  (pdf)
• Basics of Combinatorial Topology (slides) (ps)   |  (pdf)
• Shellings, The Euler-Poincare' formula, Dehn-Sommerville equations, the Upper Bound Theorem (slides) (ps)   |  (pdf)

• Zvi Har'el's web site
• The Uniform Polyhedra (web site)
• Polyhedra Collection (Bulatov web site)
• Encyclopedia of Polyhedra (George Hart web site)
• George Hart's web site
• Paper models of polyhedra
• Polyhedra
• Polyhedra Pastimes
• Unfolding Polyhedra
• Tom Getty's Polyhedra

• Dirichlet-Voronoi diagrams and Delaunay triangulations (slides) (ps)   |  (pdf)
• Quaternions and Rotation, SO(3), RP^3, SO(4) (slides) (ps)   |  (pdf)

• Convex sets, Polytopes, Combinatorial Topology, Voronoi Diagrams and Delaunay Triangulations
  (book home page, html)

• The Classification Theorem for Compact Surfaces And a Detour on Fractals   (book home page)   (pdf)
• Manifolds, Part II   (slides, ps)   |  (slides, pdf)
• Notes on Group Actions, Manifolds, Lie Groups and Lie Algebras   (html)
• Updates and Corrections for Gunter Ziegler's book (pdf)
• Lecture Notes on Differentiable Manifolds, Geometry of Surfaces, etc., by Nigel Hitchin   (html)
• An Introduction to Riemannian Geometry, by S. Gudmundsson   (html)
• Bibliography (from book)   (ps)
• Clifford algebras, Clifford groups, and the groups Pin and Spin (notes)   (ps)   |  (pdf)
• ``Semi-secret'' Notes on algebraic geometry and algebra   (Algebra, html)   |  (Algebraic geometry, html)   |  (Complex algebraic geometry, html)
• Basics of Algebra and Analysis   (html)

Papers, Surveys and Talks of Interest

• Computational Geometry, Lecture 3 (Shang-Hua Teng) (ps)
• CS 267 Graph Partitioning (Kathy Yellick) (pdf)
• Topics in Geometric Combinatorics (Francis E Su) (pdf)
• Jonathan Shewchuk's Home page (html)
• Lecture notes on Delaunay mesh generation, by Jonathan Shewchuk (1999) (pdf)
• Theoretically garanteed Delaunay mesh generation in practice, Short Course, 13th IMR (2004),
  by Jonathan Shewchuk (pdf)
• Constrained Delaunay Triangulations ...,
  by Jonathan Shewchuk (pdf)
• Voronoi Diagrams, by Franz Aurenhammer and Rolf Klein (1996) (ps)
• Partitioning the permutahedron, by Etienne Rassart (pdf)
• Random Monotone Paths on Polyhedra, by Gunter Ziegler et al (pdf)
• Topological Issues in Hexahedral meshing, by David Eppstein (pdf)
• Visualizing the connection among convex hull, Voronoi diagram and Delaunay triangulation, by John Fisher (pdf)
• Shelling and Ranking (pdf)

Papers or Surveys Suitable for a Project

• Approximating center points with iterative Radon points (ps)
• A Deterministic Linear Time Algorithm for Geometric Separators and its Applications (ps)
• Regression Depth and Center Points (pdf)
• Computing a centerpoint of a finite planar set of points in linear-time (pdf)
• The complexity of finding small triangulations of convex 3-polytopes, by A. Below, J. De Loera and J. Richter-Gebert (pdf)
• A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation, by Jim Ruppert (pdf)
• When and why Ruppert's algorithm works, by G. Miller, S. Pav and N. Walkington (pdf)
• How good are convex hull algorithms, by D. Avis, D. Bremner and R. Seidel (pdf)
• Convex Hull, Oracles, and Homology, by M. Joswig and G. Ziegler (pdf)
• Algorithms for center and Tverberg points (pdf)
• From Polytopes to Enumeration, by Ed Swartz (pdf)
• Combinatorics with a geometric flavor: some examples, by Gil Kalai (pdf)
• Polytopes Skeletons and Paths, by Gil Kalai (pdf)
• An Introduction to Hyperplane Arrangements, by Richard Stanley (pdf)
• Face Numbers of Polytopes and Complexes, by Louis Bellera and A. Bjorner (pdf)
• The g-Theorem, MA715 Course Notes, by Carl Lee (pdf)
• Triangulations and meshes in computational geometry, by Herbert Edelsbrunner (pdf)
• Computational Topology, by Tamal Dey, Herbert Edelsbrunner and Sumanta Guha (pdf)
• Lectures in Geometric Combinatorics, by Rekha R. Thomas (pdf)
• Triangulations of Point Sets, By J. De Loera, J. Rambau and F. Santos (pdf)

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published by:

Jean Gallier