Cover -- Title -- Copyright -- Contents -- Preface -- 1 POLYGONS -- 1.1 Diagonals and Triangulations -- 1.2 Basic Combinatorics -- 1.3 The Art Gallery Theorem -- 1.4 Scissors Congruence in 2D -- 1.5 Scissors Congruence in 3D -- 2 CONVEX HULLS -- 2.1 Convexity -- 2.2 The Incremental Algorithm -- 2.3 Analysis of Algorithms -- 2.4 Gift Wrapping and Graham Scan -- 2.5 Lower Bound -- 2.6 Divide-and-Conquer -- 2.7 Convex Hull in 3D -- 3 TRIANGULATIONS -- 3.1 Basic Constructions -- 3.2 The Flip Graph -- 3.3 The Associahedron -- 3.4 Delaunay Triangulations -- 3.5 Special Triangulations -- 4 VORONOI DIAGRAMS -- 4.1 Voronoi Geometry -- 4.2 Algorithms to Construct the Diagram -- 4.3 Duality and the Delaunay Triangulation -- 4.4 Convex Hull Revisited -- 5 CURVES -- 5.1 Medial Axis -- 5.2 Straight Skeleton -- 5.3 Minkowski Sums -- 5.4 Convolution of Curves -- 5.5 Curve Shortening -- 5.6 The Heat Equation -- 5.7 Curve Reconstruction -- 6 POLYHEDRA -- 6.1 Platonic Solids -- 6.2 Euler's Polyhedral Formula -- 6.3 The Gauss-Bonnet Theorem -- 6.4 Cauchy Rigidity -- 6.5 Shortest Paths -- 6.6 Geodesics -- 7 CONFIGURATION SPACES -- 7.1 Motion Planning -- 7.2 Polygonal Chains -- 7.3 Rulers and Locked Chains -- 7.4 Polygon Spaces -- 7.5 Particle Collisions -- Appendix: Computational Complexity -- Permissions -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.