Computational Geometry in CThis is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. The code in this edition is significantly improved from the first edition (more efficient and more robust), and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp. |
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Common terms and phrases
achieve adjacent angle arbitrary arrangement boundary called cell Chapter collinear complexity computational geometry cone connected constructed convex hull convex polygon coordinates counterclockwise cube data structure Define Delaunay triangulation deleted Design an algorithm determine diagonal disk dual endpoints Equation example Exercise faces floatingpoint guards halfplane horizontal implementation incremental algorithm independent set integer interior ladder Lemma length linear loop lower bound medial axis Minkowski sum monotone mountains monotone polygons motion planning moving nearest neighbor nodes nonconvex Note number of vertices O’Rourke O(log O(n log obstacles orthogonal polygon output partition plane pointer polyhedra polyhedron polytope Preparata problem programming proof quadrilateral query QuickHull random reachability region regular polytopes rightmost robot Section segments set of points shortest path shown in Figure sorting space stack star polygons tangent Theorem three dimensions threedimensional trapezoid tree twodimensional vector vertex visibility graph Voronoi diagram xyplane