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  • Dec 14, 2018

    Geometric Algorithm In Computer Science - Learnengineeringforu

    Computational geometry studies the design, analysis, and implementation of algorithms and data structures for geometric problems. These problems arise in a wide range of areas, including CAD/CAM, robotics, computer graphics, molecular biology, GIS, spatial databases, sensor networks, and machine learning. In addition to the tools developed in computer science, the study of geometric algorithms also requires ideas from various mathematical disciplines, e.g., combinatorics, topology, algebra, and differential geometry. This close interaction between various mathematical and practical areas has had a beneficial impact on both basic and applied research in computational geometry.The goal of this course is to provide an overview of the techniques developed in computational geometry as well as some of its application areas. The topics covered in the course will include:1. Geometric Fundamentals: Models of computation, lower bound techniques, geometric primitives, geometric transforms2. Convex hulls: Planar convex hulls, higher dimensional convex hulls, randomized, output-sensitive, and dynamic algorithms, applications of convex hull3. Intersection detection: segment intersection, line sweep, map overlay, halfspace intersection, polyhedra intersection4. Geometric searching: segment, interval, and priority-search trees, point location, persistent data structure, fractional cascading, range searching, nearest-neighbor searching5. Proximity problems: closest pair, Voronoi diagram, Delaunay triangulation and their subgraphs, spanners, well separated pair decomposition6. Arrangements: Arrangements of lines and hyperplanes, sweep-line and incremental algorithms, lower envelopes, levels, and zones, applications of arrangements7. Triangulations: monotone and simple polygon triangulations, point-set triangulations, optimization criteria, Steiner triangulation, Delaunay refinement8. Geometric sampling: random sampling and ε-nets, ε-approximation and discrepancy, cuttings, coresets9. Geometric optimization: linear programming, LP-type problems, parametric searching, approximation techniques10. Implementation Issues : robust computing, perturbation techniques, floating-point filters, rounding techniques

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