Introduction: algorithmic background, data structures, geometric preliminaries, models of computation. Geometric searching: point-location problems, range-searching problems. Convex hulls: problem statement and lower bounds, convex hull algorithms in the plane, Graham's scan, Jarvis's march, Quickhull techniques, divide-and-conquer algorithms, dynamic convex hull, convex hull in 3D. Proximity: a collection of problems, a computational prototype: element uniqueness, lower bounds, the closest-pair problem: a divide-and-conquer approach, the Voronoi diagram, proximity problems solved by the Voronoi diagram. Triangulation: planar triangulations, Delaunay triangulation. Intersections: application areas, planar applications: intersection of convex polygons, intersection of star-shaped polygons, intersection of line segments, 3D applications: intersection of 3D convex polyhedra, intersection of half-spaces.
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Course Learning Outcomes: Course Learning Outcome Assessment Apply knowledge of mathematics MT HW Project Utilize and extend known algorithms, design paradigms and data structures for the solution of engineering problems MT HW Project Use modern software systems and tools Project
The use of GenAI tools such as ChatGPT as a supplementary resource in homework assignments or projects must be appropriately
Introduction: algorithmic background, data structures Introduction: geometric preliminaries, models of computation Geometric searching: point-location problems Geometrc searching: range-searching problems Convex hulls: problem statement and lower bounds, convex hull algorithms in the plane, Graham's scan, Jarvis's march Convex Hull: Quickhull techniques, divide-and-conquer algorithms, dynamic convex hull, convex hull in 3D Proximity: a collection of problems, a computational prototype: element uniqueness, lower bounds, the closest-pair problem: a divide-and-conquer approach Proximity problems: the Voronoi diagram, proximity problems solved by the Voronoi diagram Triangulation: planar triangulations Triangulation: Delaunay triangulation Intersections: application areas, planar applications: the intersection of convex polygons, the intersection of star-shaped polygons Intersection problems: the intersection of line segments, 3D applications: the intersection of 3D convex polyhedra Project presentations Project presentations ECTS - Workload Table: Activities Number Hours Workload Final exam 1 2 2 Preparation for Midterm exam 1 6 6 Presentation (including preparation) 1 ,5 .5 Homework 4 4 16 Project (including preparation and presentation if applicable) 1 30 30 Midterm exam 1 2 2 Report (including preparation and presentation if applicable) 2 5 10 Preperation for Final exam 1 6 6 Individual or group work 14 3 42 Course hours 14 3 42 Total Workload: 156.5 Total Workload / 30: 156.5 / 30 5.22 ECTS Credits of the Course: 5 Type of Course: Lecture - Project Course Material: Slides - Lecture Notes - Computer (Laptop, Desktop) Teaching Methods: Lecturing - Assignment - Presentations