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Discrete geometry investigates combinatorial properties of geometric
objects such as finite point sets or convex sets in Euclidean spaces.
Computational geometry considers the design of efficient algorithms
for computing with geometric configurations, and discrete geometry serves
as its mathematical foundation.
Part I of the course is a concise introduction. The contents of Part II
varies among the years, each year covering a few selected topics in more depth.
Last update: T_MUUK (31.01.2001)
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Serves as a mathematical foundation for areas using geometric computations (e.g., computer graphics, geometric optimization) and develops geometric intuition and imagination. Last update: T_KAM (20.04.2008)
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The credit for the exercise is given after obtaining at least 30 points for solving the school and home problems. The nature of the conditions do not allow repeated attempts for obtaining the credit. Obtaining the credit is necessary before the exam. Last update: Kynčl Jan, doc. Mgr., Ph.D. (12.10.2017)
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J. Matoušek: Lectures on Discrete Geometry, Springer, 2002
J. Pach, P. Agarwal: Combinatorial Geometry, Cambridge University Press 1995
M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf: Computational geometry: Algorithms and Applications, Springer-Verlag 1997 Last update: Kynčl Jan, doc. Mgr., Ph.D. (06.10.2015)
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The exercises consist in individual solving of problems assigned during the semester. More information: http://kam.mff.cuni.cz/kvg/eng.html Last update: Kynčl Jan, doc. Mgr., Ph.D. (24.02.2016)
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There will be oral exam with time for preparation of the answers. The material required for the exam will be the same as taught in the lecture. The exam may include easier or moderately difficult problems from these topics. The exam can also be in a distance form. Last update: Kynčl Jan, doc. Mgr., Ph.D. (10.10.2020)
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Basic theorems on convex sets (Helly, Radon, Caratheodory, separation).
Minkowski's theorem on lattice points in convex bodies.
Line-point incidences.
Geometric duality. Convex polytopes: definition, basic properties,
maximum number of faces.
Voronoi diagrams.
Hyperplane arrangements.
Arrangements of algebraic surfaces, pseudolines. Last update: Töpfer Pavel, doc. RNDr., CSc. (26.01.2018)
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The lecture will be taught alternatingly in Czech (2020/2021, ...) and in English (2021/2022, ...) The language may be changed in a particular year if all attendants agree with the change. Last update: Kynčl Jan, doc. Mgr., Ph.D. (30.07.2020)
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