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CS 478

Computational Geometry

Computational Geometry is about designing algorithms and data structures that reason about shape, position, and proximity — turning intuitive questions like "which points are closest?" or "do these polygons overlap?" into provably efficient procedures with real lower bounds. You'll work through four homework sets and a term project on top of a midterm and final, implementing and analyzing the canonical machinery — convex hulls, Voronoi diagrams, Delaunay triangulations, sweep-line intersection — rather than just reading about them. Building on your algorithms background, the course is the natural bridge to graphics, robotics, GIS, and CAD, where geometric correctness and efficiency stop being optional.

Credit3ECTS5FacultyFaculty of EngineeringBölümComputer EngineeringPreCS 202

Değerlendirme 100% — 5 adım

20%
30%
20%
25%
5%
Midterm:Essay/written MT 20%
Final:Essay/written Final 30%
Homework HW 20%
Project Project 25%
In-class attendance Attendance 5%

Önerilen kaynaklar 3 kitap

📕
Zorunlu
Computational Geometry: An Introduction
F. P. Preparata and M.I. Shamos
1985 · Springer-Verlag
📖
Önerilen
Computational Geometry: Algorithms and Applications
M. de Berg, M. van Kreveld
M. Overmars · O. Schwarzkopf
📖
Önerilen
Computational Geometry in C
Joseph O'Rourke
2/1998 · Cambridge University Press Recommended - Software: Computational Geometry Pages

Haftalık müfredat 14 hafta

Hafta 1
Introduction: algorithmic background, data structures
Hafta 2
Introduction: geometric preliminaries, models of computation
Hafta 3
Geometric searching: point-location problems
Hafta 4
Geometrc searching: range-searching problems
Hafta 5
Convex hulls: problem statement and lower bounds, convex hull algorithms in the plane, Graham's scan, Jarvis's march
Hafta 6
Convex Hull: Quickhull techniques, divide-and-conquer algorithms, dynamic convex hull, convex hull in 3D
Hafta 7
Proximity: a collection of problems, a computational prototype: element uniqueness, lower bounds, the closest-pair problem: a divide-and-conquer approach
Hafta 8
Proximity problems: the Voronoi diagram, proximity problems solved by the Voronoi diagram
Hafta 9
Triangulation: planar triangulations
Hafta 10
Triangulation: Delaunay triangulation
Hafta 11
Intersections: application areas, planar applications: the intersection of convex polygons, the intersection of star-shaped polygons
Hafta 12
Intersection problems: the intersection of line segments, 3D applications: the intersection of 3D convex polyhedra
Hafta 13
Project presentations
Hafta 14
Project presentations

🤖 GenAI politikası

The use of GenAI tools such as ChatGPT as a supplementary resource in homework assignments or projects must be appropriately

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⚠️ FZ engelleyen şartlar

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

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