Computational Geometry

The course is a substitute for:

Computational Geometry (X39VGE)

Lecturer:

Tutor:

Supervisor:

Department of Computer Science and Engineering

Synopsis:

Principles of computational geometry (CG), data structures and paradigms, methods of geometric search, convex polygons and hulls, applications of convex hull, proximity problems, Voronoi diagrams, triangulation, efficient intersection algorithms, intersection of semispaces and polygonal regions, geometry of rectangles, dual mappings and spaces, convex hull in dual space, algorithms of computer graphics and CG.

Requirements:

Syllabus of lectures:

1. Subject of computational geometry (CG)

2. Data structures and paradigms in CG

3. Methods of geometric searching

4. Convex hulls and convex polygons

5. Applications of convex hull

6. Proximity problem

7. Voronoi diagram

8. Triangulation of polygons

9. Intersections of segments and lines

10. Intersection of semispaces and polygonal regions

11. Geometry of rectangles

12. Dual mappings and spaces, convex hull in dual space

13. Algorithms of computer graphics & computational geometry

14. Application of CG in Geographic Information Systems

Syllabus of tutorials:

1. Assignment of topics for individual presentations

2. Representation of Planar graph, search trees

3. Interval search, BSP trees

4. Searching in planar subdivision

5. Convex hull in 2D

6. Convex hull in 3D. Diameter of a point set.

7. Construction of higher order Voronoi diagram( VD). Generalization of VD

8. Proximity problems solved by the Voronoi diagram

9. Delaunay triangulation and minimal weight triangulation

10. Application of triangulations, stratification of the triangulation.

11. Algebra of polygonal areas. Searching of the polygon core.

12. Construction of the boundary of unified rectangles, intersection of rectangles.

13. Application of algorithms and methods of Computational Geometry in Computer Graphics.

14. Crediting

Study Objective:

Study materials:

[1] Preperata, F.P., Shamos, M.I.: Computational Geometry An Introduction. Springer-Verlag, Berlin 1985

[2] Edelsbrunner, H.: Algorithms in Combinatorial Geometry. Springer-Verlag, Berlin 1987

[3] de Berg, M.,van Kreveld, M., Overmars, M., Schvarzkopf, O.: Computational Geometry. Springer-Verlag, Berlin 1997

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: