1. Computational Geometry Definition and Application Areas
2. Computational Geometry is a subfield of the Design and Analysis of Algorithms
3. Computational Geometry is a subfield of the Design and Analysis of Algorithms deals with efficient data structures and algorithms for geometric problems
4. Computational Geometry is a subfield of the Design and Analysis of Algorithms deals with efficient data structures and algorithms for geometric problems is only about 30 years old
5. Computational Geometry is a subfield of the Design and Analysis of Algorithms deals with efficient data structures and algorithms for geometric problems is only about 30 years old started out by developing solid theoretical foundations, but became more and more applied over the last years
15. Collision detection Bounding volume heuristic: Approximate the objects by simple ones that enclose them (bounding volumes)
16. Collision detection Bounding volume heuristic: Approximate the objects by simple ones that enclose them (bounding volumes) popular bounding volumes: boxes, spheres, ellipsoids,...
17. Collision detection Bounding volume heuristic: Approximate the objects by simple ones that enclose them (bounding volumes) popular bounding volumes: boxes, spheres, ellipsoids,... if bounding volumes don’t intersect, the objects don’t intersect, either
18. Collision detection Bounding volume heuristic: Approximate the objects by simple ones that enclose them (bounding volumes) popular bounding volumes: boxes, spheres, ellipsoids,... if bounding volumes don’t intersect, the objects don’t intersect, either only if bounding volumes intersect, apply more expensive intersection test(s)
19. In this Course:Smallest enclosing ball Given: finite point set in R d
20. In this Course:Smallest enclosing ball Given: finite point set in R d Wanted: the smallest ball that contains all the points
21. In this Course:Smallest enclosing ball Given: finite point set in R d Wanted: the smallest ball that contains all the pointspopular free software (also some commerciallicenses sold): http://www.inf.ethz.ch/personal/gaertner/miniball.html
22. Boolean Operations Given two (2d,3d) shapes, compute their...
23. Boolean Operations ubiquituous in computer-aided design
24. In this Course: Arrangements of lines
25. In this Course: Arrangements of lines Link to Boolean Operations:
26. In this Course: Arrangements of lines Link to Boolean Operations: Arrangement “contains” all the unions / differences / intersections
27. Boolean Operations Important point: no roundoff errors!
28. Boolean Operations Important point: no roundoff errors!
29. Boolean Operations Important point: no roundoff errors!
30. Boolean Operations Exact computation correct: intersection is 1-dimensional
31. Boolean Operations Naive floating-point computation wrong: intersection is 2-dimensional
32. In this Course:CGAL Computational Geometry Algorithms Library
33. In this Course:CGAL Computational Geometry Algorithms Library C++ library of efficient data structures and algorithms for many computational geometry problems
34. In this Course:CGAL Computational Geometry Algorithms Library C++ library of efficient data structures and algorithms for many computational geometry problems exists since 1996 (Michael Hoffmann and Bernd Gärtner are members of the editorial board)
35. In this Course:CGAL Computational Geometry Algorithms Library C++ library of efficient data structures and algorithms for many computational geometry problems exists since 1996 (Michael Hoffmann and Bernd Gärtner are members of the editorial board) supports roundoff-free exact computations
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