Computational geometry introduction
Dive into the fundamentals of computational geometry with this introduction by Rugaia Omer Ahmed. Explore key concepts, algorithms, and applications in the field. Gain insights into geometric computations and problem-solving techniques. Enhance your understanding of spatial data structures and geometric operations. Whether you're a beginner or seeking a refresher, this resource provides a solid foundation in computational geometry.
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Presentation Transcript
Computational geometry introduction Lech -1 By Rugaia Omer Ahmed
Computational Geometry introduction
Lecture outlines Computational geometry definition Computational geometry application . Computational geometry history. Computational geometry branches . Reference Computational Geometry Algorithms and Applications Authors: Berg, M. de, Kreveld, M. van, Overmars, M., Schwarzkopf, O (1997)
Definition 1-Design of efficient algorithms and data structures for spatial data .2-Computational Geometry (CG) involves study of algorithms for solving geometric problems on a computer. The emphasis is more on discrete and combinatorial geometry 2 - ) 1 - . .
Definition 3-Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithm, and such problems are also considered to be part of computational geometry. 3 - . . .
Definition 4-Area within algorithms research dealing with Modern computational. Geometry is a recent development 4 - . 5 -
C G History It is one of the oldest fields of computing with history stretching back to antiquity. * Rules of the Chord", that is a book of algorithms written in 800 BCE. The book prescribes step-by-step procedures for constructing geometric objects . *Modern computational geometry is a recent development. . 800 . . . " * *
C G History Computational geometry emerged from the field of algorithms design and analysis in the late 1970s. 1970 The main impetus for the development of computational :geometry as a discipline was 1-Progress in computer graphics and computer-aided design 2-Manufacturing (CAD/CAM). But many problems in computational geometry are classical in nature.
C.G Application APPLICATIONS :- 1-Robotics (motion planning and visibility problems). 2-Geographic information system(GIS) (geometrical location and search, route planning). 3-Integrated circuits design (IC geometry design and verification), 4-Computer aided engineering (CAE) (mesh generation . 5-Computer vision (3D reconstruction). : - .) ( GIS) ( ( 1 - 2 - .) IC ) ( 3 -
Computational geometry: applications (2) computer-aided design and manufacturing (CAD/CAM) motion planning virtual walkthroughs 3D model of power plant (12.748.510 triangles)
Computational geometry: application geographic information systems (GIS) Mississippi delta Arlington Arlington Memphis Memphis Memphis Memphis 30 cities: 430 = 1018 possibilities
Computational geometry: application Robot motion planning
C . G Branches Branches:- 1-Combinatorial computational geometry, also called algorithmic geometry, which deals with geometric objects as discrete entities. 2-Numerical computational geometry, also called machine geometry, computer-aided- geometric design (CAGD), or geometric modeling, which deals primarily with representing real-world objects in forms suitable for computer computations in CAD/CAM systems
