Computer Graphics Techniques in Military Applications
The determination of intersection points of plane curves is a problem of Computer Graphics with many applications in Applied Mathematics, Numerical Analysis and many other scientific fields. More precisely, in military applications, the trajectories of two flying objects such as missiles, aircrafts etc, can be interpreted by two plane curves. Our scope is to find the intersection points of the given curves. The number of floating point operations (flops) of many classical methods is not satisfactory, since they demand over O(n 4) operations. Conversely, many algorithms that are fast enough, have serious problems with their numerical stability. The main objective here is to develop fast and stable algorithms computing the intersection points of plane curves. The error analysis and the computation of complexity of all the proposed methods are analysed and demonstrated through various examples.
KeywordsIntersection points Plane curves Symbolic-numeric computations Modified Sylvester matrix Singular value decomposition
The fourth author (D.T.) acknowledges financial support from State Scholarships Foundation (IKY).
- 2.Conte, S.D., Carl de Boor: Elementary Numerical Analysis: An Algorithmic Approach, 3rd edn. pp. 74–80. McGraw-Hill Book Company, New York (1980)Google Scholar
- 4.Marco, A., Martinez, J-J.: A new source of structured singular value decomposition problems. Electronic Trans. Numer. Analy. 18, 188–197 (2004)Google Scholar