A geometrical approach to the numerical stability analysis of some projective collinear mapping methods
Апстракт
This paper exposes the geometrical approach to the numerical stability analysis of the projective collinear mapping method based on Laguerre's points of the involution mapped. The ill-conditioned and corresponding unstable zones for this mapping method are defined and some alternative procedures for their corrections are proposed. As a result of the analysis, the stable and well conditioned collinear mapping technique, which can be used in the design of some 3D imaging software algorithms, are created and explained. The exposed analysis is a contribution to the theory of projective and computational geometry. Moreover, it proposes a numerical stability criterion for the practical mapping procedures in software applications which are based on the principles of the projective collineation.
Кључне речи:
Projective collineation / Numerical stability / Laguerre's points / InvolutionИзвор:
Journal for Geometry and Graphics, 2007, 11, 2, 187-198Издавач:
- Heldermann Verlag
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Popkonstantinović, Branislav AU - Petrović, Dušan PY - 2007 UR - https://machinery.mas.bg.ac.rs/handle/123456789/685 AB - This paper exposes the geometrical approach to the numerical stability analysis of the projective collinear mapping method based on Laguerre's points of the involution mapped. The ill-conditioned and corresponding unstable zones for this mapping method are defined and some alternative procedures for their corrections are proposed. As a result of the analysis, the stable and well conditioned collinear mapping technique, which can be used in the design of some 3D imaging software algorithms, are created and explained. The exposed analysis is a contribution to the theory of projective and computational geometry. Moreover, it proposes a numerical stability criterion for the practical mapping procedures in software applications which are based on the principles of the projective collineation. PB - Heldermann Verlag T2 - Journal for Geometry and Graphics T1 - A geometrical approach to the numerical stability analysis of some projective collinear mapping methods EP - 198 IS - 2 SP - 187 VL - 11 UR - https://hdl.handle.net/21.15107/rcub_machinery_685 ER -
@article{ author = "Popkonstantinović, Branislav and Petrović, Dušan", year = "2007", abstract = "This paper exposes the geometrical approach to the numerical stability analysis of the projective collinear mapping method based on Laguerre's points of the involution mapped. The ill-conditioned and corresponding unstable zones for this mapping method are defined and some alternative procedures for their corrections are proposed. As a result of the analysis, the stable and well conditioned collinear mapping technique, which can be used in the design of some 3D imaging software algorithms, are created and explained. The exposed analysis is a contribution to the theory of projective and computational geometry. Moreover, it proposes a numerical stability criterion for the practical mapping procedures in software applications which are based on the principles of the projective collineation.", publisher = "Heldermann Verlag", journal = "Journal for Geometry and Graphics", title = "A geometrical approach to the numerical stability analysis of some projective collinear mapping methods", pages = "198-187", number = "2", volume = "11", url = "https://hdl.handle.net/21.15107/rcub_machinery_685" }
Popkonstantinović, B.,& Petrović, D.. (2007). A geometrical approach to the numerical stability analysis of some projective collinear mapping methods. in Journal for Geometry and Graphics Heldermann Verlag., 11(2), 187-198. https://hdl.handle.net/21.15107/rcub_machinery_685
Popkonstantinović B, Petrović D. A geometrical approach to the numerical stability analysis of some projective collinear mapping methods. in Journal for Geometry and Graphics. 2007;11(2):187-198. https://hdl.handle.net/21.15107/rcub_machinery_685 .
Popkonstantinović, Branislav, Petrović, Dušan, "A geometrical approach to the numerical stability analysis of some projective collinear mapping methods" in Journal for Geometry and Graphics, 11, no. 2 (2007):187-198, https://hdl.handle.net/21.15107/rcub_machinery_685 .