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Homogeneous Coordinate Notation

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New Computation Methods for Geometrical Optics

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 178))

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Abstract

Homogeneous coordinate notation is one of powerful mathematical tools for engineering field. It was used to study the motion of rigid bodies [1, 2], robotics [3], theory of gearing [4], and computer graphics [5]. Previous publications of geometrical optics use vector notation, which is comparatively awkward for computations for non-axially symmetrical systems. In order to circumvent these limitations, this book employs homogeneous coordinate notation to compute various optical quantities. The discussion in this chapter is designed mainly for those readers who have not so far encountered this mathematical tool. The treatment is elementary and covers only what will needed to understand the rest of the book.

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References

  1. J.J. Uicker, On the dynamic analysis of spatial linkages using 4 × 4 Matrices, Ph.D. dissertation, Northwestern University, Evanston, ILL, 1965

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  2. J. Denavit, R.S. Hartenberg, A kinematic notation for lower pair mechanisms based on matrices. Trans. ASME J. Appl. Mech. 77, 215–221 (1955)

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  3. R.P. Paul, Robot Manipulators-Mathematics, Programming and Control (MIT press, Cambridge, Mass, 1982)

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  4. F.L. Litvin Theory of Gearing (NASA Reference Publication, Chicago 1989)

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  5. J.D. Foley, A.V. Dam, S.K. Feiner, J.F. Hughes, Computer Graphics, Principles and Practices, 2nd edn. (Addision-Wesley Publishing Company, Massachusetts 1981)

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Correspondence to Psang Dain Lin .

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© 2014 Springer Science+Business Media Singapore

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Lin, P.D. (2014). Homogeneous Coordinate Notation. In: New Computation Methods for Geometrical Optics. Springer Series in Optical Sciences, vol 178. Springer, Singapore. https://doi.org/10.1007/978-981-4451-79-6_1

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  • DOI: https://doi.org/10.1007/978-981-4451-79-6_1

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-4451-78-9

  • Online ISBN: 978-981-4451-79-6

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