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Advanced Geometrical Optics pp 3–28Cite as

Mathematical Background

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Part of the book series: Progress in Optical Science and Photonics ((POSP,volume 4))

Abstract

The homogeneous coordinate notation is a powerful mathematical tool used in a wide range of fields, including the motion of rigid bodies [1, 2], robotics [3], gearing theory [4], and computer graphics [5]. Previous publications of geometrical optics used vector notation, which is comparatively awkward for computations for non-axially symmetrical systems. In order to circumvent its limitations, this book employs homogeneous coordinate notation. Accordingly, this chapter briefly reviews the basic principles of the homogeneous coordinate notation in order to set the mathematical modeling presented in the rest of the book in proper context

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References

  1. Uicker JJ (1965) On the dynamic analysis of spatial linkages using 4 × 4 matrices. PhD dissertation, Northwestern University, Evanston, ILL, USA

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

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  3. Paul RP (1982) Robot manipulators-mathematics, programming and control. MIT press, Cambridge, Mass

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  4. Litvin FL (1989) Theory of gearing. NASA Reference Publication

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  5. Foley JD, Dam AV, Feiner SK, Hughes JF (1981), Computer graphics, principles and practices, 2nd edn. Addision-Wesley Publishing Company

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  6. Arora JS (2012) Introduction to optimum design, 3rd edn. Elservier Inc

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan

    Psang Dain Lin

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  1. Psang Dain Lin
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Correspondence to Psang Dain Lin .

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© 2017 Springer Science+Business Media Singapore

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Lin, P.D. (2017). Mathematical Background. In: Advanced Geometrical Optics. Progress in Optical Science and Photonics, vol 4. Springer, Singapore. https://doi.org/10.1007/978-981-10-2299-9_1

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  • DOI: https://doi.org/10.1007/978-981-10-2299-9_1

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2298-2

  • Online ISBN: 978-981-10-2299-9

  • eBook Packages: EngineeringEngineering (R0)

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